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id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Início</div> </a> </li> <li id="toc-História" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#História"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>História</span> </div> </a> <ul id="toc-História-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Taxa_básica_de_juros" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Taxa_básica_de_juros"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Taxa básica de juros</span> </div> </a> <ul id="toc-Taxa_básica_de_juros-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Taxa_preferencial_de_juros" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Taxa_preferencial_de_juros"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Taxa preferencial de juros</span> </div> </a> <ul id="toc-Taxa_preferencial_de_juros-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Juros_simples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Juros_simples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Juros simples</span> </div> </a> <ul id="toc-Juros_simples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Juros_compostos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Juros_compostos"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Juros compostos</span> </div> </a> <button aria-controls="toc-Juros_compostos-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>Alternar a subsecção Juros compostos</span> </button> <ul id="toc-Juros_compostos-sublist" class="vector-toc-list"> <li id="toc-Rendas_certas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rendas_certas"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Rendas certas</span> </div> </a> <ul id="toc-Rendas_certas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Taxa_de_juros_continuamente_composta" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Taxa_de_juros_continuamente_composta"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Taxa de juros continuamente composta</span> </div> </a> <ul id="toc-Taxa_de_juros_continuamente_composta-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Juros_simples_vs._compostos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Juros_simples_vs._compostos"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Juros simples vs. compostos</span> </div> </a> <ul id="toc-Juros_simples_vs._compostos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Taxa_nominal_vs._taxa_real" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Taxa_nominal_vs._taxa_real"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Taxa nominal vs. taxa real</span> </div> </a> <ul id="toc-Taxa_nominal_vs._taxa_real-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Taxa_de_juros_natural" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Taxa_de_juros_natural"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Taxa de juros natural</span> </div> </a> <ul id="toc-Taxa_de_juros_natural-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tabela_Financeira" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tabela_Financeira"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Tabela Financeira</span> </div> </a> <ul id="toc-Tabela_Financeira-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ligações_externas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ligações_externas"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Ligações externas</span> </div> </a> <ul id="toc-Ligações_externas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notas_e_referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notas_e_referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Notas e referências</span> </div> </a> <button aria-controls="toc-Notas_e_referências-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>Alternar a subsecção Notas e referências</span> </button> <ul id="toc-Notas_e_referências-sublist" class="vector-toc-list"> <li id="toc-Notas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notas"> <div class="vector-toc-text"> <span class="vector-toc-numb">12.1</span> <span>Notas</span> </div> </a> <ul id="toc-Notas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">12.2</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-sublist" class="vector-toc-list"> </ul> </li> </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="Conteúdo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="Alternar o índice" > <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">Alternar o índice</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">Juro</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="Ir para um artigo noutra língua. Disponível em 72 línguas" > <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-72" 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">72 línguas</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 — africanês" lang="af" hreflang="af" data-title="Rente" data-language-autonym="Afrikaans" data-language-local-name="africanês" 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 — alemão suíço" lang="gsw" hreflang="gsw" data-title="Zins" data-language-autonym="Alemannisch" data-language-local-name="alemão suíço" 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 — amárico" lang="am" hreflang="am" data-title="ዎለድ" data-language-autonym="አማርኛ" data-language-local-name="amárico" 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 — árabe" lang="ar" hreflang="ar" data-title="فائدة" data-language-autonym="العربية" data-language-local-name="árabe" 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) — aramaico" lang="arc" hreflang="arc" data-title="ܗܢܝܢܐ (ܡܡܫܚܘܬܐ)" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="aramaico" 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 — asturiano" lang="ast" hreflang="ast" data-title="Interés" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</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-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/R%C3%A8nte" title="Rènte — Betawi" lang="bew" hreflang="bew" data-title="Rènte" data-language-autonym="Betawi" data-language-local-name="Betawi" class="interlanguage-link-target"><span>Betawi</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 — búlgaro" lang="bg" hreflang="bg" data-title="Лихва" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</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 — bengalês" lang="bn" hreflang="bn" data-title="সুদ" data-language-autonym="বাংলা" data-language-local-name="bengalês" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kamata" title="Kamata — bósnio" lang="bs" hreflang="bs" data-title="Kamata" data-language-autonym="Bosanski" data-language-local-name="bósnio" 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 — catalão" lang="ca" hreflang="ca" data-title="Interès" data-language-autonym="Català" data-language-local-name="catalão" 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 — checo" lang="cs" hreflang="cs" data-title="Úrok" data-language-autonym="Čeština" data-language-local-name="checo" 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 — dinamarquês" lang="da" hreflang="da" data-title="Rente" data-language-autonym="Dansk" data-language-local-name="dinamarquês" 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 — alemão" lang="de" hreflang="de" data-title="Zins" data-language-autonym="Deutsch" data-language-local-name="alemão" class="interlanguage-link-target"><span>Deutsch</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 — grego" lang="el" hreflang="el" data-title="Τόκος" data-language-autonym="Ελληνικά" data-language-local-name="grego" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Interest" title="Interest — inglês" lang="en" hreflang="en" data-title="Interest" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Inter%C3%A9s" title="Interés — espanhol" lang="es" hreflang="es" data-title="Interés" data-language-autonym="Español" data-language-local-name="espanhol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Intress" title="Intress — estónio" lang="et" hreflang="et" data-title="Intress" data-language-autonym="Eesti" data-language-local-name="estónio" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Interes" title="Interes — basco" lang="eu" hreflang="eu" data-title="Interes" data-language-autonym="Euskara" data-language-local-name="basco" 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 — persa" lang="fa" hreflang="fa" data-title="بهره" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Korko" title="Korko — finlandês" lang="fi" hreflang="fi" data-title="Korko" data-language-autonym="Suomi" data-language-local-name="finlandês" class="interlanguage-link-target"><span>Suomi</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) — francês" lang="fr" hreflang="fr" data-title="Intérêt (finance)" data-language-autonym="Français" data-language-local-name="francês" 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 — galego" lang="gl" hreflang="gl" data-title="Xuro" data-language-autonym="Galego" data-language-local-name="galego" class="interlanguage-link-target"><span>Galego</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 — hebraico" lang="he" hreflang="he" data-title="ריבית" data-language-autonym="עברית" data-language-local-name="hebraico" class="interlanguage-link-target"><span>עברית</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 — croata" lang="hr" hreflang="hr" data-title="Kamata" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kamat" title="Kamat — húngaro" lang="hu" hreflang="hu" data-title="Kamat" data-language-autonym="Magyar" data-language-local-name="húngaro" class="interlanguage-link-target"><span>Magyar</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 — arménio" lang="hy" hreflang="hy" data-title="Տոկոսագումար" data-language-autonym="Հայերեն" data-language-local-name="arménio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Suku_bunga" title="Suku bunga — indonésio" lang="id" hreflang="id" data-title="Suku bunga" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Vextir" title="Vextir — islandês" lang="is" hreflang="is" data-title="Vextir" data-language-autonym="Íslenska" data-language-local-name="islandês" 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 — italiano" lang="it" hreflang="it" data-title="Interesse finanziario" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</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 — japonês" lang="ja" hreflang="ja" data-title="利子" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</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 — canarim" lang="kn" hreflang="kn" data-title="ಬಡ್ಡಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="canarim" class="interlanguage-link-target"><span>ಕನ್ನಡ</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 — coreano" lang="ko" hreflang="ko" data-title="이자" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Usura" title="Usura — latim" lang="la" hreflang="la" data-title="Usura" data-language-autonym="Latina" data-language-local-name="latim" class="interlanguage-link-target"><span>Latina</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 — laosiano" lang="lo" hreflang="lo" data-title="ດອກເບ້ຍ" data-language-autonym="ລາວ" data-language-local-name="laosiano" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Pal%C5%ABkanos" title="Palūkanos — lituano" lang="lt" hreflang="lt" data-title="Palūkanos" data-language-autonym="Lietuvių" data-language-local-name="lituano" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Procenti" title="Procenti — letão" lang="lv" hreflang="lv" data-title="Procenti" data-language-autonym="Latviešu" data-language-local-name="letão" class="interlanguage-link-target"><span>Latviešu</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 — macedónio" lang="mk" hreflang="mk" data-title="Камата" data-language-autonym="Македонски" data-language-local-name="macedónio" 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 — marata" lang="mr" hreflang="mr" data-title="व्याज" data-language-autonym="मराठी" data-language-local-name="marata" 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 — malaio" lang="ms" hreflang="ms" data-title="Faedah" data-language-autonym="Bahasa Melayu" data-language-local-name="malaio" class="interlanguage-link-target"><span>Bahasa Melayu</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 — nepalês" lang="ne" hreflang="ne" data-title="साधारण व्याज" data-language-autonym="नेपाली" data-language-local-name="nepalês" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rente" title="Rente — neerlandês" lang="nl" hreflang="nl" data-title="Rente" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Rente" title="Rente — norueguês bokmål" lang="nb" hreflang="nb" data-title="Rente" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" class="interlanguage-link-target"><span>Norsk bokmål</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 — panjabi" lang="pa" hreflang="pa" data-title="ਵਿਆਜ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" 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 — polaco" lang="pl" hreflang="pl" data-title="Odsetki" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</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 — romeno" lang="ro" hreflang="ro" data-title="Dobândă" data-language-autonym="Română" data-language-local-name="romeno" 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 — russo" lang="ru" hreflang="ru" data-title="Процентный доход" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</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 — sindi" lang="sd" hreflang="sd" data-title="وياج" data-language-autonym="سنڌي" data-language-local-name="sindi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kamata" title="Kamata — servo-croata" lang="sh" hreflang="sh" data-title="Kamata" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="servo-croata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C3%9Arok" title="Úrok — eslovaco" lang="sk" hreflang="sk" data-title="Úrok" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" 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 — esloveno" lang="sl" hreflang="sl" data-title="Obresti" data-language-autonym="Slovenščina" data-language-local-name="esloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Interesi" title="Interesi — albanês" lang="sq" hreflang="sq" data-title="Interesi" data-language-autonym="Shqip" data-language-local-name="albanês" class="interlanguage-link-target"><span>Shqip</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 — sérvio" lang="sr" hreflang="sr" data-title="Камата" data-language-autonym="Српски / srpski" data-language-local-name="sérvio" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/R%C3%A4nta" title="Ränta — sueco" lang="sv" hreflang="sv" data-title="Ränta" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</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 — tâmil" lang="ta" hreflang="ta" data-title="வட்டி" data-language-autonym="தமிழ்" data-language-local-name="tâmil" 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 — tailandês" lang="th" hreflang="th" data-title="ดอกเบี้ย" data-language-autonym="ไทย" data-language-local-name="tailandês" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/G%C3%B6terim" title="Göterim — turcomano" lang="tk" hreflang="tk" data-title="Göterim" data-language-autonym="Türkmençe" data-language-local-name="turcomano" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Patubo" title="Patubo — tagalo" lang="tl" hreflang="tl" data-title="Patubo" data-language-autonym="Tagalog" data-language-local-name="tagalo" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Faiz" title="Faiz — turco" lang="tr" hreflang="tr" data-title="Faiz" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</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) — ucraniano" lang="uk" hreflang="uk" data-title="Відсоток (фінанси)" data-language-autonym="Українська" data-language-local-name="ucraniano" 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 — iídiche" lang="yi" hreflang="yi" data-title="ריבית" data-language-autonym="ייִדיש" data-language-local-name="iídiche" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%88%A9%E6%81%AF" title="利息 — chinês" lang="zh" hreflang="zh" data-title="利息" data-language-autonym="中文" data-language-local-name="chinês" class="interlanguage-link-target"><span>中文</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 — cantonês" lang="yue" hreflang="yue" data-title="利息" data-language-autonym="粵語" data-language-local-name="cantonês" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q170924#sitelinks-wikipedia" title="Editar hiperligações interlínguas" class="wbc-editpage">Editar hiperligações</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espaços nominais"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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as páginas que contêm hiperligações para esta [j]" accesskey="j"><span>Páginas afluentes</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:Altera%C3%A7%C3%B5es_relacionadas/Juro" rel="nofollow" title="Mudanças recentes nas páginas para as quais esta contém hiperligações [k]" accesskey="k"><span>Alterações relacionadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:Carregar_ficheiro" title="Carregar ficheiros [u]" accesskey="u"><span>Carregar ficheiro</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginas_especiais" title="Lista de páginas especiais [q]" accesskey="q"><span>Páginas especiais</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Juro&oldid=66931997" title="Hiperligação permanente para esta revisão desta página"><span>Hiperligação permanente</span></a></li><li id="t-info" class="mw-list-item"><a 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.tmbox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-night .mw-parser-output .tmbox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-os .mw-parser-output .tmbox-speedy{background-color:#310402}}body.skin--responsive .mw-parser-output table.tmbox img{max-width:none!important}</style><table class="box-Mais_notas plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Ficheiro:Question_book-new.svg" class="mw-file-description"><img alt="Esta página cita fontes, mas não cobrem todo o conteúdo" src="//upload.wikimedia.org/wikipedia/commons/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/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/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">Esta página <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes" title="Wikipédia:Livro de estilo/Cite as fontes">cita fontes</a>, mas que <b><a href="/wiki/Wikip%C3%A9dia:V" class="mw-redirect" title="Wikipédia:V">não cobrem</a> todo o conteúdo</b>.<span class="hide-when-compact"> Ajude a <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Refer%C3%AAncias_e_notas_de_rodap%C3%A9" title="Wikipédia:Livro de estilo/Referências e notas de rodapé">inserir referências</a> (<small><i>Encontre fontes:</i> <span class="plainlinks"><a rel="nofollow" class="external text" href="https://wikipedialibrary.wmflabs.org/">ABW</a>  •  <a rel="nofollow" class="external text" href="https://www.periodicos.capes.gov.br">CAPES</a>  •  <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&as_epq=Juro">Google</a> (<a rel="nofollow" class="external text" href="https://www.google.com/search?hl=pt&tbm=nws&q=Juro&oq=Juro">N</a> • <a rel="nofollow" class="external text" href="http://books.google.com/books?&as_brr=0&as_epq=Juro">L</a> • <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?hl=pt&q=Juro">A</a>)</span></small>).