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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Islamic_finance"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Islamic finance</span> </div> </a> <ul id="toc-Islamic_finance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_the_history_of_mathematics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_the_history_of_mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>In the history of mathematics</span> </div> </a> <ul id="toc-In_the_history_of_mathematics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Economics" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Economics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Economics</span> </div> </a> <ul id="toc-Economics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Calculation" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Calculation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Calculation</span> </div> </a> <button aria-controls="toc-Calculation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Calculation subsection</span> </button> <ul id="toc-Calculation-sublist" class="vector-toc-list"> <li id="toc-Simple_interest" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simple_interest"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Simple interest</span> </div> </a> <ul id="toc-Simple_interest-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Compound_interest" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Compound_interest"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Compound interest</span> </div> </a> <ul id="toc-Compound_interest-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_formulations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_formulations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Other formulations</span> </div> </a> <ul id="toc-Other_formulations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Discount_instruments" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Discount_instruments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Discount instruments</span> </div> </a> <ul id="toc-Discount_instruments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rules_of_thumb" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Rules_of_thumb"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Rules of thumb</span> </div> </a> <button aria-controls="toc-Rules_of_thumb-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Rules of thumb subsection</span> </button> <ul id="toc-Rules_of_thumb-sublist" class="vector-toc-list"> <li id="toc-Rule_of_78s" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rule_of_78s"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Rule of 78s</span> </div> </a> <ul id="toc-Rule_of_78s-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rule_of_72" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rule_of_72"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Rule of 72</span> </div> </a> <ul id="toc-Rule_of_72-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Market_interest_rates" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Market_interest_rates"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Market interest rates</span> </div> </a> <button aria-controls="toc-Market_interest_rates-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Market interest rates subsection</span> </button> <ul id="toc-Market_interest_rates-sublist" class="vector-toc-list"> <li id="toc-Opportunity_cost_and_deferred_consumption" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Opportunity_cost_and_deferred_consumption"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Opportunity cost and deferred consumption</span> </div> </a> <ul id="toc-Opportunity_cost_and_deferred_consumption-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Inflation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Inflation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Inflation</span> </div> </a> <ul id="toc-Inflation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Default" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Default"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Default</span> </div> </a> <ul id="toc-Default-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Composition_of_interest_rates" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Composition_of_interest_rates"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Composition of interest rates</span> </div> </a> <ul id="toc-Composition_of_interest_rates-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Default_interest" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Default_interest"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Default interest</span> </div> </a> <ul id="toc-Default_interest-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Term" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Term"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6</span> <span>Term</span> </div> </a> <ul id="toc-Term-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Government_intervention" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Government_intervention"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.7</span> <span>Government intervention</span> </div> </a> <ul id="toc-Government_intervention-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Open_market_operations_in_the_United_States" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Open_market_operations_in_the_United_States"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.8</span> <span>Open market operations in the United States</span> </div> </a> <ul id="toc-Open_market_operations_in_the_United_States-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interest_rates_and_credit_risk" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Interest_rates_and_credit_risk"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.9</span> <span>Interest rates and credit risk</span> </div> </a> <ul id="toc-Interest_rates_and_credit_risk-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Money_and_inflation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Money_and_inflation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.10</span> <span>Money and inflation</span> </div> </a> <ul id="toc-Money_and_inflation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liquidity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liquidity"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.11</span> <span>Liquidity</span> </div> </a> <ul id="toc-Liquidity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Theories_of_interest" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Theories_of_interest"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Theories of interest</span> </div> </a> <button aria-controls="toc-Theories_of_interest-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Theories of interest subsection</span> </button> <ul id="toc-Theories_of_interest-sublist" class="vector-toc-list"> <li id="toc-Aristotle's_view_of_interest" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aristotle's_view_of_interest"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Aristotle's view of interest</span> </div> </a> <ul id="toc-Aristotle's_view_of_interest-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Development_of_the_theory_of_interest_during_the_seventeenth_and_eighteenth_centuries" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Development_of_the_theory_of_interest_during_the_seventeenth_and_eighteenth_centuries"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Development of the theory of interest during the seventeenth and eighteenth centuries</span> </div> </a> <ul id="toc-Development_of_the_theory_of_interest_during_the_seventeenth_and_eighteenth_centuries-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_classical_theory_of_the_interest_rate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_classical_theory_of_the_interest_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span><span>The classical theory of the interest rate</span></span> </div> </a> <ul id="toc-The_classical_theory_of_the_interest_rate-sublist" class="vector-toc-list"> <li id="toc-Keynes's_criticisms" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Keynes's_criticisms"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3.1</span> <span><span>Keynes's criticisms</span></span> </div> </a> <ul id="toc-Keynes's_criticisms-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Theories_of_exploitation,_productivity_and_abstinence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Theories_of_exploitation,_productivity_and_abstinence"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4</span> <span>Theories of exploitation, productivity and abstinence</span> </div> </a> <ul id="toc-Theories_of_exploitation,_productivity_and_abstinence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wicksell's_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Wicksell's_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5</span> <span><span>Wicksell's theory</span></span> </div> </a> <ul id="toc-Wicksell's_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Austrian_theories" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Austrian_theories"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.6</span> <span>Austrian theories</span> </div> </a> <ul id="toc-Austrian_theories-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pareto's_indifference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pareto's_indifference"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.7</span> <span>Pareto's indifference</span> </div> </a> <ul id="toc-Pareto's_indifference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Keynes's_theory_of_the_interest_rate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Keynes's_theory_of_the_interest_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.8</span> <span><span>Keynes's theory of the interest rate</span></span> </div> </a> <ul id="toc-Keynes's_theory_of_the_interest_rate-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-In_religious_contexts" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#In_religious_contexts"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>In religious contexts</span> </div> </a> <button aria-controls="toc-In_religious_contexts-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle In religious contexts subsection</span> </button> <ul id="toc-In_religious_contexts-sublist" class="vector-toc-list"> <li id="toc-Judaism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Judaism"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Judaism</span> </div> </a> <ul id="toc-Judaism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Islam" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Islam"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Islam</span> </div> </a> <ul id="toc-Islam-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Christianity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Christianity"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Christianity</span> </div> </a> <ul id="toc-Christianity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Interest</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 73 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-73" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">73 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Rente" title="Rente – Afrikaans" lang="af" hreflang="af" data-title="Rente" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Zins" title="Zins – Alemannic" lang="gsw" hreflang="gsw" data-title="Zins" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%8E%E1%88%88%E1%8B%B5" title="ዎለድ – Amharic" lang="am" hreflang="am" data-title="ዎለድ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D8%A7%D8%A6%D8%AF%D8%A9" title="فائدة – Arabic" lang="ar" hreflang="ar" data-title="فائدة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arc mw-list-item"><a href="https://arc.wikipedia.org/wiki/%DC%97%DC%A2%DC%9D%DC%A2%DC%90_(%DC%A1%DC%A1%DC%AB%DC%9A%DC%98%DC%AC%DC%90)" title="ܗܢܝܢܐ (ܡܡܫܚܘܬܐ) – Aramaic" lang="arc" hreflang="arc" data-title="ܗܢܝܢܐ (ܡܡܫܚܘܬܐ)" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="Aramaic" class="interlanguage-link-target"><span>ܐܪܡܝܐ</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Inter%C3%A9s" title="Interés – Asturian" lang="ast" hreflang="ast" data-title="Interés" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%81%E0%A6%A6" title="সুদ – Bangla" lang="bn" hreflang="bn" data-title="সুদ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D0%B8%D1%85%D0%B2%D0%B0" title="Лихва – Bulgarian" lang="bg" hreflang="bg" data-title="Лихва" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Zins" title="Zins – Bavarian" lang="bar" hreflang="bar" data-title="Zins" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kamata" title="Kamata – Bosnian" lang="bs" hreflang="bs" data-title="Kamata" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Inter%C3%A8s" title="Interès – Catalan" lang="ca" hreflang="ca" data-title="Interès" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C3%9Arok" title="Úrok – Czech" lang="cs" hreflang="cs" data-title="Úrok" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Rente" title="Rente – Danish" lang="da" hreflang="da" data-title="Rente" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Zins" title="Zins – German" lang="de" hreflang="de" data-title="Zins" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Intress" title="Intress – Estonian" lang="et" hreflang="et" data-title="Intress" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CF%8C%CE%BA%CE%BF%CF%82" title="Τόκος – Greek" lang="el" hreflang="el" data-title="Τόκος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Inter%C3%A9s" title="Interés – Spanish" lang="es" hreflang="es" data-title="Interés" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Interezo" title="Interezo – Esperanto" lang="eo" hreflang="eo" data-title="Interezo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Interes" title="Interes – Basque" lang="eu" hreflang="eu" data-title="Interes" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D9%87%D8%B1%D9%87" title="بهره – Persian" lang="fa" hreflang="fa" data-title="بهره" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Int%C3%A9r%C3%AAt_(finance)" title="Intérêt (finance) – French" lang="fr" hreflang="fr" data-title="Intérêt (finance)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Xuro" title="Xuro – Galician" lang="gl" hreflang="gl" data-title="Xuro" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%EC%9E%90" title="이자 – Korean" lang="ko" hreflang="ko" data-title="이자" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%B8%D5%AF%D5%B8%D5%BD%D5%A1%D5%A3%D5%B8%D6%82%D5%B4%D5%A1%D6%80" title="Տոկոսագումար – Armenian" lang="hy" hreflang="hy" data-title="Տոկոսագումար" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%9C" title="ब्याज – Hindi" lang="hi" hreflang="hi" data-title="ब्याज" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kamata" title="Kamata – Croatian" lang="hr" hreflang="hr" data-title="Kamata" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Interesto" title="Interesto – Ido" lang="io" hreflang="io" data-title="Interesto" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Suku_bunga" title="Suku bunga – Indonesian" lang="id" hreflang="id" data-title="Suku bunga" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Vextir" title="Vextir – Icelandic" lang="is" hreflang="is" data-title="Vextir" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Interesse_finanziario" title="Interesse finanziario – Italian" lang="it" hreflang="it" data-title="Interesse finanziario" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A8%D7%99%D7%91%D7%99%D7%AA" title="ריבית – Hebrew" lang="he" hreflang="he" data-title="ריבית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AC%E0%B2%A1%E0%B3%8D%E0%B2%A1%E0%B2%BF" title="ಬಡ್ಡಿ – Kannada" lang="kn" hreflang="kn" data-title="ಬಡ್ಡಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%94%E0%BA%AD%E0%BA%81%E0%BB%80%E0%BA%9A%E0%BB%89%E0%BA%8D" title="ດອກເບ້ຍ – Lao" lang="lo" hreflang="lo" data-title="ດອກເບ້ຍ" data-language-autonym="ລາວ" data-language-local-name="Lao" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Usura" title="Usura – Latin" lang="la" hreflang="la" data-title="Usura" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Procenti" title="Procenti – Latvian" lang="lv" hreflang="lv" data-title="Procenti" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Pal%C5%ABkanos" title="Palūkanos – Lithuanian" lang="lt" hreflang="lt" data-title="Palūkanos" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kamat" title="Kamat – Hungarian" lang="hu" hreflang="hu" data-title="Kamat" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BC%D0%B0%D1%82%D0%B0" title="Камата – Macedonian" lang="mk" hreflang="mk" data-title="Камата" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%9C" title="व्याज – Marathi" lang="mr" hreflang="mr" data-title="व्याज" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Faedah" title="Faedah – Malay" lang="ms" hreflang="ms" data-title="Faedah" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rente" title="Rente – Dutch" lang="nl" hreflang="nl" data-title="Rente" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%B8%E0%A4%BE%E0%A4%A7%E0%A4%BE%E0%A4%B0%E0%A4%A3_%E0%A4%B5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%9C" title="साधारण व्याज – Nepali" lang="ne" hreflang="ne" data-title="साधारण व्याज" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%88%A9%E5%AD%90" title="利子 – Japanese" lang="ja" hreflang="ja" data-title="利子" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Rente" title="Rente – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Rente" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Rente" title="Rente – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Rente" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A8%BF%E0%A8%86%E0%A8%9C" title="ਵਿਆਜ – Punjabi" lang="pa" hreflang="pa" data-title="ਵਿਆਜ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Odsetki" title="Odsetki – Polish" lang="pl" hreflang="pl" data-title="Odsetki" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Juro" title="Juro – Portuguese" lang="pt" hreflang="pt" data-title="Juro" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Dob%C3%A2nd%C4%83" title="Dobândă – Romanian" lang="ro" hreflang="ro" data-title="Dobândă" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%86%D0%B5%D0%BD%D1%82%D0%BD%D1%8B%D0%B9_%D0%B4%D0%BE%D1%85%D0%BE%D0%B4" title="Процентный доход – Russian" lang="ru" hreflang="ru" data-title="Процентный доход" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Interesi" title="Interesi – Albanian" lang="sq" hreflang="sq" data-title="Interesi" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Interest" title="Interest – Simple English" lang="en-simple" hreflang="en-simple" data-title="Interest" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%88%D9%8A%D8%A7%D8%AC" title="وياج – Sindhi" lang="sd" hreflang="sd" data-title="وياج" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C3%9Arok" title="Úrok – Slovak" lang="sk" hreflang="sk" data-title="Úrok" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Obresti" title="Obresti – Slovenian" lang="sl" hreflang="sl" data-title="Obresti" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BC%D0%B0%D1%82%D0%B0" title="Камата – Serbian" lang="sr" hreflang="sr" data-title="Камата" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kamata" title="Kamata – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Kamata" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Korko" title="Korko – Finnish" lang="fi" hreflang="fi" data-title="Korko" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/R%C3%A4nta" title="Ränta – Swedish" lang="sv" hreflang="sv" data-title="Ränta" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Patubo" title="Patubo – Tagalog" lang="tl" hreflang="tl" data-title="Patubo" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%BF" title="வட்டி – Tamil" lang="ta" hreflang="ta" data-title="வட்டி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B0%A1%E0%B1%8D%E0%B0%A1%E0%B1%80" title="వడ్డీ – Telugu" lang="te" hreflang="te" data-title="వడ్డీ" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%94%E0%B8%AD%E0%B8%81%E0%B9%80%E0%B8%9A%E0%B8%B5%E0%B9%89%E0%B8%A2" title="ดอกเบี้ย – Thai" lang="th" hreflang="th" data-title="ดอกเบี้ย" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Faiz" title="Faiz – Turkish" lang="tr" hreflang="tr" data-title="Faiz" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/G%C3%B6terim" title="Göterim – Turkmen" lang="tk" hreflang="tk" data-title="Göterim" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D1%96%D0%B4%D1%81%D0%BE%D1%82%D0%BE%D0%BA_(%D1%84%D1%96%D0%BD%D0%B0%D0%BD%D1%81%D0%B8)" title="Відсоток (фінанси) – Ukrainian" lang="uk" hreflang="uk" data-title="Відсоток (фінанси)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B3%D9%88%D8%AF" title="سود – Urdu" lang="ur" hreflang="ur" data-title="سود" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Interes" title="Interes – Waray" lang="war" hreflang="war" data-title="Interes" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%88%A9%E6%81%AF" title="利息 – Wu" lang="wuu" hreflang="wuu" data-title="利息" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A8%D7%99%D7%91%D7%99%D7%AA" title="ריבית – Yiddish" lang="yi" hreflang="yi" data-title="ריבית" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%88%A9%E6%81%AF" title="利息 – Cantonese" lang="yue" hreflang="yue" data-title="利息" data-language-autonym="粵語" data-language-local-name="Cantonese" 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For other uses, see <a href="/wiki/Interest_(disambiguation)" class="mw-disambig" title="Interest (disambiguation)">Interest (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Sum paid for the use of money</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Malawi_interest_rates.