</span> <small class="date-container"><i>(<span class="date">Abril de 2017</span>)</i></small></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro: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/220px-Federal_Funds_Rate_1954_thru_2009_effective.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Federal_Funds_Rate_1954_thru_2009_effective.svg/330px-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/440px-Federal_Funds_Rate_1954_thru_2009_effective.svg.png 2x" data-file-width="640" data-file-height="480" /></a><figcaption>A taxa efetiva de fundos federais nos Estados Unidos registrada ao longo de mais de meio século</figcaption></figure> <p><b>Juro</b> é a remuneração cobrada pelo <a href="/wiki/Empr%C3%A9stimo" title="Empréstimo">empréstimo</a> de <a href="/wiki/Dinheiro" title="Dinheiro">dinheiro</a> (ou outro item). É expresso como um <a href="/wiki/Percentagem" class="mw-redirect" title="Percentagem">percentual</a> sobre o valor emprestado (<a href="/wiki/Taxa" title="Taxa">taxa</a> de juro) e pode ser calculado de duas formas: juros simples ou juros compostos. </p><p>O juro pode ser compreendido como uma espécie de "aluguel" de dinheiro. A taxa é uma compensação paga pelo tomador do empréstimo para ter o direito de usar o dinheiro até o dia do pagamento. O credor, por outro lado, recebe uma compensação por não poder usar esse dinheiro até o dia do pagamento e por correr o risco de não receber o dinheiro de volta (risco de inadimplência). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="História"><span id="Hist.C3.B3ria"></span>História</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=1" title="Editar secção: História" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=1" title="Editar código-fonte da secção: História"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Documentos históricos redigidos pela civilização <a href="/wiki/Sum%C3%A9ria" title="Suméria">suméria</a>, por volta de 3000 a.C., revelam que o mundo antigo desenvolveu um sistema formalizado de <a href="/wiki/Cr%C3%A9dito" title="Crédito">crédito</a> baseado em dois principais produtos, o grão e a <a href="/wiki/Prata" title="Prata">prata</a>. Antes de existirem as <a href="/wiki/Moeda" title="Moeda">moedas</a>, o empréstimo de metal era feito baseado em seu peso. Arqueólogos descobriram pedaços de metais que foram usados no comércio nas civilizações de <a href="/wiki/Troia" title="Troia">Troia</a>, <a href="/wiki/Babil%C3%B4nia" class="mw-redirect" title="Babilônia">Babilônia</a>, <a href="/wiki/Egito" title="Egito">Egito</a> e <a href="/wiki/P%C3%A9rsia" title="Pérsia">Pérsia</a>. Antes do empréstimo em dinheiro ser desenvolvido, o empréstimo de <a href="/wiki/Cereal" title="Cereal">cereal</a> e de prata facilitava a dinâmica do comércio. </p><p>Na <a href="/wiki/Rep%C3%BAblica_Romana" title="República Romana">República Romana</a>, no ano do consulado de <a href="/wiki/Marco_F%C3%A1bio_Ambusto_(c%C3%B4nsul_em_360_a.C.)" title="Marco Fábio Ambusto (cônsul em 360 a.C.)">Marco Fábio Ambusto</a> (pela terceira vez) e ou <a href="/wiki/Tito_Qu%C3%ADncio_Peno_Capitolino_Crispino" class="mw-redirect" title="Tito Quíncio Peno Capitolino Crispino">Tito Quíncio</a> ou <a href="/wiki/Marco_Pop%C3%ADlio_Lenas_(c%C3%B4nsul_em_359_a.C.)" title="Marco Popílio Lenas (cônsul em 359 a.C.)">Marco Popílio</a>,<sup id="cite_ref-livio.7.18_1-0" class="reference"><a href="#cite_note-livio.7.18-1"><span>[</span>1<span>]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span>[</span>Nota 1<span>]</span></a></sup> a taxa de juros foi reduzida para 8 1/3 <a href="/wiki/Por_cento" class="mw-redirect" title="Por cento">por cento</a>, mesmo assim, os plebeus continuavam sem conseguir pagar suas dívidas.<sup id="cite_ref-livio.7.19_3-0" class="reference"><a href="#cite_note-livio.7.19-3"><span>[</span>2<span>]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Taxa_básica_de_juros"><span id="Taxa_b.C3.A1sica_de_juros"></span>Taxa básica de juros</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=2" title="Editar secção: Taxa básica de juros" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=2" title="Editar código-fonte da secção: Taxa básica de juros"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A taxa básica de juros de um país corresponde à remuneração que o <a href="/wiki/Tesouro_nacional" title="Tesouro nacional">tesouro nacional</a> paga aos seus credores, funcionando como taxa de referência para todos os contratos de crédito dessa <a href="/wiki/Economia" title="Economia">economia</a>. </p><p>No Brasil, a taxa de juros básica é a <a href="/wiki/Taxa_Selic" title="Taxa Selic">taxa Selic</a>, que é calculada como a "taxa média ajustada dos financiamentos diários apurados no Sistema Especial de Liquidação e de Custódia (Selic) para títulos federais".<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span>[</span>3<span>]</span></a></sup> Como ferramenta de <a href="/wiki/Pol%C3%ADtica_monet%C3%A1ria" title="Política monetária">política monetária</a>, o governo brasileiro interfere na taxa de juros da economia através do <a href="/wiki/Comit%C3%AA_de_Pol%C3%ADtica_Monet%C3%A1ria" title="Comitê de Política Monetária">Comitê de Política Monetária</a> (COPOM), que tem o papel de definir a meta da taxa Selic<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span>[</span>Nota 2<span>]</span></a></sup> com o objetivo de manter a <a href="/wiki/Infla%C3%A7%C3%A3o" title="Inflação">inflação</a> dentro da meta estabelecida pelo <a href="/wiki/Conselho_Monet%C3%A1rio_Nacional" title="Conselho Monetário Nacional">Conselho Monetário Nacional</a> (CMN).<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span>[</span>4<span>]</span></a></sup> </p><p>De forma análoga, nos <a href="/wiki/Estados_Unidos" title="Estados Unidos">Estados Unidos</a>, a taxa básica de juros é fixada pelo <i><a href="https://en.wikipedia.org/wiki/Federal_Open_Market_Committee" class="extiw" title="en:Federal Open Market Committee">Federal Open Market Committee</a></i> (Comitê Federal de <a href="/wiki/Mercado" title="Mercado">Mercado</a> Aberto) do <i><a href="/wiki/Federal_Reserve_System" class="mw-redirect" title="Federal Reserve System">Fed</a></i> (o sistema de <a href="/wiki/Banco_central" title="Banco central">bancos centrais</a> dos <a href="/wiki/EUA" class="mw-redirect" title="EUA">EUA</a>), com base na remuneração dos <i>Federal Funds</i>, que são os <a href="/wiki/T%C3%ADtulos" class="mw-redirect mw-disambig" title="Títulos">títulos</a> que lastreiam empréstimos interbancários <i><a href="/wiki/Overnight" class="mw-redirect" title="Overnight">overnight</a></i> e