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Malawi_interest_rates.JPG/290px-Malawi_interest_rates.JPG" decoding="async" width="290" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Malawi_interest_rates.JPG/435px-Malawi_interest_rates.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Malawi_interest_rates.JPG/580px-Malawi_interest_rates.JPG 2x" data-file-width="648" data-file-height="486" /></a><figcaption>A bank sign in Malawi listing the interest rates for deposit accounts at the institution and the base rate for lending money to its customers</figcaption></figure> <p>In <a href="/wiki/Finance" title="Finance">finance</a> and <a href="/wiki/Economics" title="Economics">economics</a>, <b>interest</b> is payment from a <a href="/wiki/Debtor" title="Debtor">debtor</a> or deposit-taking financial institution to a <a href="/wiki/Lender" class="mw-redirect" title="Lender">lender</a> or depositor of an amount above repayment of the <a href="/wiki/Principal_sum" class="mw-redirect" title="Principal sum">principal sum</a> (that is, the amount borrowed), at a particular rate.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It is distinct from a <a href="/wiki/Fee" title="Fee">fee</a> which the borrower may pay to the lender or some third party. It is also distinct from <a href="/wiki/Dividend" title="Dividend">dividend</a> which is paid by a company to its shareholders (owners) from its <a href="/wiki/Profit_(economics)" title="Profit (economics)">profit</a> or <a href="/wiki/Reserve_(accounting)" title="Reserve (accounting)">reserve</a>, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by <a href="/wiki/Risk" title="Risk">risk</a> taking entrepreneurs when the revenue earned exceeds the total costs.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>For example, a customer would usually pay interest to <a href="/wiki/Debt" title="Debt">borrow</a> from a bank, so they pay the bank an amount which is more than the amount they borrowed; or a customer may earn interest on their savings, and so they may withdraw more than they originally deposited. In the case of savings, the customer is the lender, and the bank plays the role of the borrower. </p><p>Interest differs from <a href="/wiki/Profit_(accounting)" title="Profit (accounting)">profit</a>, in that interest is received by a lender, whereas profit is received by the <a href="/wiki/Ownership" title="Ownership">owner</a> of an <a href="/wiki/Asset" title="Asset">asset</a>, <a href="/wiki/Investment" title="Investment">investment</a> or <a href="/wiki/Business" title="Business">enterprise</a>. (Interest may be part or the whole of the profit on an <a href="/wiki/Investment" title="Investment">investment</a>, but the two concepts are distinct from each other from an <a href="/wiki/Accounting" title="Accounting">accounting</a> perspective.) </p><p>The <a href="/wiki/Interest_rate" title="Interest rate">rate of interest</a> is equal to the interest amount paid or received over a particular period divided by the <a href="/wiki/Principal_sum" class="mw-redirect" title="Principal sum">principal sum</a> borrowed or lent (usually expressed as a percentage). </p><p><a href="/wiki/Compound_interest" title="Compound interest">Compound interest</a> means that interest is earned on prior interest in addition to the principal. Due to compounding, the total amount of debt grows exponentially, and its mathematical study led to the discovery of the number <i><a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a></i>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In practice, interest is most often calculated on a daily, monthly, or yearly basis, and its impact is influenced greatly by its compounding rate. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Compound_interest#History" title="Compound interest">Compound interest § History</a></div> <p>Credit is thought to have preceded the existence of coinage by several thousands of years. The first recorded instance of credit is a collection of old <a href="/wiki/Sumer" title="Sumer">Sumerian</a> documents from 3000 BC that show systematic use of credit to loan both grain and metals.<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The rise of interest as a concept is unknown, though its use in Sumeria argue that it was well established as a concept by 3000BC if not earlier, with historians believing that the concept in its modern sense may have arisen from the lease of animal or seeds for productive purposes.<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The argument that acquired seeds and animals could reproduce themselves was used to justify interest, but ancient Jewish religious prohibitions against <a href="/wiki/Usury" title="Usury">usury</a> (נשך <i>NeSheKh</i>) represented a "different view".<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The first written evidence of compound interest dates roughly 2400 BC.<sup id="cite_ref-bbc-th_7-0" class="reference"><a href="#cite_note-bbc-th-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The annual interest rate was roughly 20%. Compound interest was necessary for the development of agriculture and important for urbanization.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Accuracy_dispute#Disputed_statement" title="Wikipedia:Accuracy dispute"><span title="The material near this tag is possibly inaccurate or nonfactual. (June 2019)">dubious</span></a> – <a href="/wiki/Talk:Interest#Dubious" title="Talk:Interest">discuss</a></i>]</sup> </p><p>While the traditional Middle Eastern views on interest were the result of the urbanized, economically developed character of the societies that produced them, the new Jewish prohibition on interest showed a pastoral, tribal influence.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> In the early 2nd millennium BC, since silver used in exchange for livestock or grain could not multiply of its own, the <a href="/wiki/Laws_of_Eshnunna" title="Laws of Eshnunna">Laws of Eshnunna</a> instituted a legal interest rate, specifically on deposits of <a href="/wiki/Dowry" title="Dowry">dowry</a>. Early Muslims called this <i>riba</i>, translated today as the charging of interest.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/First_Council_of_Nicaea" title="First Council of Nicaea">First Council of Nicaea</a>, in 325, forbade <a href="/wiki/Clergy" title="Clergy">clergy</a> from engaging in <a href="/wiki/Usury" title="Usury">usury</a><sup id="cite_ref-m6_11-0" class="reference"><a href="#cite_note-m6-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> which was defined as lending on interest above 1 percent per month (12.7% <a href="/wiki/Annual_equivalent_rate" class="mw-redirect" title="Annual equivalent rate">AER</a>). Ninth-century <a href="/wiki/Ecumenical_council" title="Ecumenical council">ecumenical councils</a> applied this regulation to the <a href="/wiki/Laity" title="Laity">laity</a>.<sup id="cite_ref-m6_11-1" class="reference"><a href="#cite_note-m6-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-noonan_12-0" class="reference"><a href="#cite_note-noonan-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Catholic_Church" title="Catholic Church">Catholic Church</a> opposition to interest hardened in the era of the <a href="/wiki/Scholasticism" title="Scholasticism">Scholastics</a>, when even defending it was considered a <a href="/wiki/Heresy" title="Heresy">heresy</a>. St. <a href="/wiki/Thomas_Aquinas" title="Thomas Aquinas">Thomas Aquinas</a>, the leading theologian of the <a href="/wiki/Catholic_Church" title="Catholic Church">Catholic Church</a>, argued that the charging of interest is wrong because it amounts to "<a href="/wiki/Usury#Usury_in_scholastic_theology" title="Usury">double charging</a>", charging for both the thing and the use of the thing. </p><p>In the <a href="/wiki/Medieval_economy" class="mw-redirect" title="Medieval economy">medieval economy</a>, loans were entirely a consequence of necessity (bad harvests, fire in a workplace) and, under those conditions, it was considered morally reproachable to charge interest.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2009)">citation needed</span></a></i>]</sup> It was also considered morally dubious, since no goods were produced through the lending of money, and thus it should not be compensated, unlike other activities with direct physical output such as blacksmithing or farming.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> For the same reason, interest has often been looked down upon in <a href="/wiki/Muslim_World" class="mw-redirect" title="Muslim World">Islamic civilization</a>, with almost all scholars agreeing that the Qur'an explicitly forbids charging interest. </p><p>Medieval jurists developed several financial instruments to encourage responsible lending and circumvent prohibitions on usury, such as the <a href="/wiki/Contractum_trinius" title="Contractum trinius">Contractum trinius</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:UsuryDurer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/UsuryDurer.jpg/170px-UsuryDurer.jpg" decoding="async" width="170" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/UsuryDurer.jpg/255px-UsuryDurer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/UsuryDurer.jpg/340px-UsuryDurer.jpg 2x" data-file-width="2008" data-file-height="2758" /></a><figcaption>Of <a href="/wiki/Usury" title="Usury">Usury</a>, from <a href="/wiki/Sebastian_Brant" title="Sebastian Brant">Brant's</a> <i>Stultifera Navis</i> (<a href="/wiki/Narrenschiff" class="mw-redirect" title="Narrenschiff">the Ship of Fools</a>); <a href="/wiki/Woodcut" title="Woodcut">woodcut</a> attributed to <a href="/wiki/Albrecht_D%C3%BCrer" title="Albrecht Dürer">Albrecht Dürer</a></figcaption></figure> <p>In the <a href="/wiki/Renaissance" title="Renaissance">Renaissance</a> era, greater mobility of people facilitated an increase in commerce and the appearance of appropriate conditions for <a href="/wiki/Entrepreneur" class="mw-redirect" title="Entrepreneur">entrepreneurs</a> to start new, lucrative businesses. Given that borrowed money was no longer strictly for consumption but for production as well, interest was no longer viewed in the same manner. </p><p>The first attempt to control interest rates through manipulation of the <a href="/wiki/Money_supply" title="Money supply">money supply</a> was made by the <a href="/wiki/Banque_de_France" class="mw-redirect" title="Banque de France">Banque de France</a> in 1847.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (April 2016)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Islamic_finance">Islamic finance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=2" title="Edit section: Islamic finance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Islamic_banking_and_finance" title="Islamic banking and finance">Islamic banking and finance</a></div> <p>The latter half of the 20th century saw the rise of interest-free <a href="/wiki/Islamic_banking_and_finance" title="Islamic banking and finance">Islamic banking and finance</a>, a movement that applies Islamic law to financial institutions and the economy. Some countries, including Iran, Sudan, and Pakistan, have taken steps to eradicate interest from their financial systems.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Rather than charging interest, the interest-free lender shares the risk by investing as a partner in profit loss sharing scheme, because predetermined loan repayment as interest is prohibited, as well as making money out of money is unacceptable. All financial transactions must be asset-backed and must not charge any interest or fee for the service of lending. </p> <div class="mw-heading mw-heading3"><h3 id="In_the_history_of_mathematics">In the history of mathematics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=3" title="Edit section: In the history of mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is thought that <a href="/wiki/Jacob_Bernoulli" title="Jacob Bernoulli">Jacob Bernoulli</a> discovered the mathematical constant <a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a> by studying a question about <a href="/wiki/Compound_interest" title="Compound interest">compound interest</a>.<sup id="cite_ref-OConnor_15-0" class="reference"><a href="#cite_note-OConnor-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> He realized that if an account that starts with $1.00 and pays say 100% interest per year, at the end of the year, the value is $2.00; but if the interest is computed and added twice in the year, the $1 is multiplied by 1.5 twice, yielding $1.00×1.5<sup>2</sup> = $2.25. </p><p>Bernoulli noticed that if the frequency of compounding is increased without limit, this sequence can be modeled as follows: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{n\rightarrow \infty }\left(1+{\dfrac {1}{n}}\right)^{n}=e,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mstyle> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <mi>e</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{n\rightarrow \infty }\left(1+{\dfrac {1}{n}}\right)^{n}=e,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c46849ae744c9bb3a81a19b1777d0bbf242a39b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.362ex; height:6.176ex;" alt="{\displaystyle \lim _{n\rightarrow \infty }\left(1+{\dfrac {1}{n}}\right)^{n}=e,}"></span></dd></dl> <p>where <i>n</i> is the number of times the interest is to be compounded in a year. </p> <div class="mw-heading mw-heading2"><h2 id="Economics">Economics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=4" title="Edit section: Economics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In economics, the rate of interest is the price of <a href="/wiki/Credit_(finance)" class="mw-redirect" title="Credit (finance)">credit</a>, and it plays the role of the <a href="/wiki/Cost_of_capital" title="Cost of capital">cost of capital</a>. In a <a href="/wiki/Free_market" title="Free market">free market</a> economy, interest rates are subject to the law of <a href="/wiki/Supply_and_demand" title="Supply and demand">supply and demand</a> of the <a href="/wiki/Money_supply" title="Money supply">money supply</a>, and one explanation of the tendency of interest rates to be generally greater than zero is the scarcity of <a href="/wiki/Loanable_funds" title="Loanable funds">loanable funds</a>. </p><p>Over centuries, various schools of thought have developed explanations of interest and interest rates. The <a href="/wiki/School_of_Salamanca" title="School of Salamanca">School of Salamanca</a> justified paying interest in terms of the benefit to the borrower, and interest received by the lender in terms of a premium for the <a href="/wiki/Credit_risk" title="Credit risk">risk of default</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> In the sixteenth century, <a href="/wiki/Mart%C3%ADn_de_Azpilcueta" title="Martín de Azpilcueta">Martín de Azpilcueta</a> applied a <a href="/wiki/Time_preference" title="Time preference">time preference</a> argument: it is preferable to receive a given good now rather than in the future. Accordingly, interest is compensation for the time the lender forgoes the benefit of spending the money. </p><p>On the question of why interest rates are normally greater than zero, in 1770, French economist <a href="/wiki/Anne-Robert-Jacques_Turgot,_Baron_de_Laune" class="mw-redirect" title="Anne-Robert-Jacques Turgot, Baron de Laune">Anne-Robert-Jacques Turgot, Baron de Laune</a> proposed the <a href="/wiki/Theory_of_fructification" title="Theory of fructification">theory of fructification</a>. By applying an <a href="/wiki/Opportunity_cost" title="Opportunity cost">opportunity cost</a> argument, comparing the loan rate with the <a href="/wiki/Rate_of_return" title="Rate of return">rate of return</a> on agricultural land, and a mathematical argument, applying the formula for the value of a <a href="/wiki/Perpetuity" title="Perpetuity">perpetuity</a> to a plantation, he argued that the land value would rise without limit, as the interest rate approached zero. For the land value to remain positive and finite keeps the interest rate above zero. </p><p><a href="/wiki/Adam_Smith" title="Adam Smith">Adam Smith</a>, <a href="/wiki/Carl_Menger" title="Carl Menger">Carl Menger</a>, and <a href="/wiki/Fr%C3%A9d%C3%A9ric_Bastiat" title="Frédéric Bastiat">Frédéric Bastiat</a> also propounded theories of interest rates.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> In the late 19th century, Swedish economist <a href="/wiki/Knut_Wicksell" title="Knut Wicksell">Knut Wicksell</a> in his 1898 <i>Interest and Prices</i> elaborated a comprehensive theory of economic crises based upon a distinction between <a href="/wiki/Real_interest_rate" title="Real interest rate">natural</a> and <a href="/wiki/Nominal_interest_rate" title="Nominal interest rate">nominal interest rates</a>. In the 1930s, Wicksell's approach was refined by <a href="/wiki/Bertil_Ohlin" title="Bertil Ohlin">Bertil Ohlin</a> and <a href="/wiki/Dennis_Robertson_(economist)" title="Dennis Robertson (economist)">Dennis Robertson</a> and became known as the <a href="/wiki/Loanable_funds" title="Loanable funds">loanable funds</a> theory. Other notable interest rate theories of the period are those of <a href="/wiki/Irving_Fisher" title="Irving Fisher">Irving Fisher</a> and <a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">John Maynard Keynes</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Calculation">Calculation<span class="anchor" id="Calculation_of_interest"></span><span class="anchor" id="Types_of_interest"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=5" title="Edit section: Calculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Simple_interest">Simple interest</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=6" title="Edit section: Simple interest"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Simple interest</b> is calculated only on the principal amount, or on that portion of the principal amount that remains. It excludes the effect of <a href="/wiki/Compound_interest" title="Compound interest">compounding</a>. Simple interest can be applied over a time period other than a year, for example, every month. </p><p>Simple interest is calculated according to the following formula: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {r\cdot B\cdot m}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <mo>⋅</mo> <mi>B</mi> <mo>⋅</mo> <mi>m</mi> </mrow> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r\cdot B\cdot m}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26be178df5cbc88670b172428a2381da72b58f31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.047ex; height:5.176ex;" alt="{\displaystyle {\frac {r\cdot B\cdot m}{n}}}"></span></dd></dl> <p>where </p> <dl><dd><i>r</i> is the simple annual <a href="/wiki/Interest_rate" title="Interest rate">interest rate</a></dd> <dd><i>B</i> is the initial balance</dd> <dd><i>m</i> is the number of time periods elapsed and</dd> <dd><i>n</i> is the frequency of applying interest.</dd></dl> <p>For example, imagine that a credit card holder has an outstanding balance of $2500 and that the simple annual <a href="/wiki/Interest_rate" title="Interest rate">interest rate</a> is 12.99% <i>per annum</i>, applied monthly, so the frequency of applying interest is 12 per year. Over one month, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {0.1299\times \$2500}{12}}=\$27.06}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.1299</mn> <mo>×</mo> <mi mathvariant="normal">$</mi> <mn>2500</mn> </mrow> <mn>12</mn> </mfrac> </mrow> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>27.06</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {0.1299\times \$2500}{12}}=\$27.06}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89f9c8cccb944d665bbad1c2e0b1b7de3ce5e7ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.506ex; height:5.343ex;" alt="{\displaystyle {\frac {0.1299\times \$2500}{12}}=\$27.06}"></span></dd></dl> <p>interest is due (rounded to the nearest cent). </p><p>Simple interest applied over 3 months would be </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {0.1299\times \$2500\times 3}{12}}=\$81.19}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.1299</mn> <mo>×</mo> <mi mathvariant="normal">$</mi> <mn>2500</mn> <mo>×</mo> <mn>3</mn> </mrow> <mn>12</mn> </mfrac> </mrow> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>81.19</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {0.1299\times \$2500\times 3}{12}}=\$81.19}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3ed5938e2fc7cd2c919f6a874d1d2b3a233aff4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:29.508ex; height:5.343ex;" alt="{\displaystyle {\frac {0.1299\times \$2500\times 3}{12}}=\$81.19}"></span></dd></dl> <p>If the card holder pays off only interest at the end of each of the 3 months, the total amount of interest paid would be </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {0.1299\times \$2500}{12}}\times 3=\$27.06{\text{ per month}}\times 3{\text{ months}}=\$81.18}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.1299</mn> <mo>×</mo> <mi mathvariant="normal">$</mi> <mn>2500</mn> </mrow> <mn>12</mn> </mfrac> </mrow> <mo>×</mo> <mn>3</mn> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>27.06</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> per month</mtext> </mrow> <mo>×</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> months</mtext> </mrow> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>81.18</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {0.1299\times \$2500}{12}}\times 3=\$27.06{\text{ per month}}\times 3{\text{ months}}=\$81.18}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d359a7c42318b23f9047b8ee5e684824289413f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:62.14ex; height:5.343ex;" alt="{\displaystyle {\frac {0.1299\times \$2500}{12}}\times 3=\$27.06{\text{ per month}}\times 3{\text{ months}}=\$81.18}"></span></dd></dl> <p>which is the simple interest applied over 3 months, as calculated above. (The one cent difference arises due to rounding to the nearest cent.) </p> <div class="mw-heading mw-heading3"><h3 id="Compound_interest">Compound interest</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=7" title="Edit section: Compound interest"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Compound_interest" title="Compound interest">Compound interest</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Rate_of_return" title="Rate of return">Rate of return</a></div> <p>Compound interest includes interest earned on the interest that was previously accumulated. </p><p>Compare, for example, a bond paying 6 percent semiannually (that is, coupons of 3 percent twice a year) with a certificate of deposit (<a href="/wiki/Guaranteed_Investment_Certificate" class="mw-redirect" title="Guaranteed Investment Certificate">GIC</a>) that pays 6 percent interest once a year. The total interest payment is $6 per $100 par value in both cases, but the holder of the semiannual bond receives half the $6 per year after only 6 months (<a href="/wiki/Time_preference" title="Time preference">time preference</a>), and so has the opportunity to reinvest the first $3 coupon payment after the first 6 months, and earn additional interest. </p><p>For example, suppose an investor buys $10,000 par value of a US dollar bond, which pays coupons twice a year, and that the bond's simple annual coupon rate is 6 percent per year. This means that every 6 months, the issuer pays the holder of the bond a coupon of 3 dollars per 100 dollars par value. At the end of 6 months, the issuer pays the holder: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {r\cdot B\cdot m}{n}}={\frac {6\%\times \$10\,000\times 1}{2}}=\$300}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <mo>⋅</mo> <mi>B</mi> <mo>⋅</mo> <mi>m</mi> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> <mo>×</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> <mo>×</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>300</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r\cdot B\cdot m}{n}}={\frac {6\%\times \$10\,000\times 1}{2}}=\$300}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adc252ed80cc6a589dc4f51f09752c48e269d126" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:38.034ex; height:5.343ex;" alt="{\displaystyle {\frac {r\cdot B\cdot m}{n}}={\frac {6\%\times \$10\,000\times 1}{2}}=\$300}"></span></dd></dl> <p>Assuming the market price of the bond is 100, so it is trading at par value, suppose further that the holder immediately reinvests the coupon by spending it on another $300 par value of the bond. In total, the investor therefore now holds: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \$10\,000+\$300=\left(1+{\frac {r}{n}}\right)\cdot B=\left(1+{\frac {6\%}{2}}\right)\times \$10\,000}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> <mo>+</mo> <mi mathvariant="normal">$</mi> <mn>300</mn> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>n</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <mi>B</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \$10\,000+\$300=\left(1+{\frac {r}{n}}\right)\cdot B=\left(1+{\frac {6\%}{2}}\right)\times \$10\,000}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b8724051a07bab83abf4c71bb7d22cb7109057c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:55.062ex; height:6.176ex;" alt="{\displaystyle \$10\,000+\$300=\left(1+{\frac {r}{n}}\right)\cdot B=\left(1+{\frac {6\%}{2}}\right)\times \$10\,000}"></span></dd></dl> <p>and so earns a coupon at the end of the next 6 months of: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}{\frac {r\cdot B\cdot m}{n}}&={\frac {6\%\times \left(\$10\,000+\$300\right)}{2}}\\&={\frac {6\%\times \left(1+{\frac {6\%}{2}}\right)\times \$10\,000}{2}}\\&=\$309\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <mo>⋅</mo> <mi>B</mi> <mo>⋅</mo> <mi>m</mi> </mrow> <mi>n</mi> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> <mo>+</mo> <mi mathvariant="normal">$</mi> <mn>300</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>309</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\frac {r\cdot B\cdot m}{n}}&={\frac {6\%\times \left(\$10\,000+\$300\right)}{2}}\\&={\frac {6\%\times \left(1+{\frac {6\%}{2}}\right)\times \$10\,000}{2}}\\&=\$309\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54abb9784edb0c8d6bf1dc181b90b38c31690b1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.671ex; width:39.68ex; height:16.509ex;" alt="{\displaystyle {\begin{aligned}{\frac {r\cdot B\cdot m}{n}}&={\frac {6\%\times \left(\$10\,000+\$300\right)}{2}}\\&={\frac {6\%\times \left(1+{\frac {6\%}{2}}\right)\times \$10\,000}{2}}\\&=\$309\end{aligned}}}"></span></dd></dl> <p>Assuming the bond remains priced at par, the investor accumulates at the end of a full 12 months a total value of: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\$10,000+\$300+\$309&=\$10\,000+{\frac {6\%\times \$10,000}{2}}+{\frac {6\%\times \left(1+{\frac {6\%}{2}}\right)\times \$10\,000}{2}}\\&=\$10\,000\times \left(1+{\frac {6\%}{2}}\right)^{2}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi mathvariant="normal">$</mi> <mn>10</mn> <mo>,</mo> <mn>000</mn> <mo>+</mo> <mi mathvariant="normal">$</mi> <mn>300</mn> <mo>+</mo> <mi mathvariant="normal">$</mi> <mn>309</mn> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> <mo>×</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mo>,</mo> <mn>000</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> <mo>×</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\$10,000+\$300+\$309&=\$10\,000+{\frac {6\%\times \$10,000}{2}}+{\frac {6\%\times \left(1+{\frac {6\%}{2}}\right)\times \$10\,000}{2}}\\&=\$10\,000\times \left(1+{\frac {6\%}{2}}\right)^{2}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d62475866b3b483368446caccd28d3d86de888a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.505ex; width:81.448ex; height:14.176ex;" alt="{\displaystyle {\begin{aligned}\$10,000+\$300+\$309&=\$10\,000+{\frac {6\%\times \$10,000}{2}}+{\frac {6\%\times \left(1+{\frac {6\%}{2}}\right)\times \$10\,000}{2}}\\&=\$10\,000\times \left(1+{\frac {6\%}{2}}\right)^{2}\end{aligned}}}"></span></dd></dl> <p>and the investor earned in total: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\$10\,000\times \left(1+{\frac {6\%}{2}}\right)^{2}-\$10\,000\\=\$10\,000\times \left(\left(1+{\frac {6\%}{2}}\right)^{2}-1\right)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> <mo>×</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mi mathvariant="normal">$</mi> <mn>10</mn> <mspace width="thinmathspace" /> <mn>000</mn> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\$10\,000\times \left(1+{\frac {6\%}{2}}\right)^{2}-\$10\,000\\=\$10\,000\times \left(\left(1+{\frac {6\%}{2}}\right)^{2}-1\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ddfe078db2e07d5822c1cc0ab6d3c0afe262fc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.505ex; width:33.569ex; height:14.176ex;" alt="{\displaystyle {\begin{aligned}\$10\,000\times \left(1+{\frac {6\%}{2}}\right)^{2}-\$10\,000\\=\$10\,000\times \left(\left(1+{\frac {6\%}{2}}\right)^{2}-1\right)\end{aligned}}}"></span></dd></dl> <p>The formula for the <b>annual equivalent compound interest rate</b> is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(1+{\frac {r}{n}}\right)^{n}-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>n</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {r}{n}}\right)^{n}-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09507e4aaa804eeb8ee45e5e516d824522cdfb52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.231ex; height:4.843ex;" alt="{\displaystyle \left(1+{\frac {r}{n}}\right)^{n}-1}"></span></dd></dl> <p>where </p> <dl><dd>r is the simple annual rate of interest</dd> <dd>n is the frequency of applying interest</dd></dl> <p>For example, in the case of a 6% simple annual rate, the annual equivalent compound rate is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(1+{\frac {6\%}{2}}\right)^{2}-1=1.03^{2}-1=6.09\%}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi mathvariant="normal">%</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo>=</mo> <msup> <mn>1.03</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo>=</mo> <mn>6.09</mn> <mi mathvariant="normal">%</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {6\%}{2}}\right)^{2}-1=1.03^{2}-1=6.09\%}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d56f83621f48e17182280ee69df11ee19df5e520" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:37.874ex; height:6.509ex;" alt="{\displaystyle \left(1+{\frac {6\%}{2}}\right)^{2}-1=1.03^{2}-1=6.09\%}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Other_formulations">Other formulations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=8" title="Edit section: Other formulations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The outstanding <a href="/wiki/Balance_(accounting)" title="Balance (accounting)">balance</a> <i>B<sub>n</sub></i> of a loan after <i>n</i> regular payments increases each period by a growth factor according to the periodic interest, and then decreases by the amount paid <i>p</i> at the end of each period: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{n}={\big (}1+r{\big )}B_{n-1}-p,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mn>1</mn> <mo>+</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>−</mo> <mi>p</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{n}={\big (}1+r{\big )}B_{n-1}-p,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/626646bbcf171eb5b30253e5e08c89ac9a246c02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:23.002ex; height:3.176ex;" alt="{\displaystyle B_{n}={\big (}1+r{\big )}B_{n-1}-p,}"></span></dd></dl> <p>where </p> <dl><dd><i>i</i> = simple annual loan rate in decimal form (for example, 10% = 0.10. The loan rate is the rate used to compute payments and balances.)</dd> <dd><i>r</i> = period interest rate (for example, <i>i</i>/12 for monthly payments) <a rel="nofollow" class="external autonumber" href="http://www.fdic.gov/regulations/laws/rules/6500-1650.html#6500226.14">[2]</a></dd> <dd><i>B</i><sub>0</sub> = initial balance, which equals the <a href="/wiki/Principal_sum" class="mw-redirect" title="Principal sum">principal sum</a></dd></dl> <p>By repeated substitution, one obtains expressions for <i>B</i><sub><i>n</i></sub>, which are linearly proportional to <i>B</i><sub>0</sub> and <i>p</i>, and use of the formula for the partial sum of a <a href="/wiki/Geometric_series" title="Geometric series">geometric series</a> results in </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{n}=(1+r)^{n}B_{0}-{\frac {(1+r)^{n}-1}{r}}p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>r</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>r</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mi>r</mi> </mfrac> </mrow> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{n}=(1+r)^{n}B_{0}-{\frac {(1+r)^{n}-1}{r}}p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d7e0241355a2db0cab6d5227cb06cc04e7b81fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:33.907ex; height:5.676ex;" alt="{\displaystyle B_{n}=(1+r)^{n}B_{0}-{\frac {(1+r)^{n}-1}{r}}p}"></span></dd></dl> <p>A solution of this expression for <i>p</i> in terms of <i>B</i><sub>0</sub> and <i>B</i><sub><i>n</i></sub> reduces to </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=r\left[{\frac {(1+r)^{n}B_{0}-B_{n}}{(1+r)^{n}-1}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>r</mi> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>r</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>r</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=r\left[{\frac {(1+r)^{n}B_{0}-B_{n}}{(1+r)^{n}-1}}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f3ee5f10636fe810c67647a429fd5a914b82c88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-left: -0.089ex; width:25.805ex; height:6.509ex;" alt="{\displaystyle p=r\left[{\frac {(1+r)^{n}B_{0}-B_{n}}{(1+r)^{n}-1}}\right]}"></span></dd></dl> <p>To find the payment if the loan is to be finished in <i>n</i> payments, one sets <i>B</i><sub><i>n</i></sub> = 0. </p><p>The PMT function found in <a href="/wiki/Spreadsheet" title="Spreadsheet">spreadsheet</a> programs can be used to calculate the monthly payment of a loan: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\mathrm {PMT} ({\text{rate}},{\text{num}},{\text{PV}},{\text{FV}},)=\mathrm {PMT} (r,n,-B_{0},B_{n},)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">T</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>rate</mtext> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>num</mtext> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>PV</mtext> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>FV</mtext> </mrow> <mo>,</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">T</mi> </mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>n</mi> <mo>,</mo> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\mathrm {PMT} ({\text{rate}},{\text{num}},{\text{PV}},{\text{FV}},)=\mathrm {PMT} (r,n,-B_{0},B_{n},)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bcb3cf5ecd77f1ca14485fb9a65cb4f334a03236" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:55.301ex; height:2.843ex;" alt="{\displaystyle p=\mathrm {PMT} ({\text{rate}},{\text{num}},{\text{PV}},{\text{FV}},)=\mathrm {PMT} (r,n,-B_{0},B_{n},)}"></span></dd></dl> <p>An interest-only payment on the current balance would be </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{I}=rB.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> </mrow> </msub> <mo>=</mo> <mi>r</mi> <mi>B</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{I}=rB.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5cad884f27506a4c9fcdb6d64cb8429129675b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:8.878ex; height:2.509ex;" alt="{\displaystyle p_{I}=rB.}"></span></dd></dl> <p>The total interest, <i>I</i><sub><i>T</i></sub>, paid on the loan is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{T}=np-B_{0}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>n</mi> <mi>p</mi> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{T}=np-B_{0}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e05f1a9740471523eb21a0578e7180e29c3b9dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.38ex; height:2.509ex;" alt="{\displaystyle I_{T}=np-B_{0}.}"></span></dd></dl> <p>The formulas for a regular savings program are similar, but the payments are added to the balances instead of being subtracted, and the formula for the payment is the negative of the one above. These formulas are only approximate since actual loan balances are affected by rounding. To avoid an underpayment at the end of the loan, the payment must be rounded up to the next cent. </p><p>Consider a similar loan but with a new period equal to <i>k</i> periods of the problem above. If <i>r</i><sub><i>k</i></sub> and <i>p</i><sub><i>k</i></sub> are the new rate and payment, we now have </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{k}=B'_{0}=(1+r_{k})B_{0}-p_{k}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{k}=B'_{0}=(1+r_{k})B_{0}-p_{k}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/269513dc1685e5cf9785aa61920673783411b825" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.381ex; height:3.009ex;" alt="{\displaystyle B_{k}=B'_{0}=(1+r_{k})B_{0}-p_{k}.}"></span></dd></dl> <p>Comparing this with the expression for B<sub>k</sub> above, we note that </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{k}=(1+r)^{k}-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>r</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{k}=(1+r)^{k}-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee2768dc9ca9d21d126cd5886d2e69f2ba65ff42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.188ex; height:3.176ex;" alt="{\displaystyle r_{k}=(1+r)^{k}-1}"></span></dd></dl> <p>and </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{k}={\frac {p}{r}}r_{k}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mi>r</mi> </mfrac> </mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{k}={\frac {p}{r}}r_{k}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c37df9bd3d178fee32d3b38bc6ebe3f4d5a887a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.089ex; width:10.236ex; height:4.843ex;" alt="{\displaystyle p_{k}={\frac {p}{r}}r_{k}.}"></span></dd></dl> <p>The last equation allows us to define a constant that is the same for both problems: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B^{*}={\frac {p}{r}}={\frac {p_{k}}{r_{k}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B^{*}={\frac {p}{r}}={\frac {p_{k}}{r_{k}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd1cf3bbafea93588517a030cd48599856ee7fb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.115ex; height:5.176ex;" alt="{\displaystyle B^{*}={\frac {p}{r}}={\frac {p_{k}}{r_{k}}}}"></span></dd></dl> <p>and <i>B</i><sub><i>k</i></sub> can be written as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{k}=(1+r_{k})B_{0}-r_{k}B^{*}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{k}=(1+r_{k})B_{0}-r_{k}B^{*}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6df8ded957cbc620f49891ecfd278925e0dbf0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.162ex; height:2.843ex;" alt="{\displaystyle B_{k}=(1+r_{k})B_{0}-r_{k}B^{*}.