que têm como finalidade a manutenção do nível das reservas bancárias depositadas no banco central. </p><p>Ao reduzir a taxa básica de juros da economia, as empresas tendem a preferir investir os recursos em aumento de produção, contratação de pessoal, pesquisa etc porque o retorno do investimento pode ser maior do que o que é pago pelo governo e/ou porque tomar empréstimos fica mais barato. Ao mesmo tempo, as famílias também conseguem crédito mais barato para consumir através de parcelamento mais barato. Esse efeito causa aumento da atividade econômica, riqueza e emprego do país através do aumenta da demanda e oferta de produtos e serviços. Por outro lado, também causa, como efeito colateral, o aumento de preços, ou inflação. </p><p>Ao aumentar a taxa de juros, os consumidores tendem a diminuir o consumo devido ao alto <a href="/wiki/Pre%C3%A7o" title="Preço">preço</a> dos empréstimos e as empresas tendem a emprestar para o governo, ao invés de financiarem suas operações. Nesse caso, o efeito colateral é a queda (ou manutenção) dos preços. </p> <div class="mw-heading mw-heading2"><h2 id="Taxa_preferencial_de_juros">Taxa preferencial de juros</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=3" title="Editar secção: Taxa preferencial de juros" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=3" title="Editar código-fonte da secção: Taxa preferencial de juros"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A taxa preferencial de juros (em inglês, <i>prime rate</i>) é a taxa de juros bancária cobrada dos clientes preferenciais, isto é, aqueles que têm as melhores avaliações de crédito. É determinada pelas condições de mercado (custos bancários, expectativas inflacionárias, remuneração de outros ativos, etc.). Em geral, a taxa preferencial de juros adotada por grandes <a href="/wiki/Banco" title="Banco">bancos</a> tende a ser a referência para todo o setor bancário e normalmente será a menor taxa do mercado.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span>[</span>5<span>]</span></a></sup> </p><p>Geralmente a taxa preferencial supera em alguns pontos a taxa básica. Mas, na Inglaterra e na <a href="/wiki/Eurozona" class="mw-redirect" title="Eurozona">Eurozona</a>, a taxa preferencial de juros corresponde exatamente à taxa vigente no mercado interbancário, e funciona como taxa básica de juros. É o caso da <a href="/wiki/London_Interbank_Offered_Rate" title="London Interbank Offered Rate">Libor</a> e da <a href="/wiki/Euribor" title="Euribor">Euribor</a>. A Libor (<i>London Interbank Offered Rate</i>) é a taxa preferencial de juros que remunera grandes empréstimos entre os bancos internacionais operantes no mercado londrino e é também utilizada como base da remuneração de empréstimos em <a href="/wiki/D%C3%B3lar" title="Dólar">dólar</a> a empresas e instituições governamentais. Euribor (<i>Euro Interbank Offered Rate</i>) é a taxa de juros usada nas operações interbancárias, feitas em <a href="/wiki/Euro" title="Euro">euro</a>, entre os países da Eurozona.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span>[</span>6<span>]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Juros_simples">Juros simples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=4" title="Editar secção: Juros simples" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=4" title="Editar código-fonte da secção: Juros simples"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>No regime dos juros simples, a taxa de juros é aplicada sobre o valor inicial de forma linear em todos os períodos, ou seja, não considera que o valor sobre o qual incidem juros muda ao longo do tempo. </p><p>A fórmula de juros simples pode ser escrita da seguinte maneira: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{f}=V_{p}(1+j\cdot n),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> <mo>⋅</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}=V_{p}(1+j\cdot n),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c372018ce5bd47745040dca79defafa0d1cc0595" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.495ex; height:3.009ex;" alt="{\displaystyle V_{f}=V_{p}(1+j\cdot n),}"></span> onde </p> <ul><li><b><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 V_{f}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/102b5ce921c1a2d3110a75d0de32023e797f1471" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.784ex; height:2.843ex;" alt="{\displaystyle V_{f}:}"></span></b> Valor Futuro</li> <li><b><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 V_{p}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{p}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b48a4a1a78b56299d7f36ee4c013347d2f9ff746" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.706ex; height:2.843ex;" alt="{\displaystyle V_{p}:}"></span></b> Valor Presente</li> <li><b><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 j:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e9642903d734b23433b712074be5a3e270a8d5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:2.277ex; height:2.509ex;" alt="{\displaystyle j:}"></span></b> Taxa de juros</li> <li><b><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 n:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/caa288b1ace2a3baa0acbf8685c92ec2a534a63a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.687ex; height:1.676ex;" alt="{\displaystyle n:}"></span></b> Número de períodos</li></ul> <p><b>Exemplo</b> </p><p>Uma pessoa toma emprestado $100 (<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 V_{p}=100}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{p}=100}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b413df946f4d3d2aa3669f9e44ef7c2e1c406e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9ex; height:2.843ex;" alt="{\displaystyle V_{p}=100}"></span>) para pagar em 2 meses (<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 n=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a02c8bd752d2cc859747ca1f3a508281bdbc3b34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=2}"></span>) com taxa de juros de 10% ao mês (<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 j=0,1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j=0,1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b8d1bb5b558a01f533d1804bf0d986772e977c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:7.442ex; height:2.509ex;" alt="{\displaystyle j=0,1}"></span>), calculados conforme o regime de juros simples. Depois de 2 meses essa pessoa irá pagar $120, conforme a fórmula: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}V_{f}&=100\cdot \left(1+0,1\cdot 2\right)\\&=100\cdot \left(1+0,2\right)\\&=100\cdot 1,2\\&=120\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> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>⋅</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>120</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}V_{f}&=100\cdot \left(1+0,1\cdot 2\right)\\&=100\cdot \left(1+0,2\right)\\&=100\cdot 1,2\\&=120\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3094d62396e68141bd2b5be15d46f3d1f7acea3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.505ex; width:23.521ex; height:12.176ex;" alt="{\displaystyle {\begin{aligned}V_{f}&=100\cdot \left(1+0,1\cdot 2\right)\\&=100\cdot \left(1+0,2\right)\\&=100\cdot 1,2\\&=120\end{aligned}}}"></span> </p><p><b>Obtendo-se o valor dos juros diretamente</b> </p><p>Uma pessoa toma emprestado $100 (<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 V_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4f7059b11d4da978f72a794124be758e9ed2b85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.414ex; height:2.843ex;" alt="{\displaystyle V_{p}}"></span>) para pagar em 2 meses (<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>) com taxa de juros de 10% ao mês (<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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>). Depois de 2 meses essa pessoa irá pagar $20 de juros, conforme a fórmula: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J=V_{p}\cdot j\cdot n,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>⋅</mo> <mi>j</mi> <mo>⋅</mo> <mi>n</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=V_{p}\cdot j\cdot n,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1626db897768d68502ca01d2fa3db63fdb9617ce" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.342ex; height:2.843ex;" alt="{\displaystyle J=V_{p}\cdot j\cdot n,}"></span> onde </p> <ul><li><b><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 J:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a47ac6849ac64c8bf0227507e24e4617d4e8e360" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.763ex; height:2.176ex;" alt="{\displaystyle J:}"></span></b> Valor dos Juros</li></ul> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}J&=100\cdot 0,1\cdot 2\\&=20\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>J</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>⋅</mo> <mn>2</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>20</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}J&=100\cdot 0,1\cdot 2\\&=20\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0ca44b30be9473f7754acaf39567e154029b7e1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.688ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}J&=100\cdot 0,1\cdot 2\\&=20\end{aligned}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Juros_compostos">Juros compostos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=5" title="Editar secção: Juros compostos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=5" title="Editar código-fonte da secção: Juros compostos"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>No regime de juros compostos, os juros corrigíveis de cada período são somados ao capital para o cálculo de novos juros nos períodos seguintes. Nesse caso, o valor da dívida é sempre corrigida e a taxa de juros é calculada sobre esse novo valor. A fórmula de juros compostos pode ser escrita da seguinte maneira: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{f}=V_{p}(1+j)^{n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}=V_{p}(1+j)^{n},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11328e3ce23e91974dc9f7f5e47c9dd946668d8f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.64ex; height:3.009ex;" alt="{\displaystyle V_{f}=V_{p}(1+j)^{n},}"></span> onde </p> <ul><li><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 V_{f}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/102b5ce921c1a2d3110a75d0de32023e797f1471" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.784ex; height:2.843ex;" alt="{\displaystyle V_{f}:}"></span> Valor Futuro</li> <li><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 V_{p}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{p}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b48a4a1a78b56299d7f36ee4c013347d2f9ff746" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.706ex; height:2.843ex;" alt="{\displaystyle V_{p}:}"></span> Valor Presente</li> <li><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 j:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e9642903d734b23433b712074be5a3e270a8d5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:2.277ex; height:2.509ex;" alt="{\displaystyle j:}"></span> Taxa de juros</li> <li><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 n:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/caa288b1ace2a3baa0acbf8685c92ec2a534a63a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.687ex; height:1.676ex;" alt="{\displaystyle n:}"></span> Número de períodos</li></ul> <p><b>Exemplo:</b> Uma pessoa toma emprestado $ 100 (<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 V_{p}=100}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{p}=100}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b413df946f4d3d2aa3669f9e44ef7c2e1c406e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9ex; height:2.843ex;" alt="{\displaystyle V_{p}=100}"></span>) com taxa de juros de 10% ao mês (<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 j=0,1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j=0,1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b8d1bb5b558a01f533d1804bf0d986772e977c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:7.442ex; height:2.509ex;" alt="{\displaystyle j=0,1}"></span>), calculados conforme o regime de juros compostos. Depois de 2 meses (<b><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 n=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a02c8bd752d2cc859747ca1f3a508281bdbc3b34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=2}"></span></b>) essa pessoa irá pagar $121, conforme a fórmula: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}V_{f}&=100\cdot \left(1+0,1\right)^{2}\\&=100\cdot \left(1,1\right)^{2}\\&=100\cdot 1,1\cdot 1,1\\&=110\cdot 1,1\\&=121\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> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>⋅</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>110</mn> <mo>⋅</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>121</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}V_{f}&=100\cdot \left(1+0,1\right)^{2}\\&=100\cdot \left(1,1\right)^{2}\\&=100\cdot 1,1\cdot 1,1\\&=110\cdot 1,1\\&=121\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0469c68ff7868355f99270951a5ad3e6540d4be5" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.338ex; width:21.733ex; height:15.843ex;" alt="{\displaystyle {\begin{aligned}V_{f}&=100\cdot \left(1+0,1\right)^{2}\\&=100\cdot \left(1,1\right)^{2}\\&=100\cdot 1,1\cdot 1,1\\&=110\cdot 1,1\\&=121\end{aligned}}}"></span> </p><p>Para o caso mais geral, quando o juro é capitalizado mais de que uma vez por período, a fórmula é </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{f}=V_{p}\left(1+{\frac {j}{n}}\right)^{nt}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>j</mi> <mi>n</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}=V_{p}\left(1+{\frac {j}{n}}\right)^{nt}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/239debbc2695b5e4cbfb01749a7e0209b8278484" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:19.471ex; height:6.509ex;" alt="{\displaystyle V_{f}=V_{p}\left(1+{\frac {j}{n}}\right)^{nt}}"></span> </p><p>onde, </p> <ul><li><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 V_{f}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/102b5ce921c1a2d3110a75d0de32023e797f1471" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.784ex; height:2.843ex;" alt="{\displaystyle V_{f}:}"></span> Valor Futuro</li> <li><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 V_{p}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{p}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b48a4a1a78b56299d7f36ee4c013347d2f9ff746" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.706ex; height:2.843ex;" alt="{\displaystyle V_{p}:}"></span> Valor Presente</li> <li><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 j:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e9642903d734b23433b712074be5a3e270a8d5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:2.277ex; height:2.509ex;" alt="{\displaystyle j:}"></span> taxa de juro nominal para o período</li> <li><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 n:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/caa288b1ace2a3baa0acbf8685c92ec2a534a63a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.687ex; height:1.676ex;" alt="{\displaystyle n:}"></span> número de vezes que o juro é capitalizado por período</li> <li><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 t:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/330e62970a056d1e706aa4d09beb560a5c1571d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.132ex; height:2.009ex;" alt="{\displaystyle t:}"></span> número de períodos</li></ul> <p><b>Cálculo do montante de juros a partir do capital</b> </p><p>A partir da expressão abaixo, dado o capital, a taxa e o tempo de capitalização, se obtém diretamente o montante dos juros. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J=V_{p}[(1+j)^{n}-1]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo stretchy="false">[</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=V_{p}[(1+j)^{n}-1]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33cd2d4f5b7ab47347245c5db1a560d5d3496fad" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.269ex; height:3.009ex;" alt="{\displaystyle J=V_{p}[(1+j)^{n}-1]}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Rendas_certas">Rendas certas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=6" title="Editar secção: Rendas certas" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=6" title="Editar código-fonte da secção: Rendas certas"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rendas Certas, <b>Aplicações Constantes</b> ou <b>Anuidades</b> são termos que se referem a aplicações sucessivas de capital (<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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>), remunerado a uma taxa de juros (<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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>), durante um período de tempo (<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>), onde valor e taxa são constantes em cada período, segundo a fórmula. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=A\times {\frac {(1+j)^{n}-1}{j}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mi>A</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mi>j</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=A\times {\frac {(1+j)^{n}-1}{j}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17c074b00ee0e34a06364208dbfef21a11df0546" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.274ex; height:6.176ex;" alt="{\displaystyle R=A\times {\frac {(1+j)^{n}-1}{j}}}"></span> </p><p>Essa fórmula se baseia no cálculo da parcela na <a href="/wiki/Tabela_Price" title="Tabela Price">Tabela Price</a>. </p><p><b>Exemplo ilustrativo:</b> </p><p>Uma pessoa inicia uma <a href="/wiki/Poupan%C3%A7a" title="Poupança">poupança</a> aplicando mensalmente $100, com rendimento de 1% ao mês. Ao fazer o 12º depósito qual será o seu saldo? </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}R&=100\times {\frac {(1+0,01)^{12}-1}{0,01}}\\&=100\times {\frac {1,1268-1}{0,01}}\\&=100\times {\frac {0,1268}{0,01}}\\&=100\times 12,68\\&\approx 1.268\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>R</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>01</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>0</mn> <mo>,</mo> <mn>01</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>,</mo> <mn>1268</mn> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>0</mn> <mo>,</mo> <mn>01</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0</mn> <mo>,</mo> <mn>1268</mn> </mrow> <mrow> <mn>0</mn> <mo>,</mo> <mn>01</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>×</mo> <mn>12</mn> <mo>,</mo> <mn>68</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>≈</mo> <mn>1.268</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}R&=100\times {\frac {(1+0,01)^{12}-1}{0,01}}\\&=100\times {\frac {1,1268-1}{0,01}}\\&=100\times {\frac {0,1268}{0,01}}\\&=100\times 12,68\\&\approx 1.268\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1058061f4c1bf1de83f1e26f45925c8488fa6367" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -11.505ex; width:28.99ex; height:24.176ex;" alt="{\displaystyle {\begin{aligned}R&=100\times {\frac {(1+0,01)^{12}-1}{0,01}}\\&=100\times {\frac {1,1268-1}{0,01}}\\&=100\times {\frac {0,1268}{0,01}}\\&=100\times 12,68\\&\approx 1.268\end{aligned}}}"></span> </p> <dl><dd>É importante ter em mente que no caso acima o último depósito não é capitalizado, ou seja, o último valor se acumula ao montante mas não tem ainda juro de remuneração.