}"></span></dd></dl> <p>Solving for <i>r</i><sub><i>k</i></sub>, we find a formula for <i>r</i><sub><i>k</i></sub> involving known quantities and <i>B</i><sub><i>k</i></sub>, the balance after <i>k</i> periods: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{k}={\frac {B_{0}-B_{k}}{B^{*}-B_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{k}={\frac {B_{0}-B_{k}}{B^{*}-B_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6987156aadf731e41bc34ca1b84701bd316e039" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.583ex; height:5.843ex;" alt="{\displaystyle r_{k}={\frac {B_{0}-B_{k}}{B^{*}-B_{0}}}}"></span>.</dd></dl> <p>Since <i>B</i><sub>0</sub> could be any balance in the loan, the formula works for any two balances separate by <i>k</i> periods and can be used to compute a value for the annual interest rate. </p><p><i>B</i>* is a <a href="/wiki/Scale_invariant" class="mw-redirect" title="Scale invariant">scale invariant</a>, since it does not change with changes in the length of the period. </p><p>Rearranging the equation for <i>B</i><sup>*</sup>, one obtains a transformation coefficient (<a href="/wiki/Scale_factor" class="mw-redirect" title="Scale factor">scale factor</a>): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{k}={\frac {p_{k}}{p}}={\frac {r_{k}}{r}}={\frac {(1+r)^{k}-1}{r}}=k\left[1+{\frac {(k-1)r}{2}}+\cdots \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mi>p</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>r</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mi>k</mi> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>k</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mi>r</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{k}={\frac {p_{k}}{p}}={\frac {r_{k}}{r}}={\frac {(1+r)^{k}-1}{r}}=k\left[1+{\frac {(k-1)r}{2}}+\cdots \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b1914300905ee6d4cadcc5e32dbd20d7c706d58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:56.222ex; height:6.509ex;" alt="{\displaystyle \lambda _{k}={\frac {p_{k}}{p}}={\frac {r_{k}}{r}}={\frac {(1+r)^{k}-1}{r}}=k\left[1+{\frac {(k-1)r}{2}}+\cdots \right]}"></span> (see <a href="/wiki/Binomial_theorem" title="Binomial theorem">binomial theorem</a>)</dd></dl> <p>and we see that <i>r</i> and <i>p</i> transform in the same manner: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{k}=\lambda _{k}r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{k}=\lambda _{k}r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0839ee14d653543c0fec9ce92b8a1bd7e601c7cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.728ex; height:2.509ex;" alt="{\displaystyle r_{k}=\lambda _{k}r}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{k}=\lambda _{k}p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{k}=\lambda _{k}p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b45377f0dfbdcd0dba1a2fd7bfa70b4c8a72f266" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:9.059ex; height:2.509ex;" alt="{\displaystyle p_{k}=\lambda _{k}p}"></span>.</dd></dl> <p>The change in the balance transforms likewise: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta B_{k}=B'-B=(\lambda _{k}rB-\lambda _{k}p)=\lambda _{k}\,\Delta B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>B</mi> <mo>′</mo> </msup> <mo>−</mo> <mi>B</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mi>r</mi> <mi>B</mi> <mo>−</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi mathvariant="normal">Δ</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta B_{k}=B'-B=(\lambda _{k}rB-\lambda _{k}p)=\lambda _{k}\,\Delta B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d04ad536488285f3afa630f091ff8271b153a0c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.188ex; height:3.009ex;" alt="{\displaystyle \Delta B_{k}=B'-B=(\lambda _{k}rB-\lambda _{k}p)=\lambda _{k}\,\Delta B}"></span>,</dd></dl> <p>which gives an insight into the meaning of some of the coefficients found in the formulas above. The annual rate, <i>r</i><sub>12</sub>, assumes only one payment per year and is not an "effective" rate for monthly payments. With monthly payments, the monthly interest is paid out of each payment and so should not be compounded, and an annual rate of 12·<i>r</i> would make more sense. If one just made interest-only payments, the amount paid for the year would be 12·<i>r</i>·<i>B</i><sub>0</sub>. </p><p>Substituting <i>p</i><sub><i>k</i></sub> = <i>r</i><sub><i>k</i></sub> <i>B</i>* into the equation for the <i>B</i><sub><i>k</i></sub>, we obtain </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{k}=B_{0}-r_{k}(B^{*}-B_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{k}=B_{0}-r_{k}(B^{*}-B_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da07812bb0278d75d836d2fb284c5719abf97f56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.033ex; height:2.843ex;" alt="{\displaystyle B_{k}=B_{0}-r_{k}(B^{*}-B_{0})}"></span>.</dd></dl> <p>Since <i>B</i><sub><i>n</i></sub> = 0, we can solve for <i>B</i>*: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B^{*}=B_{0}\left({\frac {1}{r_{n}}}+1\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B^{*}=B_{0}\left({\frac {1}{r_{n}}}+1\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e64cad9d475849064032a2e6de1186b74ea29574" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.683ex; height:6.176ex;" alt="{\displaystyle B^{*}=B_{0}\left({\frac {1}{r_{n}}}+1\right).}"></span></dd></dl> <p>Substituting back into the formula for the <i>B</i><sub><i>k</i></sub> shows that they are a linear function of the <i>r</i><sub><i>k</i></sub> and therefore the <i>λ</i><sub><i>k</i></sub>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{k}=B_{0}\left(1-{\frac {r_{k}}{r_{n}}}\right)=B_{0}\left(1-{\frac {\lambda _{k}}{\lambda _{n}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{k}=B_{0}\left(1-{\frac {r_{k}}{r_{n}}}\right)=B_{0}\left(1-{\frac {\lambda _{k}}{\lambda _{n}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a96c723c59a2f3aff92351bb610db234643c0e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:36.821ex; height:6.176ex;" alt="{\displaystyle B_{k}=B_{0}\left(1-{\frac {r_{k}}{r_{n}}}\right)=B_{0}\left(1-{\frac {\lambda _{k}}{\lambda _{n}}}\right)}"></span>.</dd></dl> <p>This is the easiest way of estimating the balances if the <i>λ</i><sub><i>k</i></sub> are known. Substituting into the first formula for <i>B</i><sub><i>k</i></sub> above and solving for <i>λ</i><sub><i>k</i>+1</sub>, we obtain </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{k+1}=1+(1+r)\lambda _{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>r</mi> <mo stretchy="false">)</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{k+1}=1+(1+r)\lambda _{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0ae9f4ea7075bc84802bb73c41125b19797bf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.951ex; height:2.843ex;" alt="{\displaystyle \lambda _{k+1}=1+(1+r)\lambda _{k}}"></span>.</dd></dl> <p><i>λ</i><sub>0</sub> and <i>λ</i><sub><i>n</i></sub> can be found using the formula for <i>λ</i><sub><i>k</i></sub> above or computing the <i>λ</i><sub><i>k</i></sub> recursively from <i>λ</i><sub>0</sub> = 0 to <i>λ</i><sub><i>n</i></sub>. </p><p>Since <i>p</i> = <i>rB</i>*, the formula for the payment reduces to </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\left(r+{\frac {1}{\lambda _{n}}}\right)B_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>r</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\left(r+{\frac {1}{\lambda _{n}}}\right)B_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66c4436f5ff753eb2de80c6c341ab173cba33f06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.089ex; width:18.283ex; height:6.176ex;" alt="{\displaystyle p=\left(r+{\frac {1}{\lambda _{n}}}\right)B_{0}}"></span></dd></dl> <p>and the average interest rate over the period of the loan is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{\text{loan}}={\frac {I_{T}}{nB_{0}}}=r+{\frac {1}{\lambda _{n}}}-{\frac {1}{n}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>loan</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mrow> <mi>n</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>r</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{loan}}={\frac {I_{T}}{nB_{0}}}=r+{\frac {1}{\lambda _{n}}}-{\frac {1}{n}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1a9746f1a22cbbdad74c345bbd9e443aa99b358" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.559ex; height:5.676ex;" alt="{\displaystyle r_{\text{loan}}={\frac {I_{T}}{nB_{0}}}=r+{\frac {1}{\lambda _{n}}}-{\frac {1}{n}},}"></span></dd></dl> <p>which is less than <i>r</i> if <i>n</i> > 1. </p> <div class="mw-heading mw-heading2"><h2 id="Discount_instruments">Discount instruments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=9" title="Edit section: Discount instruments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>US and Canadian T-Bills (short term Government debt) have a different calculation for interest. Their interest is calculated as (100 − <i>P</i>)/<i>P</i> where <i>P</i> is the price paid. Instead of normalizing it to a year, the interest is prorated by the number of days <i>t</i>: (365/<i>t</i>)·100. (See also: <a href="/wiki/Day_count_convention" title="Day count convention">Day count convention</a>). The total calculation is ((100 − <i>P</i>)/<i>P</i>)·((365/<i>t</i>)·100). This is equivalent to calculating the price by a process called <b>discounting at a simple interest rate.</b></li></ul> <div class="mw-heading mw-heading2"><h2 id="Rules_of_thumb">Rules of thumb</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=10" title="Edit section: Rules of thumb"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Rule_of_78s">Rule of 78s</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=11" title="Edit section: Rule of 78s"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Rule_of_78s" title="Rule of 78s">Rule of 78s</a></div> <p>In the age before electronic computers were widely available, flat rate consumer loans in the United States of America would be priced using the Rule of 78s, or "sum of digits" method. (The sum of the integers from 1 to 12 is 78.) The technique required only a simple calculation. </p><p>Payments remain constant over the life of the loan; however, payments are allocated to interest in progressively smaller amounts. In a one-year loan, in the first month, 12/78 of all interest owed over the life of the loan is due; in the second month, 11/78; progressing to the twelfth month where only 1/78 of all interest is due. The practical effect of the Rule of 78s is to make early pay-offs of term loans more expensive. For a one-year loan, approximately 3/4 of all interest due is collected by the sixth month, and pay-off of the principal then will cause the effective interest rate to be much higher than the APR used to calculate the payments.<sup id="cite_ref-bankrate.com_18-0" class="reference"><a href="#cite_note-bankrate.com-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>In 1992, the <a href="/wiki/United_States" title="United States">United States</a> outlawed the use of "Rule of 78s" interest in connection with mortgage refinancing and other consumer loans over five years in term.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Certain other jurisdictions have outlawed application of the Rule of 78s in certain types of loans, particularly consumer loans.<sup id="cite_ref-bankrate.com_18-1" class="reference"><a href="#cite_note-bankrate.com-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Rule_of_72">Rule of 72</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=12" title="Edit section: Rule of 72"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Rule_of_72" title="Rule of 72">Rule of 72</a></div> <p>To approximate how long it takes for money to double at a given interest rate, that is, for accumulated compound interest to reach or exceed the initial deposit, divide 72 by the percentage interest rate. For example, compounding at an annual interest rate of 6 percent, it will take 72/6 = 12 years for the money to double. </p><p>The rule provides a good indication for interest rates up to 10%. </p><p>In the case of an interest rate of 18 percent, the rule of 72 predicts that money will double after 72/18 = 4 years. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1.18^{4}=1.9388{\text{ (4 d.p.)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>1.18</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>=</mo> <mn>1.9388</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> (4 d.p.)</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1.18^{4}=1.9388{\text{ (4 d.p.)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ca76380bcef07a1fa2979e40802cb980756f36c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.758ex; height:3.176ex;" alt="{\displaystyle 1.18^{4}=1.9388{\text{ (4 d.p.)}}}"></span></dd></dl> <p>In the case of an interest rate of 24 percent, the rule predicts that money will double after 72/24 = 3 years. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1.24^{3}=1.9066{\text{ (4 d.p.)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>1.24</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mn>1.9066</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> (4 d.p.)</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1.24^{3}=1.9066{\text{ (4 d.p.)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/460d184e66c91a5899fc682ba022d45fa2146b5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.758ex; height:3.176ex;" alt="{\displaystyle 1.24^{3}=1.9066{\text{ (4 d.p.)}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Market_interest_rates">Market interest rates</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=13" title="Edit section: Market interest rates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Interest" title="Special:EditPage/Interest">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">January 2009</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>There are markets for investments (which include the money market, bond market, as well as retail financial institutions like banks) that set <a href="/wiki/Interest_rate" title="Interest rate">interest rates</a>. Each specific debt takes into account the following factors in determining its interest rate: </p> <div class="mw-heading mw-heading3"><h3 id="Opportunity_cost_and_deferred_consumption">Opportunity cost and deferred consumption</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=14" title="Edit section: Opportunity cost and deferred consumption"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Opportunity_cost" title="Opportunity cost">Opportunity cost</a> encompasses any other use to which the money could be put, including lending to others, investing elsewhere, holding cash, or spending the funds. </p><p>Charging interest equal to inflation preserves the lender's purchasing power, but does not compensate for the <a href="/wiki/Time_value_of_money" title="Time value of money">time value of money</a> in <a href="/wiki/Real_versus_nominal_value_(economics)" class="mw-redirect" title="Real versus nominal value (economics)">real terms</a>. The lender may prefer to invest in another product rather than consume. The return they might obtain from competing investments is a factor in determining the interest rate they demand. </p> <div class="mw-heading mw-heading3"><h3 id="Inflation">Inflation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=15" title="Edit section: Inflation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since the lender is deferring consumption, they will <i>wish</i>, as a bare minimum, to recover enough to pay the increased cost of goods due to <a href="/wiki/Inflation" title="Inflation">inflation</a>. Because future inflation is unknown, there are three ways this might be achieved: </p> <ul><li>Charge X% interest "plus inflation" Many governments issue "real-return" or "inflation indexed" bonds. The principal amount or the interest payments are continually increased by the rate of inflation. See the discussion at <a href="/wiki/Real_interest_rate" title="Real interest rate">real interest rate</a>.</li> <li>Decide on the "expected" inflation rate. This still leaves the lender exposed to the risk of "unexpected" inflation.</li> <li>Allow the interest rate to be periodically changed. While a "fixed interest rate" remains the same throughout the life of the debt, "variable" or "floating" rates can be reset. There are derivative products that allow for hedging and swaps between the two.</li></ul> <p>However interest rates are set by the market, and it happens frequently that they are insufficient to compensate for inflation: for example at times of high inflation during, for example, the oil crisis; and during 2011 when real yields on many inflation-linked government stocks are negative. </p> <div class="mw-heading mw-heading3"><h3 id="Default">Default</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=16" title="Edit section: Default"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There is always the risk the borrower will become <a href="/wiki/Bankrupt" class="mw-redirect" title="Bankrupt">bankrupt</a>, <a href="/wiki/Theft" title="Theft">abscond</a> or otherwise <a href="/wiki/Default_(finance)" title="Default (finance)">default</a> on the loan. The <a href="/wiki/Risk_premium" title="Risk premium">risk premium</a> attempts to measure the integrity of the borrower, the risk of his enterprise succeeding and the security of any collateral pledged. For example, loans to developing countries have higher risk premiums than those to the US government due to the difference in creditworthiness. An operating line of credit to a business will have a higher rate than a <a href="/wiki/Mortgage_loan" class="mw-redirect" title="Mortgage loan">mortgage loan</a>. </p><p>The <a href="/wiki/Creditworthiness" class="mw-redirect" title="Creditworthiness">creditworthiness</a> of businesses is measured by <a href="/wiki/Credit_rating_agency" title="Credit rating agency">bond rating services</a> and individual's <a href="/wiki/Credit_score" title="Credit score">credit scores</a> by <a href="/wiki/Credit_bureau" title="Credit bureau">credit bureaus</a>. The risks of an individual debt may have a large standard deviation of possibilities. The lender may want to cover his maximum risk, but lenders with portfolios of debt can lower the risk premium to cover just the most probable outcome. </p> <div class="mw-heading mw-heading3"><h3 id="Composition_of_interest_rates">Composition of interest rates</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=17" title="Edit section: Composition of interest rates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In economics, interest is considered the price of credit, therefore, it is also subject to distortions due to <a href="/wiki/Inflation" title="Inflation">inflation</a>. The nominal interest rate, which refers to the price before adjustment to inflation, is the one visible to the consumer (that is, the interest tagged in a loan contract, credit card statement, etc.). Nominal interest is composed of the <a href="/wiki/Real_interest_rate" title="Real interest rate">real interest rate</a> plus inflation, among other factors. An approximate formula for the nominal interest is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i=r+\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mi>r</mi> <mo>+</mo> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=r+\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3d4497135978e1f55dacf4a259fe049a347e668" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.122ex; height:2.343ex;" alt="{\displaystyle i=r+\pi }"></span></dd></dl> <p>Where </p> <dl><dd><i>i</i> is the nominal interest rate</dd> <dd><i>r</i> is the real interest rate</dd> <dd>and <span class="texhtml mvar" style="font-style:italic;">π</span> is inflation.</dd></dl> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Fisher_equation" title="Fisher equation">Fisher equation</a></div> <p>However, not all borrowers and lenders have access to the same interest rate, even if they are subject to the same inflation. Furthermore, expectations of future inflation vary, so a forward-looking interest rate cannot depend on a single real interest rate plus a single expected rate of inflation. </p><p>Interest rates also depend on <a href="/wiki/Credit_risk" title="Credit risk">credit quality or risk of default</a>. <a href="/wiki/Government_debt" title="Government debt">Governments</a> are normally highly reliable <a href="/wiki/Debtor" title="Debtor">debtors</a>, and the interest rate on government securities is normally lower than the interest rate available to other borrowers. </p><p>The equation: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i=r+\pi +c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mi>r</mi> <mo>+</mo> <mi>π</mi> <mo>+</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=r+\pi +c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b3556ed56ffda97259163244ca3094e5ad3d3e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.969ex; height:2.343ex;" alt="{\displaystyle i=r+\pi +c}"></span></dd></dl> <p>relates expectations of inflation and credit risk to nominal and expected real interest rates, over the life of a loan, where </p> <dl><dd><i>i</i> is the nominal interest applied</dd> <dd><i>r</i> is the real interest expected</dd> <dd><span class="texhtml mvar" style="font-style:italic;">π</span> is the inflation expected and</dd> <dd><i>c</i> is <a href="/wiki/Yield_spread" title="Yield spread">yield spread</a> according to the perceived credit risk.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Default_interest">Default interest</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=18" title="Edit section: Default interest"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Default interest is the rate of interest that a borrower must pay after material breach of a loan covenant. </p><p>The default interest is usually much higher than the original interest rate since it is reflecting the aggravation in the financial risk of the borrower. Default interest compensates the lender for the added risk. </p><p>From the borrower's perspective, this means failure to make their regular payment for one or two payment periods or failure to pay taxes or insurance premiums for the loan collateral will lead to substantially higher interest for the entire remaining term of the loan. </p><p>Banks tend to add default interest to the loan agreements in order to separate between different scenarios. </p><p>In some jurisdictions, default interest clauses are unenforceable as against public policy. </p> <div class="mw-heading mw-heading3"><h3 id="Term">Term</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=19" title="Edit section: Term"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Shorter terms often have less risk of default and exposure to inflation because the near future is easier to predict. In these circumstances, short-term interest rates are lower than longer-term interest rates (an upward sloping <a href="/wiki/Yield_curve" title="Yield curve">yield curve</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Government_intervention">Government intervention</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=20" title="Edit section: Government intervention"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Interest rates are generally determined by the market, but government intervention - usually by a <a href="/wiki/Central_bank" title="Central bank">central bank</a> - may strongly influence short-term interest rates, and is one of the main tools of <a href="/wiki/Monetary_policy" title="Monetary policy">monetary policy</a>. The central bank offers to borrow (or lend) large quantities of money at a rate which they determine (sometimes this is money that they have created <i>ex nihilo</i>, that is, printed) which has a major influence on supply and demand and hence on market interest rates. </p> <div class="mw-heading mw-heading3"><h3 id="Open_market_operations_in_the_United_States">Open market operations in the United States</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=21" title="Edit section: Open market operations in the United States"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Federal_Funds_Rate_1954_thru_2009_effective.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Federal_Funds_Rate_1954_thru_2009_effective.svg/375px-Federal_Funds_Rate_1954_thru_2009_effective.svg.png" decoding="async" width="375" height="281" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Federal_Funds_Rate_1954_thru_2009_effective.svg/563px-Federal_Funds_Rate_1954_thru_2009_effective.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Federal_Funds_Rate_1954_thru_2009_effective.svg/750px-Federal_Funds_Rate_1954_thru_2009_effective.svg.png 2x" data-file-width="640" data-file-height="480" /></a><figcaption>The effective federal funds rate charted over more than fifty years<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2011)">citation needed</span></a></i>]</sup></figcaption></figure> <p>The <a href="/wiki/Federal_Reserve" title="Federal Reserve">Federal Reserve</a> (Fed) implements monetary policy largely by targeting the <a href="/wiki/Federal_funds_rate" title="Federal funds rate">federal funds rate</a>. This is the rate that banks charge each other for overnight loans of <a href="/wiki/Federal_funds" title="Federal funds">federal funds</a>. Federal funds are the reserves held by banks at the Fed. </p><p><a href="/wiki/Open_market_operations" class="mw-redirect" title="Open market operations">Open market operations</a> are one tool within monetary policy implemented by the Federal Reserve to steer short-term interest rates. Using the power to buy and sell treasury <a href="/wiki/Security_(finance)" title="Security (finance)">securities</a>, the Open Market Desk at the <a href="/wiki/Federal_Reserve_Bank_of_New_York" title="Federal Reserve Bank of New York">Federal Reserve Bank of New York</a> can supply the market with dollars by purchasing <a href="/wiki/United_States_Treasury_security#Treasury_note" title="United States Treasury security">U.S. Treasury notes</a>, hence increasing the nation's money supply. By increasing the money supply or <a href="/w/index.php?title=Aggregate_Supply_of_Funding&action=edit&redlink=1" class="new" title="Aggregate Supply of Funding (page does not exist)">Aggregate Supply of Funding</a> (ASF), interest rates will fall due to the excess of dollars banks will end up with in their reserves. <a href="/wiki/Excess_reserves" title="Excess reserves">Excess reserves</a> may be lent in the <a href="/wiki/Federal_funds" title="Federal funds">Fed funds</a> market to other banks, thus driving down rates. </p> <div class="mw-heading mw-heading3"><h3 id="Interest_rates_and_credit_risk">Interest rates and credit risk</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=22" title="Edit section: Interest rates and credit risk"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is increasingly recognized that during the business cycle, <a href="/wiki/Interest_rate" title="Interest rate">interest rates</a> and <a href="/wiki/Credit_risk" title="Credit risk">credit risk</a> are tightly interrelated. The <a href="/wiki/Jarrow-Turnbull_model" class="mw-redirect" title="Jarrow-Turnbull model">Jarrow-Turnbull model</a> was the first model of credit risk that explicitly had random interest rates at its core. Lando (2004), <a href="/wiki/Darrell_Duffie" title="Darrell Duffie">Darrell Duffie</a> and Singleton (2003), and van Deventer and Imai (2003) discuss interest rates when the issuer of the interest-bearing instrument can default. </p> <div class="mw-heading mw-heading3"><h3 id="Money_and_inflation">Money and inflation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=23" title="Edit section: Money and inflation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Loans and bonds have some of the characteristics of money and are included in the broad money supply. </p><p>National governments (provided, of course, that the country has retained its own currency) can influence interest rates and thus the supply and demand for such loans, thus altering the total of loans and bonds issued. Generally speaking, a higher real interest rate reduces the broad money supply. </p><p>Through the <a href="/wiki/Quantity_theory_of_money" title="Quantity theory of money">quantity theory of money</a>, increases in the money supply lead to inflation. This means that interest rates can affect inflation in the future.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Liquidity">Liquidity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=24" title="Edit section: Liquidity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Market_liquidity" title="Market liquidity">Liquidity</a> is the ability to quickly re-sell an asset for fair or near-fair value. All else equal, an investor will want a higher return on an illiquid asset than a liquid one, to compensate for the loss of the option to sell it at any time. U.S. Treasury bonds are highly liquid with an active secondary market, while some other debts are less liquid. In the <a href="/wiki/Mortgage" title="Mortgage">mortgage</a> market, the lowest rates are often issued on loans that can be re-sold as securitized loans. Highly non-traditional loans such as seller financing often carry higher interest rates due to a lack of liquidity. </p> <div class="mw-heading mw-heading2"><h2 id="Theories_of_interest">Theories of interest</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=25" title="Edit section: Theories of interest"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Aristotle's_view_of_interest"><span id="Aristotle.27s_view_of_interest"></span>Aristotle's view of interest</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=26" title="Edit section: Aristotle's view of interest"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> and <a href="/wiki/Scholasticism" title="Scholasticism">the Scholastics</a> held that it was unjust to claim payment except in compensation for one's own efforts and sacrifices, and that since money is by its nature sterile, there is no loss in being temporarily separated from it. Compensation for risk or for the trouble of setting up a loan was not necessarily impermissible on these grounds.<sup id="cite_ref-FOOTNOTESchumpeter195461_21-0" class="reference"><a href="#cite_note-FOOTNOTESchumpeter195461-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Development_of_the_theory_of_interest_during_the_seventeenth_and_eighteenth_centuries">Development of the theory of interest during the seventeenth and eighteenth centuries</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=27" title="Edit section: Development of the theory of interest during the seventeenth and eighteenth centuries"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Nicholas_Barbon" title="Nicholas Barbon">Nicholas Barbon</a> (c.1640–c.1698) described as a "mistake" the view that interest is a monetary value, arguing that because money is typically borrowed to buy assets (goods and stock), the interest that is charged on a loan is a type of rent – "a payment for the use of goods".<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTESchumpeter195461_21-1" class="reference"><a href="#cite_note-FOOTNOTESchumpeter195461-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> According to Schumpeter, Barbon's theories were forgotten until similar views were put forward by <a href="/wiki/Joseph_Massie_(economist)" title="Joseph Massie (economist)">Joseph Massie</a> in 1750.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> </p><p>In 1752 <a href="/wiki/David_Hume" title="David Hume">David Hume</a> published his essay "Of money" which relates interest to the "demand for borrowing", the "riches available to supply that demand" and the "profits arising from commerce". Schumpeter<sup id="cite_ref-FOOTNOTESchumpeter1954_27-0" class="reference"><a href="#cite_note-FOOTNOTESchumpeter1954-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (June 2019)">page needed</span></a></i>]</sup> considered Hume's theory superior to that of Ricardo and Mill, but the reference to profits concentrates to a surprising degree on 'commerce' rather than on industry. </p><p><a href="/wiki/Anne_Robert_Jacques_Turgot" title="Anne Robert Jacques Turgot">Turgot</a> brought the theory of interest close to its classical form. Industrialists </p> <blockquote><p>share their profits with capitalists who supply the funds (<i>Réflexions</i>, LXXI). The share that goes to the latter is determined like all other prices (LXXV) by the play of supply and demand amongst borrowers and lenders, so that the analysis is from the outset firmly planted in the general theory of prices.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>note 2<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading3"><h3 id="The_classical_theory_of_the_interest_rate"><span id="classicalinterest">The classical theory of the interest rate</span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=28" title="Edit section: The classical theory of the interest rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The classical theory was the work of a number of authors, including Turgot, <a href="/wiki/David_Ricardo" title="David Ricardo">Ricardo</a>,<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>note 3<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Mountifort_Longfield" title="Mountifort Longfield">Mountifort Longfield</a>,<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> <a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">J. S. Mill</a>, and <a href="/wiki/Irving_Fisher" title="Irving Fisher">Irving Fisher</a>.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> It was strongly criticised by <a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">Keynes</a><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>note 4<span class="cite-bracket">]</span></a></sup> whose remarks nonetheless made a positive contribution to it. </p><p>Mill's theory is set out the chapter "Of the rate of interest" in his "Principles of political economy".<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>note 5<span class="cite-bracket">]</span></a></sup> He says that the interest rate adjusts to maintain equilibrium between the demands for lending and borrowing.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Individuals lend in order to defer consumption or for the sake of the greater quantity they will be able to consume at a later date owing to interest earned. They borrow in order to anticipate consumption (whose relative desirability is reflected by the <a href="/wiki/Time_value_of_money" title="Time value of money">time value of money</a>), but entrepreneurs also borrow to fund investment and governments borrow for their own reasons. The three sources of demand compete for loans.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>For entrepreneurial borrowing to be in equilibrium with lending: </p> <blockquote><p>The interest for money... is... regulated... by the rate of profits which can be made by the employment of capital...<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>Ricardo's and Mill's 'profit' is made more precise by the concept of the marginal efficiency of capital (the expression, though not the concept, is due to Keynes<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>note 6<span class="cite-bracket">]</span></a></sup>), which may be defined as the annual revenue which will be yielded by an extra increment of capital as a proportion of its cost. So the interest rate <i>r</i> in equilibrium will be equal to the marginal efficiency of capital <i>r<span class="nowrap" style="padding-left:0.1em;">'</span></i>. Rather than work with <i>r</i> and <i>r<span class="nowrap" style="padding-left:0.1em;">'</span></i> as separate variables, we can assume that they are equal and let the single variable <i>r</i> denote their common value. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Millinterestrate.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Millinterestrate.svg/220px-Millinterestrate.svg.png" decoding="async" width="220" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Millinterestrate.svg/330px-Millinterestrate.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Millinterestrate.svg/440px-Millinterestrate.svg.png 2x" data-file-width="242" data-file-height="240" /></a><figcaption>Classical theory of the determination of the interest rate. The solid red curve in the diagram shows the desired level of saving <i>s</i> as a function of <i>r</i> for the current income <i>ŷ</i>.</figcaption></figure> <p>The investment schedule <i>i</i> (<i>r</i>) shows how much investment is possible with a return of at least <i>r</i>.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>note 7<span class="cite-bracket">]</span></a></sup> In a stationary economy it is likely to resemble the blue curve in the diagram, with a step shape arising from the assumption that opportunities to invest with yields greater than <i>r̂</i> have been largely exhausted while there is untapped scope to invest with a lower return.<sup id="cite_ref-Mill_§3;_Longfield_40-0" class="reference"><a href="#cite_note-Mill_§3;_Longfield-40"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p><p>Saving is the excess of deferred over anticipated consumption, and its dependence on income is much as described by Keynes (see <a href="/wiki/The_General_Theory_of_Employment,_Interest_and_Money#bookiii" title="The General Theory of Employment, Interest and Money">The General Theory</a>), but in classical theory definitely an increasing function of <i>r</i>. (The dependence of <i>s</i> on income <i>y</i> was not relevant to classical concerns prior to the development of theories of <a href="/wiki/Unemployment" title="Unemployment">unemployment</a>.) The rate of interest is given by the intersection of the solid red saving curve with the blue investment schedule. But so long as the investment schedule is almost vertical, a change in income (leading in extreme cases to the broken red saving curve) will make little difference to the interest rate. </p><p>In some cases the analysis will be less simple. The introduction of a new technique, leading to demand for new forms of capital, will shift the step to the right and reduce its steepness.<sup id="cite_ref-Mill_§3;_Longfield_40-1" class="reference"><a href="#cite_note-Mill_§3;_Longfield-40"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> Or a sudden increase in the desire to anticipate consumption (perhaps through military spending in time of war) will absorb most available loans; the interest rate will increase and investment will be reduced to the amount whose return exceeds it.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> This is illustrated by the dotted red saving curve. </p> <div class="mw-heading mw-heading4"><h4 id="Keynes's_criticisms"><span id="Keynes.27s_criticisms"></span><span id="keynescriticisms">Keynes's criticisms</span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=29" title="Edit section: Keynes's criticisms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the case of extraordinary spending in time of war the government may wish to borrow more than the public would be willing to lend at a normal interest rate. If the dotted red curve started negative and showed no tendency to increase with <i>r</i>, then the government would be trying to buy what the public was unwilling to sell at any price. Keynes mentions this possibility as a point "which might, perhaps, have warned the classical school that something was wrong" (p. 182). </p><p>He also remarks (on the same page) that the classical theory does not explain the usual supposition that "an increase in the quantity of money has a tendency to reduce the rate of interest, at any rate in the first instance". </p><p>Keynes's diagram of the investment schedule lacks the step shape which can be seen as part of the classical theory. He objects that </p> <blockquote><p>the functions used by classical theory... do not furnish material for a theory of the rate of interest; but they could be used to tell us... what the rate of interest will have to be, if the level of employment [which determines income] is maintained at a given figure.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>Later (p. 184) Keynes claims that "it involves a circular argument" to construct a theory of interest from the investment schedule since </p> <blockquote><p>the 'marginal efficiency of capital' partly depends on the scale of current investment, and we must already know the rate of interest before we can calculate what this scale will be.</p></blockquote> <div class="mw-heading mw-heading3"><h3 id="Theories_of_exploitation,_productivity_and_abstinence"><span id="Theories_of_exploitation.2C_productivity_and_abstinence"></span>Theories of exploitation, productivity and abstinence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=30" title="Edit section: Theories of exploitation, productivity and abstinence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The classical theory of interest explains it as the capitalist's share of business profits, but the pre-marginalist authors were unable to reconcile these profits with the <a href="/wiki/Labor_theory_of_value" title="Labor theory of value">labor theory of value</a> (excluding Longfield, who was essentially a marginalist). Their responses often had a moral tone: Ricardo and Marx viewed profits as exploitation, and <a href="/wiki/John_Ramsay_McCulloch" title="John Ramsay McCulloch">McCulloch</a>'s productivity theory justified profits by portraying capital equipment as an embodiment of accumulated labor.<sup id="cite_ref-FOOTNOTESchumpeter1954_27-1" class="reference"><a href="#cite_note-FOOTNOTESchumpeter1954-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (June 2019)">page needed</span></a></i>]</sup> The theory that interest is a payment for abstinence is attributed to <a href="/wiki/Nassau_William_Senior" title="Nassau William Senior">Nassau Senior</a>, and according to Schumpeter<sup id="cite_ref-FOOTNOTESchumpeter1954_27-2" class="reference"><a href="#cite_note-FOOTNOTESchumpeter1954-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (June 2019)">page needed</span></a></i>]</sup> was intended neutrally, but it can easily be understood as making a moral claim and was sharply criticised by Marx and <a href="/wiki/Ferdinand_Lassalle" title="Ferdinand Lassalle">Lassalle</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Wicksell's_theory"><span id="Wicksell.27s_theory"></span><span id="wicksellinterst">Wicksell's theory</span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=31" title="Edit section: Wicksell's theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Knut_Wicksell" title="Knut Wicksell">Knut Wicksell</a> published his "Interest and Prices" in 1898, elaborating a comprehensive theory of economic crises based upon a distinction between natural and nominal interest rates. </p> <blockquote><p>Wicksell's contribution, in fact, was twofold. First he separated the monetary rate of interest from the hypothetical "natural" rate that would have resulted from equilibrium of capital supply and demand in a barter economy, and he assumed that as a result of the presence of money alone, the effective market rate could fail to correspond to this ideal rate in actuality. Next he supposed that through the mechanism of credit, the rate of interest had an influence on prices; that a rise of the monetary rate above the "natural" level produced a fall, and a decline below that level a rise, in prices. But Wicksell went on to conclude that if the natural rate coincided with the monetary rate, stability of prices would follow.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>In the 1930s Wicksell's approach was refined by <a href="/wiki/Bertil_Ohlin" title="Bertil Ohlin">Bertil Ohlin</a> and <a href="/wiki/Dennis_Robertson_(economist)" title="Dennis Robertson (economist)">Dennis Robertson</a> and became known as the <a href="/wiki/Loanable_funds" title="Loanable funds">loanable funds</a> theory. </p> <div class="mw-heading mw-heading3"><h3 id="Austrian_theories">Austrian theories</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=32" title="Edit section: Austrian theories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Eugen_B%C3%B6hm_von_Bawerk" class="mw-redirect" title="Eugen Böhm von Bawerk">Eugen Böhm von Bawerk</a> and other members of the <a href="/wiki/Austrian_School" class="mw-redirect" title="Austrian School">Austrian School</a> also put forward notable theories of the interest rate. </p><p> The doyen of the Austrian school, Murray N. Rothbard, sees the emphasis on the loan market which makes up the general analysis on interest as a mistaken view to take. As he explains in his primary economic work, <i>Man, Economy, and State</i>, the market rate of interest is but a <i>manifestation</i> of the natural phenomenon of time preference, which is to prefer present goods to future goods.<sup id="cite_ref-FOOTNOTERothbard2001_44-0" class="reference"><a href="#cite_note-FOOTNOTERothbard2001-44"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> To Rothbard, <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style></p><blockquote class="templatequote"><p>Too many writers consider the rate of interest as only the price of loans on the loan market. In reality...the rate of interest pervades all time markets, and the productive loan market is a strictly subsidiary time market of only derivative importance.<sup id="cite_ref-FOOTNOTERothbard2001371_45-0" class="reference"><a href="#cite_note-FOOTNOTERothbard2001371-45"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup></p></blockquote><p> Interest is explainable by the rate of time preference among the people. To point to the loan market is insufficient at best. Rather, the rate of interest is what would be observed between the "stages of production", indeed a time market itself, where capital goods which are used to make consumers' goods are ordered out further in time away from the final consumers' goods stage of the economy where consumption takes place. It is <i>this</i> spread (between these various stages which will tend toward uniformity), with consumers' goods representing present goods and producers' goods representing future goods, that the real rate of interest is observed. Rothbard has said that <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"><p>Interest rate is equal to the rate of price spread in the various stages.<sup id="cite_ref-FOOTNOTERothbard2001371_45-1" class="reference"><a href="#cite_note-FOOTNOTERothbard2001371-45"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup></p></blockquote><p> Rothbard has furthermore criticized the Keynesian conception of interest, saying <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"><p>One grave and fundamental Keynesian error is to persist in regarding the interest rate as a contract rate on loans, instead of the price spreads between stages of production.<sup id="cite_ref-FOOTNOTERothbard2001789_46-0" class="reference"><a href="#cite_note-FOOTNOTERothbard2001789-46"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading3"><h3 id="Pareto's_indifference"><span id="Pareto.27s_indifference"></span>Pareto's indifference</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=33" title="Edit section: Pareto's indifference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Vilfredo_Pareto" title="Vilfredo Pareto">Pareto</a> held that </p> <blockquote><p>The interest rate, being one of the many elements of the general system of equilibrium, was, of course, simultaneously determined with all of them so that there was no point at all in looking for any particular element that 'caused' interest.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>note 8<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading3"><h3 id="Keynes's_theory_of_the_interest_rate"><span id="Keynes.27s_theory_of_the_interest_rate"></span><span id="keynesinterest">Keynes's theory of the interest rate</span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=34" title="Edit section: Keynes's theory of the interest rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Interest is one of the main components of the economic theories developed in <a href="/wiki/Keynes" class="mw-redirect" title="Keynes">Keynes</a>'s 1936 <i>General theory of employment, interest, and money</i>. In his initial account of <a href="/wiki/Liquidity_preference" title="Liquidity preference">liquidity preference</a> (the demand for money), this demand is solely a function of the interest rate; and since the supply is given and equilibrium is assumed, the interest rate is determined by the money supply. He later writes that interest cannot be separated from other economic variables and needs to be analysed together with them (see <a href="/wiki/The_General_Theory_of_Employment,_Interest_and_Money#interestliquidity" title="The General Theory of Employment, Interest and Money">The General Theory</a>). </p> <div class="mw-heading mw-heading2"><h2 id="In_religious_contexts">In religious contexts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=35" title="Edit section: In religious contexts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Judaism">Judaism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=36" title="Edit section: Judaism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Loans_and_interest_in_Judaism" title="Loans and interest in Judaism">Loans and interest in Judaism</a></div> <p>Jews are forbidden from usury in dealing with fellow Jews, and this lending is to be considered <a href="/wiki/Tzedakah" title="Tzedakah">tzedakah</a>, or charity. However, there are permissions to charge interest on loans to <a href="/wiki/Gentile" title="Gentile">non-Jews</a>.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Several historical rulings in <a href="/wiki/Halakha" title="Halakha">Jewish law</a> have mitigated the allowances for usury toward non-Jews. For instance, the 15th-century commentator <a href="/wiki/Isaac_Abarbanel" title="Isaac Abarbanel">Rabbi Isaac Abrabanel</a> specified that the rubric for allowing interest does not apply to Christians or Muslims, because their faith systems have a common ethical basis originating from Judaism. The medieval commentator <a href="/wiki/David_Kimhi" title="David Kimhi">Rabbi David Kimchi</a> extended this principle to non-Jews who show consideration for Jews, saying they should be treated with the same consideration when they borrow.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Islam">Islam</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=37" title="Edit section: Islam"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Riba" title="Riba">Riba</a> and <a href="/wiki/Islamic_banking_and_finance" title="Islamic banking and finance">Islamic banking and finance</a></div> <p>The following quotations are English translations from the <a href="/wiki/Qur%27an" class="mw-redirect" title="Qur'an">Qur'an</a>: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Those who charge usury are in the same position as those controlled by the devil's influence. This is because they claim that usury is the same as commerce. However, God permits commerce, and prohibits usury. Thus, whoever heeds this commandment from his Lord, and refrains from usury, he may keep his past earnings, and his judgment rests with God. As for those who persist in usury, they incur Hell, wherein they abide forever.</p><div class="templatequotecite">— <cite>Al-Baqarah 2:275</cite></div></blockquote> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>God condemns usury, and blesses charities. God dislikes every sinning disbeliever. Those who believe and do good works and establish worship and pay the poor-due, their reward is with their Lord and there shall no fear come upon them neither shall they grieve. O you who believe, you shall observe God and refrain from all kinds of usury, if you are believers. If you do not, then expect a war from God and His messenger. But if you repent, you may keep your capitals, without inflicting injustice, or incurring injustice. If the debtor is unable to pay, wait for a better time. If you give up the loan as a charity, it would be better for you, if you only knew.</p><div class="templatequotecite">— <cite>Al-Baqarah 2:276–280</cite></div></blockquote> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>O you who believe, you shall not take usury, compounded over and over. Observe God, that you may succeed.</p><div class="templatequotecite">— <cite>Al-'Imran 3:130</cite></div></blockquote> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>And for practicing usury, which was forbidden, and for consuming the people's money illicitly. We have prepared for the disbelievers among them painful retribution.</p><div class="templatequotecite">— <cite>Al-Nisa 4:161</cite></div></blockquote> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>The usury that is practiced to increase some people's wealth, does not gain anything at God. But if people give to charity, seeking God's pleasure, these are the ones who receive their reward many fold.</p><div class="templatequotecite">— <cite>Ar-Rum 30:39</cite></div></blockquote> <p>The attitude of Muhammad to usury is articulated in his Last Sermon: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>O People, just as you regard this month, this day, this city as Sacred, so regard the life and property of every Muslim as a sacred trust. Return the goods entrusted to you to their rightful owners. Hurt no one so that no one may hurt you. Remember that you will indeed meet your Lord, and that He will indeed reckon your deeds. Allah has forbidden you to take usury, therefore all usurious obligation shall henceforth be waived. Your capital, however, is yours to keep. You will neither inflict nor suffer any inequity. Allah has Judged that there shall be no usury and that all the usury due to Abbas ibn 'Abd'al Muttalib (Prophet's uncle) shall henceforth be waived ...<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources"><span title="The material near this tag may rely on an unreliable source. (July 2017)">unreliable source?</span></a></i>]</sup></p></blockquote> <p><span class="anchor" id="Scholastic_theology"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Christianity">Christianity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=38" title="Edit section: Christianity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Old_Testament" title="Old Testament">Old Testament</a> "condemns the practice of charging interest because a loan should be an act of compassion and taking care of one's neighbor"; it teaches that "making a profit off a loan is exploiting that person and dishonoring God's covenant (Exodus 22:25–27)".<sup id="cite_ref-Considine2016_52-0" class="reference"><a href="#cite_note-Considine2016-52"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p><p>The first of the <a href="/wiki/Scholastic_theology" class="mw-redirect" title="Scholastic theology">scholastic</a> Christian theologians, <a href="/wiki/Saint_Anselm_of_Canterbury" class="mw-redirect" title="Saint Anselm of Canterbury">Saint Anselm of Canterbury</a>, led the shift in thought that labeled charging interest the same as theft.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2023)">citation needed</span></a></i>]</sup> St. <a href="/wiki/Thomas_Aquinas" title="Thomas Aquinas">Thomas Aquinas</a>, the leading scholastic theologian of the <a href="/wiki/Roman_Catholic_Church" class="mw-redirect" title="Roman Catholic Church">Roman Catholic Church</a>, argued charging of interest is wrong because it amounts to "double charging", charging for both the thing and the use of the thing.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Outlawing usury did not prevent investment, but stipulated that in order for the investor to share in the profit he must share the risk. In short he must be a joint-venturer. Simply to invest the money and expect it to be returned regardless of the success of the venture was to make money simply by having money and not by taking any risk or by doing any work or by any effort or sacrifice at all, which is usury. Thus a banker or credit-lender could charge for such actual work or effort as he did carry out, for example, any fair administrative charges. The Catholic Church, in a decree of the <a href="/wiki/Fifth_Council_of_the_Lateran" title="Fifth Council of the Lateran">Fifth Council of the Lateran</a>, expressly allowed such charges in respect of credit-unions run for the benefit of the poor known as "<a href="/wiki/Montes_pietatis" class="mw-redirect" title="Montes pietatis">montes pietatis</a>".<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p>In the 13th century <a href="/wiki/Henry_of_Segusio" title="Henry of Segusio">Cardinal Hostiensis</a> enumerated thirteen situations in which charging interest was not immoral.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> The most important of these was <i>lucrum cessans</i> (profits given up) which allowed for the lender to charge interest "to compensate him for profit foregone in investing the money himself".<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> This idea is very similar to opportunity cost. Many scholastic thinkers who argued for a ban on interest charges also argued for the legitimacy of <i>lucrum cessans</i> profits (for example, <a href="/wiki/Pierre_Jean_Olivi" class="mw-redirect" title="Pierre Jean Olivi">Pierre Jean Olivi</a> and <a href="/wiki/St._Bernardino_of_Siena" class="mw-redirect" title="St. Bernardino of Siena">St. Bernardino of Siena</a>). However, Hostiensis' exceptions, including for <i>lucrum cessans</i>, were never accepted as official by the Roman Catholic Church. </p><p>The <a href="/wiki/Westminster_Confession_of_Faith" title="Westminster Confession of Faith">Westminster Confession of Faith</a>, a confession of faith upheld by the <a href="/wiki/Reformed_Church" class="mw-redirect" title="Reformed Church">Reformed Churches</a>, teaches that usury — defined as charging interest at any rate — is a <a href="/wiki/Sin_in_Christianity" class="mw-redirect" title="Sin in Christianity">sin</a> prohibited by the <a href="/wiki/Ten_Commandments" title="Ten Commandments">eighth commandment</a>.<sup id="cite_ref-Cox1853_57-0" class="reference"><a href="#cite_note-Cox1853-57"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p><p>The Roman Catholic Church has always condemned usury, but in modern times, with the rise of capitalism and the disestablishment of the Catholic Church in majority Catholic countries, this prohibition on usury has not been enforced. </p><p>The <a href="/wiki/Congregation_of_the_Missionary_Sons_of_the_Immaculate_Heart_of_Mary" class="mw-redirect" title="Congregation of the Missionary Sons of the Immaculate Heart of Mary">Congregation of the Missionary Sons of the Immaculate Heart of Mary</a>, a Catholic Christian <a href="/wiki/Religious_order" title="Religious order">religious order</a>, teaches that:<sup id="cite_ref-Considine2016_52-1" class="reference"><a href="#cite_note-Considine2016-52"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>It might initially seem like little is at stake when it comes to interest, but this is an issue of human dignity. A person is made in God's own image and therefore may never be treated as a thing. Interest can diminish the human person to a thing to be manipulated for money. In an article for The Catholic Worker, Dorothy Day articulated this well: "Can I talk about the people living off usury . . . not knowing the way that their infertile money has bred more money by wise investment in God knows what devilish nerve gas, drugs, napalm, missiles, or vanities, when housing and employment . . . for the poor were needed, and money could have been invested there?" Her thoughts were a precursor to what Pope Francis now calls an "economy that kills." To sin is to say "no" to God and God's presence by harming others, ourselves, or all of creation. Charging interest is indeed sinful when doing so takes advantage of a person in need as well as when it means investing in corporations involved in the harming of God's creatures.<sup id="cite_ref-Considine2016_52-2" class="reference"><a href="#cite_note-Considine2016-52"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=39" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Actuarial_notation" title="Actuarial notation">Actuarial notation</a></li> <li><a href="/wiki/Credit_card_interest" title="Credit card interest">Credit card interest</a></li> <li><a href="/wiki/Credit_rating_agency" title="Credit rating agency">Credit rating agency</a></li> <li><a href="/wiki/DIRTI_5" title="DIRTI 5">DIRTI 5</a></li> <li><a href="/wiki/Discounting" title="Discounting">Discount</a></li> <li><a href="/wiki/Fisher_equation" title="Fisher equation">Fisher equation</a></li> <li><a href="/wiki/Hire_purchase" title="Hire purchase">Hire purchase</a></li> <li><a href="/wiki/Interest_expense" title="Interest expense">Interest expense</a></li> <li><a href="/wiki/Leasing" class="mw-redirect" title="Leasing">Leasing</a></li> <li><a href="/wiki/Promissory_note" title="Promissory note">Promissory note</a></li> <li><a href="/wiki/Risk-free_interest_rate" class="mw-redirect" title="Risk-free interest rate">Risk-free interest rate</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=40" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">"Barbon's Discourse, on this point at all events, did not meet with success. The tract seems indeed to have been forgotten very soon. Thus, Barbon's fundamental idea remained in abeyance until 1750, when it was again expounded—for all we know, independently rediscovered—by Massie,<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> whose analysis not only went further than Barbon's but also gathered force from its criticism of the views of Petty and Locke."<sup id="cite_ref-FOOTNOTESchumpeter1954314_25-0" class="reference"><a href="#cite_note-FOOTNOTESchumpeter1954314-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Schumpeter;<sup id="cite_ref-FOOTNOTESchumpeter1954316_28-0" class="reference"><a href="#cite_note-FOOTNOTESchumpeter1954316-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> the references are to paragraph numbers in Turgot's "Réflexions sur la formation et la distribution des richesses" written in 1766, first published in 1769-70 in a journal, and then separately in 1776.</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text">Isolated remarks in the chapters "Effects of accumulation on profits and interest" and "On currency and banks" in "Principles of political economy and taxation"</span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text">"The general theory of employment, interest and money", especially the appendix to Chapter 14. Page numbers refer to the widely available edition published by Macmillan for the Royal Economic Society as part of Keynes's collected writings, which appear to correspond to those of the first edition.</span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text">See also his chapters "Of the law of the increase of capital" and "Of profits"</span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text">Chapter 11 of The General Theory is titled "The Marginal Efficiency of Capital." <a href="/wiki/Alfred_Marshall" title="Alfred Marshall">Marshall</a> used the term <i>marginal utility of capital</i> and Fisher <i>rate of return over cost</i>. Fisher also referred to it as representing the "investment opportunity side of interest theory".</span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text">Keynes called this function the 'schedule of the marginal efficiency of capital' and also the 'investment demand schedule'.</span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text">Unsourced observation in Schumpeter<sup id="cite_ref-FOOTNOTESchumpeter1954892_47-0" class="reference"><a href="#cite_note-FOOTNOTESchumpeter1954892-47"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Ibid plainlinks metadata ambox ambox-style" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">Constructs such as <i><a href="/wiki/Ibid." title="Ibid.">ibid.</a></i>, <i><a href="/wiki/Loc._cit." title="Loc. cit.">loc. cit.</a></i> and <i><a href="/wiki/Idem" title="Idem">idem</a></i> are <b>discouraged by <a href="/wiki/Wikipedia:IBID" class="mw-redirect" title="Wikipedia:IBID">Wikipedia's style guide</a> for footnotes</b>, as they are easily broken. Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Interest&action=edit">improve this article</a> by replacing them with <a href="/wiki/Wikipedia:Footnotes#Naming_a_ref_tag_so_it_can_be_used_more_than_once" class="mw-redirect" title="Wikipedia:Footnotes">named references</a> (<i><a href="/wiki/Template:Refref/core" title="Template:Refref/core">quick guide</a></i>), or an abbreviated title. <span class="date-container"><i>(<span class="date">May 2019</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20171227123013/https://en.oxforddictionaries.com/definition/interest">"Definition of interest in English"</a>. <i>English Oxford Living Dictionaries</i>. Oxford University Press. Archived from <a rel="nofollow" class="external text" href="https://en.oxforddictionaries.com/definition/interest">the original</a> on December 27, 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">27 December</span> 2017</span>. <q>Money paid regularly at a particular rate for the use of money lent, or for delaying the repayment of a debt.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=English+Oxford+Living+Dictionaries&rft.atitle=Definition+of+interest+in+English&rft_id=https%3A%2F%2Fen.oxforddictionaries.com%2Fdefinition%2Finterest&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.merriam-webster.com/dictionary/dividend">"Definition of dividend"</a>. <i>Merriam Webster</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171227122331/https://www.merriam-webster.com/dictionary/dividend">Archived</a> from the original on 27 December 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">27 December</span> 2017</span>. <q>a share in a pro rata distribution (as of profits) to stockholders.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Merriam+Webster&rft.atitle=Definition+of+dividend&rft_id=https%3A%2F%2Fwww.merriam-webster.com%2Fdictionary%2Fdividend&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.economicsonline.co.uk/Business_economics/Profits.html">"Profit"</a>. <i>Economics Online</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171227123044/http://www.economicsonline.co.uk/Business_economics/Profits.html">Archived</a> from the original on 27 December 2017<span class="reference-accessdate">. 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Retrieved <span class="nowrap">2020-08-31</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=PBS+NewsHour&rft.atitle=What%27s+the+Relationship+Between+Inflation+and+Interest+Rates%3F&rft.date=2009-06-23&rft_id=https%3A%2F%2Fwww.pbs.org%2Fnewshour%2Feconomy%2Fwhats-the-relationship-between&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTESchumpeter195461-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESchumpeter195461_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESchumpeter195461_21-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSchumpeter1954">Schumpeter 1954</a>, p. 61.</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text">Barbon, "A discourse of trade", 1690</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">William Letwin, "Origins of Scientific Economics: English Economic Thought, 1660–1776".</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMassie1750" class="citation book cs1">Massie, Joseph (1750). <i>Essay on the Governing Causes of the Natural Rate of Interest</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essay+on+the+Governing+Causes+of+the+Natural+Rate+of+Interest&rft.date=1750&rft.aulast=Massie&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTESchumpeter1954314-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchumpeter1954314_25-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchumpeter1954">Schumpeter 1954</a>, p. 314.</span> </li> <li id="cite_note-FOOTNOTESchumpeter1954-27"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESchumpeter1954_27-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESchumpeter1954_27-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTESchumpeter1954_27-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSchumpeter1954">Schumpeter 1954</a>.</span> </li> <li id="cite_note-FOOTNOTESchumpeter1954316-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchumpeter1954316_28-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchumpeter1954">Schumpeter 1954</a>, p. 316.</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text">"Lectures on political economy", IX.</span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text">"The rate of interest", 1907.</span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text">"Of the rate of interest", §1.</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text">§2.</span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text">Ricardo, chapter "On currency and banks"</span> </li> <li id="cite_note-Mill_§3;_Longfield-40"><span class="mw-cite-backlink">^ <a href="#cite_ref-Mill_§3;_Longfield_40-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Mill_§3;_Longfield_40-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Mill §3; Longfield.</span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text">§3.</span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text">p181.</span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><a href="/wiki/%C3%89tienne_Mantoux" title="Étienne Mantoux">Étienne Mantoux</a>, "Mr Keynes' <i>General Theory</i>", <i>Revue d'Économie Politique</i>, 1937, tr. in <a href="/wiki/Henry_Hazlitt" title="Henry Hazlitt">Henry Hazlitt</a>, "The critics of Keynesian economics", 1960.</span> </li> <li id="cite_note-FOOTNOTERothbard2001-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERothbard2001_44-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRothbard2001">Rothbard 2001</a>.</span> </li> <li id="cite_note-FOOTNOTERothbard2001371-45"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTERothbard2001371_45-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTERothbard2001371_45-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFRothbard2001">Rothbard 2001</a>, p. 371.</span> </li> <li id="cite_note-FOOTNOTERothbard2001789-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERothbard2001789_46-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRothbard2001">Rothbard 2001</a>, p. 789.</span> </li> <li id="cite_note-FOOTNOTESchumpeter1954892-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchumpeter1954892_47-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchumpeter1954">Schumpeter 1954</a>, p. 892.</span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobinson" class="citation web cs1">Robinson, George. <a rel="nofollow" class="external text" href="http://www.myjewishlearning.com/practices/Ethics/Business_Ethics/In_Practice/Business_Ethics_and_Jewish_Law/Usury_and_Moneylending/Interest-Free_Loans.shtml">"Interest-Free Loans in Judaism"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210305180632/https://www.myjewishlearning.com/article/interest-free-loans-in-judaism/">Archived</a> from the original on 5 March 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">12 March</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Interest-Free+Loans+in+Judaism&rft.aulast=Robinson&rft.aufirst=George&rft_id=http%3A%2F%2Fwww.myjewishlearning.com%2Fpractices%2FEthics%2FBusiness_Ethics%2FIn_Practice%2FBusiness_Ethics_and_Jewish_Law%2FUsury_and_Moneylending%2FInterest-Free_Loans.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.jewishvirtuallibrary.org/moneylending">"Encyclopedia Judaica: Moneylending"</a>. <i>Jewish Virtual Library</i>. 2008. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20211016152612/https://www.jewishvirtuallibrary.org/moneylending">Archived</a> from the original on October 16, 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">October 16,</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Jewish+Virtual+Library&rft.atitle=Encyclopedia+Judaica%3A+Moneylending&rft.date=2008&rft_id=http%3A%2F%2Fwww.jewishvirtuallibrary.org%2Fmoneylending&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.islamicity.com/mosque/lastserm.HTM">"IslamiCity.com - Mosque - The Prophet Muhammad's (PBUH) Last Sermon"</a>. <i>www.islamicity.com</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190129193339/http://www.islamicity.com/Mosque/lastserm.HTM">Archived</a> from the original on 2019-01-29<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-01-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.islamicity.com&rft.atitle=IslamiCity.com+-+Mosque+-+The+Prophet+Muhammad%27s+%28PBUH%29+Last+Sermon&rft_id=http%3A%2F%2Fwww.islamicity.com%2Fmosque%2Flastserm.HTM&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-Considine2016-52"><span class="mw-cite-backlink">^ <a href="#cite_ref-Considine2016_52-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Considine2016_52-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Considine2016_52-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFConsidine2016" class="citation web cs1">Considine, Kevin P. (2016). <a rel="nofollow" class="external text" href="https://www.uscatholic.org/articles/201603/it-sinful-charge-interest-loan-30591">"Is it sinful to charge interest on a loan?"</a>. <a href="/wiki/Claretians#Publications" title="Claretians">U.S. Catholic</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200729220743/https://www.uscatholic.org/articles/201603/it-sinful-charge-interest-loan-30591">Archived</a> from the original on 29 July 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">4 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Is+it+sinful+to+charge+interest+on+a+loan%3F&rft.pub=U.S.+Catholic&rft.date=2016&rft.aulast=Considine&rft.aufirst=Kevin+P.&rft_id=https%3A%2F%2Fwww.uscatholic.org%2Farticles%2F201603%2Fit-sinful-charge-interest-loan-30591&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text">Thomas Aquinas. <a href="/wiki/Summa_Theologica" title="Summa Theologica">Summa Theologica</a>, "Of Cheating, Which Is Committed in Buying and Selling". Translated by The Fathers of the English Dominican Province. pp. 1–10 <a rel="nofollow" class="external autonumber" href="http://www.saylor.org/site/wp-content/uploads/2012/06/ECON301-2.1.2-2nd.pdf">[1]</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160303221333/http://www.saylor.org/site/wp-content/uploads/2012/06/ECON301-2.1.2-2nd.pdf">Archived</a> 2016-03-03 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> Retrieved June 19, 2012</span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation conference cs1"><a rel="nofollow" class="external text" href="http://www.intratext.com/ixt/ENG0067/_PE.HTM"><i>Session Ten: On the reform of credit organisations (Montes pietatis)</i></a>. <a href="/wiki/Fifth_Lateran_Council" class="mw-redirect" title="Fifth Lateran Council">Fifth Lateran Council</a>. <a href="/wiki/Rome" title="Rome">Rome</a>, <a href="/wiki/Italy" title="Italy">Italy</a>: <a href="/wiki/Catholic_Church" title="Catholic Church">Catholic Church</a>. 4 May 1515<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-04-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Session+Ten%3A+On+the+reform+of+credit+organisations+%28Montes+pietatis%29&rft.place=Rome%2C+Italy&rft.pub=Catholic+Church&rft.date=1515&rft_id=http%3A%2F%2Fwww.intratext.com%2Fixt%2FENG0067%2F_PE.HTM&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoover1967" class="citation journal cs1">Roover, Raymond (Autumn 1967). "The Scholastics, Usury, and Foreign Exchange". <i>Business History Review</i>. <b>41</b> (3). The Business History Review, Vol. 41, No. 3: <span class="nowrap">257–</span>271. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F3112192">10.2307/3112192</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/3112192">3112192</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:154706783">154706783</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Business+History+Review&rft.atitle=The+Scholastics%2C+Usury%2C+and+Foreign+Exchange&rft.ssn=fall&rft.volume=41&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E257-%3C%2Fspan%3E271&rft.date=1967&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A154706783%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F3112192%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F3112192&rft.aulast=Roover&rft.aufirst=Raymond&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><a href="#CITEREFRothbard2001">Rothbard 2001</a>, p. 46</span> </li> <li id="cite_note-Cox1853-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cox1853_57-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCox1853" class="citation book cs1">Cox, Robert (1853). <i>Sabbath Laws and Sabbath Duties: Considered in Relation to Their Natural and Scriptural Grounds, and to the Principles of Religious Liberty</i>. Maclachlan and Stewart. p. 180.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sabbath+Laws+and+Sabbath+Duties%3A+Considered+in+Relation+to+Their+Natural+and+Scriptural+Grounds%2C+and+to+the+Principles+of+Religious+Liberty&rft.pages=180&rft.pub=Maclachlan+and+Stewart&rft.date=1853&rft.aulast=Cox&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=41" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuffie,_Darrell_and_Kenneth_J._Singleton2003" class="citation book cs1">Duffie, Darrell and Kenneth J. Singleton (2003). <i>Credit Risk: Pricing, Measurement, and Management</i>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-09046-7" title="Special:BookSources/978-0-691-09046-7"><bdi>978-0-691-09046-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Credit+Risk%3A+Pricing%2C+Measurement%2C+and+Management&rft.pub=Princeton+University+Press&rft.date=2003&rft.isbn=978-0-691-09046-7&rft.au=Duffie%2C+Darrell+and+Kenneth+J.+Singleton&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKellison,_Stephen_G.1970" class="citation book cs1">Kellison, Stephen G. (1970). <i>The Theory of Interest</i>. Richard D. Irwin, Inc. Library of Congress Catalog Card No. 79-98251.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Interest&rft.pub=Richard+D.+Irwin%2C+Inc.&rft.date=1970&rft.au=Kellison%2C+Stephen+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLando,_David2004" class="citation book cs1">Lando, David (2004). <i>Credit Risk Modeling: Theory and Applications</i>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-08929-4" title="Special:BookSources/978-0-691-08929-4"><bdi>978-0-691-08929-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Credit+Risk+Modeling%3A+Theory+and+Applications&rft.pub=Princeton+University+Press&rft.date=2004&rft.isbn=978-0-691-08929-4&rft.au=Lando%2C+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFvan_Deventer,_Donald_R._and_Kenji_Imai2003" class="citation book cs1">van Deventer, Donald R. and Kenji Imai (2003). <i>Credit Risk Models and the Basel Accords</i>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-82091-9" title="Special:BookSources/978-0-470-82091-9"><bdi>978-0-470-82091-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Credit+Risk+Models+and+the+Basel+Accords&rft.pub=John+Wiley+%26+Sons&rft.date=2003&rft.isbn=978-0-470-82091-9&rft.au=van+Deventer%2C+Donald+R.+and+Kenji+Imai&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRothbard2001" class="citation book cs1">Rothbard, Murray N. (2001). <i>Man, economy, and state : a treatise on economic principles</i> (Rev ed.). <a href="/wiki/Auburn,_Alabama" title="Auburn, Alabama">Auburn, Alabama</a>: <a href="/wiki/Mises_Institute" title="Mises Institute">Mises Institute</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0945466323" title="Special:BookSources/0945466323"><bdi>0945466323</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/47279566">47279566</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Man%2C+economy%2C+and+state+%3A+a+treatise+on+economic+principles&rft.place=Auburn%2C+Alabama&rft.edition=Rev&rft.pub=Mises+Institute&rft.date=2001&rft_id=info%3Aoclcnum%2F47279566&rft.isbn=0945466323&rft.aulast=Rothbard&rft.aufirst=Murray+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchumpeter1954" class="citation book cs1"><a href="/wiki/Joseph_Schumpeter" title="Joseph Schumpeter">Schumpeter, Joseph</a> (1954). <i>History of Economic Analysis</i>. Allen & Unwin.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=History+of+Economic+Analysis&rft.pub=Allen+%26+Unwin&rft.date=1954&rft.aulast=Schumpeter&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterest" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Interest&action=edit&section=42" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wiktionary-logo-en-v2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/interest" class="extiw" title="wiktionary:interest">interest</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://www.margill.com/en/interest-calculation-white-paper">White Paper: More than Math, The Lost Art of Interest calculation</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080913200854/http://www.moneymadeclear.fsa.gov.uk/products/mortgages/mortgages.html">Mortgages made clear</a> <a href="/wiki/Financial_Services_Authority" title="Financial Services Authority">Financial Services Authority</a> (UK)</li> <li>List of current interest rates: <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100309111447/http://www.worldinterestrates.info/">World Interest Rates</a></li> <li><a rel="nofollow" class="external text" href="https://archive.today/20120731053417/http://www.forexmotion.com/index.php/en/exchange-rates.html">Forex Motion</a></li> <li><a rel="nofollow" class="external text" href="http://www.whichwaytopay.com/world-interest-rates.asp">"Which way to pay"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110419232406/http://www.whichwaytopay.com/world-interest-rates.asp">Archived</a> 2011-04-19 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul></li> <li><a rel="nofollow" class="external text" href="http://thebanks.eu/compare-countries-by-deposit-rates">Deposit Rates in European Countries</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output 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<li><a href="/wiki/Vendor_finance" title="Vendor finance">Vendor finance</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Management</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bankruptcy" title="Bankruptcy">Bankruptcy</a></li> <li><a href="/wiki/Debt_consolidation" title="Debt consolidation">Consolidation</a></li> <li><a href="/wiki/Debt_management_plan" title="Debt management plan">Management plan</a></li> <li><a href="/wiki/Debt_relief" title="Debt relief">Relief</a> (<a href="/wiki/History_of_debt_relief" title="History of debt relief">history</a>)</li> <li><a href="/wiki/Debt_restructuring" title="Debt restructuring">Restructuring</a></li> <li><a href="/wiki/Debt_snowball_method" title="Debt snowball method">Debt snowball method</a></li> <li><a href="/wiki/Debtor-in-possession_financing" title="Debtor-in-possession financing">Debtor-in-possession (DIP) financing</a></li> <li><a href="/wiki/Loan_guarantee" title="Loan guarantee">Loan guarantee</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Debt_collection" title="Debt collection">Collection</a> <b>·</b> <a href="/wiki/Debt_evasion" title="Debt evasion">Evasion</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bad_debt" title="Bad debt">Bad debt</a></li> <li><a href="/wiki/Charge-off" title="Charge-off">Charge-off</a></li> <li><a href="/wiki/Debt_compliance" title="Debt compliance">Compliance</a></li> <li><a href="/wiki/Debt_bondage" title="Debt bondage">Debt bondage</a></li> <li><a href="/wiki/Debtors%27_prison" title="Debtors' prison">Debtors' prison</a></li> <li><a href="/wiki/Distraint" title="Distraint">Distraint</a></li> <li><a href="/wiki/Garnishment" title="Garnishment">Garnishment</a></li> <li><a href="/wiki/Phantom_debt" title="Phantom debt">Phantom debt</a></li> <li><a href="/wiki/Strategic_default" title="Strategic default">Strategic default</a></li> <li><a href="/wiki/Tax_refund_interception" title="Tax refund interception">Tax refund interception</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bond_market" title="Bond market">Markets</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Consumer_debt" title="Consumer debt">Consumer</a></li> <li><a href="/wiki/Corporate_bond" title="Corporate bond">Corporate</a></li> <li><a href="/wiki/Debt-trap_diplomacy" title="Debt-trap diplomacy">Diplomacy</a></li> <li><a href="/wiki/Government_debt" title="Government debt">Government</a> <ul><li><a href="/wiki/Government_budget_balance" title="Government budget balance">Government budget balance</a></li></ul></li> <li><a href="/wiki/Medical_debt" title="Medical debt">Medical</a></li> <li><a href="/wiki/Municipal_bond" title="Municipal bond">Municipal</a></li> <li><a href="/wiki/Venture_debt" title="Venture debt">Venture</a></li> <li><a href="/wiki/Debt_buyer_(United_States)" title="Debt buyer (United States)">Buyer</a></li> <li><a href="/wiki/Deposit_account" title="Deposit account">Deposit account</a></li> <li><a href="/wiki/Fixed_income" title="Fixed income">Fixed income</a></li> <li><a href="/wiki/Money_market" title="Money market">Money market</a></li> <li><a href="/wiki/Securitization" title="Securitization">Securitization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Economics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Consumer_leverage_ratio" title="Consumer leverage ratio">Consumer leverage ratio</a></li> <li><a href="/wiki/External_debt" title="External debt">External</a> / <a href="/wiki/Internal_debt" title="Internal debt">Internal</a> / <a href="/wiki/Odious_debt" title="Odious debt">Odious debt</a></li> <li><a href="/wiki/Debt-to-GDP_ratio" title="Debt-to-GDP ratio">Debt-to-GDP ratio</a></li> <li><a href="/wiki/List_of_countries_by_government_debt" title="List of countries by government debt">List of countries by government debt</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div> <ul><li><a href="/wiki/Default_(finance)" title="Default (finance)">Default</a></li> <li><a href="/wiki/Insolvency" title="Insolvency">Insolvency</a></li> <li><a class="mw-selflink selflink">Interest</a></li> <li><a href="/wiki/Interest_rate" title="Interest rate">Interest rate</a></li> <li><a href="/wiki/Promissory_note" title="Promissory note">Promissory note</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link 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style="width:1%"><a href="/wiki/Economics#Empirical_research" title="Economics">Empirical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Econometrics" title="Econometrics">Econometrics</a> <ul><li><a href="/wiki/Economic_statistics" title="Economic statistics">Economic statistics</a></li></ul></li> <li><a href="/wiki/Experimental_economics" title="Experimental economics">Experimental economics</a></li> <li><a href="/wiki/Economic_history" title="Economic history">Economic history</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Applied_economics" title="Applied economics">Applied</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <div class="excerpt-block"><div class="excerpt"> <ul><li><a href="/wiki/Agricultural_economics" title="Agricultural economics">Agriculture</a></li> <li><a href="/wiki/Business_economics" title="Business economics">Business</a></li> <li><a href="/wiki/Cultural_economics" title="Cultural economics">Cultural</a></li> <li><a href="/wiki/Demographic_economics" title="Demographic economics">Demographic</a></li> <li><a href="/wiki/Development_economics" title="Development economics">Development</a></li> <li><a href="/wiki/Ecological_economics" title="Ecological economics">Ecological</a></li> <li><a href="/wiki/Education_economics" title="Education economics">Education</a></li> <li><a href="/wiki/Engineering_economics" title="Engineering economics">Engineering</a></li> <li><a href="/wiki/Environmental_economics" title="Environmental economics">Environmental</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary</a></li> <li><a href="/wiki/Financial_economics" title="Financial economics">Financial</a></li> <li><a href="/wiki/Economic_geography" title="Economic geography">Geographic</a></li> <li><a href="/wiki/Happiness_economics" title="Happiness economics">Happiness</a></li> <li><a href="/wiki/Health_economics" title="Health economics">Health</a></li> <li><a href="/wiki/Economic_history" title="Economic history">History</a></li> <li><a href="/wiki/Information_economics" title="Information economics">Information</a></li> <li><a href="/wiki/Institutional_economics" title="Institutional economics">Institutions</a></li> <li><a href="/wiki/Labour_economics" title="Labour economics">Labour</a></li> <li><a href="/wiki/Law_and_economics" title="Law and economics">Law</a></li> <li><a href="/wiki/Managerial_economics" title="Managerial economics">Management</a></li> <li><a href="/wiki/Organizational_economics" title="Organizational economics">Organization</a></li> <li><a href="/wiki/Economics_of_participation" title="Economics of participation">Participation</a></li> <li><a href="/wiki/Personnel_economics" title="Personnel economics">Personnel</a></li> <li><a href="/wiki/Economic_planning" title="Economic planning">Planning</a></li> <li><a href="/wiki/Economic_policy" title="Economic policy">Policy</a></li> <li><a href="/wiki/Public_economics" title="Public economics">Public sector</a></li> <li><a href="/wiki/Public_choice" title="Public choice">Public choice</a></li> <li><a href="/wiki/Social_choice" class="mw-redirect" title="Social choice">Social choice</a></li> <li><a href="/wiki/Regional_economics" title="Regional economics">Regional</a></li> <li><a href="/wiki/Natural_resource_economics" title="Natural resource economics">Resources</a></li> <li><a href="/wiki/Rural_economics" title="Rural economics">Rural</a></li> <li><a href="/wiki/Service_economy" title="Service economy">Service</a></li> <li><a href="/wiki/Transport_economics" title="Transport economics">Transport</a></li> <li><a href="/wiki/Urban_economics" title="Urban economics">Urban</a></li> <li><a href="/wiki/Welfare_economics" title="Welfare economics">Welfare</a></li></ul></div></div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Schools_of_economic_thought" title="Schools of economic thought">Schools</a><br />(<a href="/wiki/History_of_economic_thought" title="History of economic thought">history</a>)<br /></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Attention_economy" title="Attention economy">Attention</a></li> <li><a href="/wiki/Mainstream_economics" title="Mainstream economics">Mainstream</a></li> <li><a href="/wiki/Heterodox_economics" title="Heterodox economics">Heterodox</a></li> <li><a href="/wiki/American_School_(economics)" title="American School (economics)">American (National)</a></li> <li><a href="/wiki/Ancient_economic_thought" title="Ancient economic thought">Ancient thought</a></li> <li><a href="/wiki/Anarchist_economics" class="mw-redirect" title="Anarchist economics">Anarchist</a> <ul><li><a href="/wiki/Mutualism_(economic_theory)" title="Mutualism (economic theory)">Mutualism</a></li></ul></li> <li><a href="/wiki/Austrian_School" class="mw-redirect" title="Austrian School">Austrian</a></li> <li><a href="/wiki/Behavioral_economics" title="Behavioral economics">Behavioral</a></li> <li><a href="/wiki/Buddhist_economics" title="Buddhist economics">Buddhist</a></li> <li><a href="/wiki/Chartalism" title="Chartalism">Chartalism</a> <ul><li><a href="/wiki/Modern_monetary_theory" title="Modern monetary theory">Modern monetary theory</a></li></ul></li> <li><a href="/wiki/Chicago_school_of_economics" title="Chicago school of economics">Chicago</a></li> <li><a href="/wiki/Classical_economics" title="Classical economics">Classical</a></li> <li><a href="/wiki/Critique_of_political_economy" title="Critique of political economy">Critique of political economy</a></li> <li><a href="/wiki/Economic_democracy" title="Economic democracy">Democratic</a></li> <li><a href="/wiki/Disequilibrium_macroeconomics" title="Disequilibrium macroeconomics">Disequilibrium</a></li> <li><a href="/wiki/Ecological_economics" title="Ecological economics">Ecological</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary</a></li> <li><a href="/wiki/Feminist_economics" title="Feminist economics">Feminist</a></li> <li><a href="/wiki/Georgism" title="Georgism">Georgism</a></li> <li><a href="/wiki/Happiness_economics" title="Happiness economics">Happiness</a></li> <li><a href="/wiki/Historical_school_of_economics" title="Historical school of economics">Historical</a></li> <li><a href="/wiki/Humanistic_economics" title="Humanistic economics">Humanistic</a></li> <li><a href="/wiki/Institutional_economics" title="Institutional economics">Institutional</a></li> <li><a href="/wiki/Keynesian_economics" title="Keynesian economics">Keynesian</a> <ul><li><a href="/wiki/Neo-Keynesian_economics" class="mw-redirect" title="Neo-Keynesian economics">Neo-</a> (<a href="/wiki/Neoclassical_synthesis" title="Neoclassical synthesis">neoclassical–Keynesian synthesis</a>)</li> <li><a href="/wiki/New_Keynesian_economics" title="New Keynesian economics">New</a></li> <li><a href="/wiki/Post-Keynesian_economics" title="Post-Keynesian economics">Post-</a> <ul><li><a href="/wiki/Monetary_circuit_theory" title="Monetary circuit theory">Circuitism</a></li></ul></li></ul></li> <li><a href="/wiki/Malthusianism" title="Malthusianism">Malthusianism</a></li> <li><a href="/wiki/Marginalism" title="Marginalism">Marginalism</a></li> <li><a href="/wiki/Marxian_economics" title="Marxian economics">Marxian</a> <ul><li><a href="/wiki/Neo-Marxian_economics" class="mw-redirect" title="Neo-Marxian economics">Neo-</a></li></ul></li> <li><a href="/wiki/Mercantilism" title="Mercantilism">Mercantilism</a></li> <li><a href="/wiki/Mixed_economy" title="Mixed economy">Mixed</a></li> <li><a href="/wiki/Neoclassical_economics" title="Neoclassical economics">Neoclassical</a> <ul><li><a href="/wiki/Lausanne_School" title="Lausanne School">Lausanne</a></li></ul></li> <li><a href="/wiki/New_classical_macroeconomics" title="New classical macroeconomics">New classical</a> <ul><li><a href="/wiki/Real_business-cycle_theory" title="Real business-cycle theory">Real business-cycle theory</a></li></ul></li> <li><a href="/wiki/New_institutional_economics" title="New institutional economics">New institutional</a></li> <li><a href="/wiki/Physiocracy" title="Physiocracy">Physiocracy</a></li> <li><a href="/wiki/Socialist_economics" title="Socialist economics">Socialist</a></li> <li><a href="/wiki/Stockholm_School_(economics)" title="Stockholm School (economics)">Stockholm</a></li> <li><a href="/wiki/Supply-side_economics" title="Supply-side economics">Supply-side</a></li> <li><a href="/wiki/Thermoeconomics" title="Thermoeconomics">Thermo</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Economist" title="Economist">Economists</a><br /></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bernard_de_Mandeville" class="mw-redirect" title="Bernard de Mandeville">de Mandeville</a></li> <li><a href="/wiki/Fran%C3%A7ois_Quesnay" title="François Quesnay">Quesnay</a></li> <li><a href="/wiki/Adam_Smith" title="Adam Smith">Smith</a></li> <li><a href="/wiki/Thomas_Robert_Malthus" title="Thomas Robert Malthus">Malthus</a></li> <li><a href="/wiki/Jean-Baptiste_Say" title="Jean-Baptiste Say">Say</a></li> <li><a href="/wiki/David_Ricardo" title="David Ricardo">Ricardo</a></li> <li><a href="/wiki/Johann_Heinrich_von_Th%C3%BCnen" title="Johann Heinrich von Thünen">von Thünen</a></li> <li><a href="/wiki/Friedrich_List" title="Friedrich List">List</a></li> <li><a href="/wiki/Fr%C3%A9d%C3%A9ric_Bastiat" title="Frédéric Bastiat">Bastiat</a></li> <li><a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Cournot</a></li> <li><a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">Mill</a></li> <li><a href="/wiki/Hermann_Heinrich_Gossen" title="Hermann Heinrich Gossen">Gossen</a></li> <li><a href="/wiki/Karl_Marx" title="Karl Marx">Marx</a></li> <li><a href="/wiki/L%C3%A9on_Walras" title="Léon Walras">Walras</a></li> <li><a href="/wiki/William_Stanley_Jevons" title="William Stanley Jevons">Jevons</a></li> <li><a href="/wiki/Henry_George" title="Henry George">George</a></li> <li><a href="/wiki/Carl_Menger" title="Carl Menger">Menger</a></li> <li><a href="/wiki/Alfred_Marshall" title="Alfred Marshall">Marshall</a></li> <li><a href="/wiki/Francis_Ysidro_Edgeworth" title="Francis Ysidro Edgeworth">Edgeworth</a></li> <li><a href="/wiki/John_Bates_Clark" title="John Bates Clark">Clark</a></li> <li><a href="/wiki/Vilfredo_Pareto" title="Vilfredo Pareto">Pareto</a></li> <li><a href="/wiki/Eugen_von_B%C3%B6hm-Bawerk" title="Eugen von Böhm-Bawerk">von Böhm-Bawerk</a></li> <li><a href="/wiki/Friedrich_von_Wieser" title="Friedrich von Wieser">von Wieser</a></li> <li><a href="/wiki/Thorstein_Veblen" title="Thorstein Veblen">Veblen</a></li> <li><a href="/wiki/Irving_Fisher" title="Irving Fisher">Fisher</a></li> <li><a href="/wiki/Arthur_Cecil_Pigou" title="Arthur Cecil Pigou">Pigou</a></li> <li><a href="/wiki/Eli_Heckscher" title="Eli Heckscher">Heckscher</a></li> <li><a href="/wiki/Ludwig_von_Mises" title="Ludwig von Mises">von Mises</a></li> <li><a href="/wiki/Joseph_Schumpeter" title="Joseph Schumpeter">Schumpeter</a></li> <li><a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">Keynes</a></li> <li><a href="/wiki/Frank_Knight" title="Frank Knight">Knight</a></li> <li><a href="/wiki/Karl_Polanyi" title="Karl Polanyi">Polanyi</a></li> <li><a href="/wiki/Ragnar_Frisch" title="Ragnar Frisch">Frisch</a></li> <li><a href="/wiki/Piero_Sraffa" title="Piero Sraffa">Sraffa</a></li> <li><a href="/wiki/Gunnar_Myrdal" title="Gunnar Myrdal">Myrdal</a></li> <li><a href="/wiki/Friedrich_Hayek" title="Friedrich Hayek">Hayek</a></li> <li><a href="/wiki/Micha%C5%82_Kalecki" title="Michał Kalecki">Kalecki</a></li> <li><a href="/wiki/Wilhelm_R%C3%B6pke" title="Wilhelm Röpke">Röpke</a></li> <li><a href="/wiki/Simon_Kuznets" title="Simon Kuznets">Kuznets</a></li> <li><a href="/wiki/Jan_Tinbergen" title="Jan Tinbergen">Tinbergen</a></li> <li><a href="/wiki/Joan_Robinson" title="Joan Robinson">Robinson</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li> <li><a href="/wiki/John_Hicks" title="John Hicks">Hicks</a></li> <li><a href="/wiki/Oskar_R._Lange" title="Oskar R. Lange">Lange</a></li> <li><a href="/wiki/Wassily_Leontief" title="Wassily Leontief">Leontief</a></li> <li><a href="/wiki/John_Kenneth_Galbraith" title="John Kenneth Galbraith">Galbraith</a></li> <li><a href="/wiki/Tjalling_Koopmans" title="Tjalling Koopmans">Koopmans</a></li> <li><a href="/wiki/E._F._Schumacher" title="E. F. Schumacher">Schumacher</a></li> <li><a href="/wiki/Milton_Friedman" title="Milton Friedman">Friedman</a></li> <li><a href="/wiki/Paul_Samuelson" title="Paul Samuelson">Samuelson</a></li> <li><a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Simon</a></li> <li><a href="/wiki/James_M._Buchanan" title="James M. Buchanan">Buchanan</a></li> <li><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Arrow</a></li> <li><a href="/wiki/William_Baumol" title="William Baumol">Baumol</a></li> <li><a href="/wiki/Robert_Solow" title="Robert Solow">Solow</a></li> <li><a href="/wiki/Murray_Rothbard" title="Murray Rothbard">Rothbard</a></li> <li><a href="/wiki/Alan_Greenspan" title="Alan Greenspan">Greenspan</a></li> <li><a href="/wiki/Thomas_Sowell" title="Thomas Sowell">Sowell</a></li> <li><a href="/wiki/Gary_Becker" title="Gary Becker">Becker</a></li> <li><a href="/wiki/Elinor_Ostrom" title="Elinor Ostrom">Ostrom</a></li> <li><a href="/wiki/Amartya_Sen" title="Amartya Sen">Sen</a></li> <li><a href="/wiki/Robert_Lucas_Jr." title="Robert Lucas Jr.">Lucas</a></li> <li><a href="/wiki/Joseph_Stiglitz" title="Joseph Stiglitz">Stiglitz</a></li> <li><a href="/wiki/Richard_Thaler" title="Richard Thaler">Thaler</a></li> <li><a href="/wiki/Hans-Hermann_Hoppe" title="Hans-Hermann Hoppe">Hoppe</a></li> <li><a href="/wiki/Paul_Krugman" title="Paul Krugman">Krugman</a></li> <li><a href="/wiki/Thomas_Piketty" title="Thomas Piketty">Piketty</a></li> <li><i><a href="/wiki/Category:Economists" title="Category:Economists">more</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Economics_lists" title="Category:Economics lists">Lists</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glossary_of_economics" title="Glossary of economics">Glossary</a></li> <li><a href="/wiki/List_of_economists" title="List of economists">Economists</a></li> <li><a href="/wiki/List_of_important_publications_in_economics" title="List of important publications in economics">Publications</a> (<a href="/wiki/List_of_economics_journals" title="List of economics journals">journals</a>)</li> <li><a href="/wiki/Schools_of_economic_thought" title="Schools of economic 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//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4067845-3">Germany</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Interest rates"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85067247">United States</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Intérêt (économie politique)"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11974115k">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Intérêt (économie politique)"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11974115k">BnF data</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00569550">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="úroky"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph135596&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007555621505171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://hls-dhs-dss.ch/fr/articles/013923">Historical Dictionary of Switzerland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalog.archives.gov/id/10637866">NARA</a></span></li></ul></div></td></tr></tbody></table></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Interest&oldid=1263831953">https://en.wikipedia.org/w/index.php?title=Interest&oldid=1263831953</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Interest" 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