</dd></dl> <p><b>Propriedades multiplicativas em rendas certas</b> </p><p>Outra forma de se chegar no valor do montante de renda (<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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>) é com o produto da aplicação periódica (<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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>) e somatório dos Fatores <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 F_{t},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1484a9bb94f05cbfef14a376681426383a806fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.967ex; height:2.509ex;" alt="{\displaystyle F_{t},}"></span> que, por sua vez, representam o crescimento dos valores aplicados ao longo do tempo (<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 F_{t}=(1+0,01)^{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>01</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t}=(1+0,01)^{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7542f7735d705cb83378d04794f416cb68dd9ab5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.578ex; height:3.009ex;" alt="{\displaystyle F_{t}=(1+0,01)^{t}}"></span>) </p><p><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=A\cdot \sum {F_{t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mi>A</mi> <mo>⋅</mo> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=A\cdot \sum {F_{t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18a06fab6dbdbeb64b1a5a4ec9f5c652c899e4b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:14.347ex; height:3.843ex;" alt="{\displaystyle R=A\cdot \sum {F_{t}}}"></span> </p><p><b>Exemplo:</b> </p><p>Um plano de previdência com depósitos de $100 constantes, durante 4 meses, a uma taxa de 1% a.m. (ao mês) acumula o montante aproximado de: </p><p>Na tabela abaixo temos o somatório dos fatores de 1% de juros, então, basta aplicar a expressão acima: </p> <table class="wikitable" style="text-align: right;"> <tbody><tr> <th>Período(<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 _{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01ef3599df36b4ac4f398352aa38136e6f8a3a0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:0.826ex; height:1.676ex;" alt="{\displaystyle _{t}}"></span>) </th> <th><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+j)^{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1+j)^{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fee09013c80334e4afe14d048c85b7a0ac15d0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.596ex; height:3.009ex;" alt="{\displaystyle (1+j)^{t}}"></span> </th> <th>Fator <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 F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> </th></tr> <tr> <td><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 _{t}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{t}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68ccb51a9e1551e10b997846d4aa781917f81aa7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.087ex; height:2.509ex;" alt="{\displaystyle _{t}=1}"></span> </td> <td><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+0,01)^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>01</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1+0,01)^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0635aa3919ea8ef6893b493eb48cab1da4c7c311" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.388ex; height:3.176ex;" alt="{\displaystyle (1+0,01)^{1}}"></span> </td> <td><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 1,01}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>,</mo> <mn>01</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1,01}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50e5089e954905c16e373283b74cf60a84a52852" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.521ex; height:2.509ex;" alt="{\displaystyle 1,01}"></span> </td></tr> <tr> <td><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 _{t}=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{t}=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2828120000d63ebc36993458cac42bb9ad3e8962" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.087ex; height:2.509ex;" alt="{\displaystyle _{t}=2}"></span> </td> <td><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+0,01)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>01</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1+0,01)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b7609ed130ce0cd73941f2750cf4cde282e03c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.388ex; height:3.176ex;" alt="{\displaystyle (1+0,01)^{2}}"></span> </td> <td><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 1,0201}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>,</mo> <mn>0201</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1,0201}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd3df56f0f106f7c343b0f08fa4c5e041dddc027" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.846ex; height:2.509ex;" alt="{\displaystyle 1,0201}"></span> </td></tr> <tr> <td><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 _{t}=3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{t}=3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15d52656955ffbb7e9d052f5b9acca63d68a6927" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.087ex; height:2.509ex;" alt="{\displaystyle _{t}=3}"></span> </td> <td><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+0,01)^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>01</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1+0,01)^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d95aff8926d8b58332c40424bfc6ed12fab54b8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.388ex; height:3.176ex;" alt="{\displaystyle (1+0,01)^{3}}"></span> </td> <td><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 1,030301}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>,</mo> <mn>030301</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1,030301}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4b1c04d852b63b9c521ae204778015f7bede974" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.171ex; height:2.509ex;" alt="{\displaystyle 1,030301}"></span> </td></tr> <tr> <td><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 _{t}=4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{t}=4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0642471d919e2fd09e9a27a587f46b4f8d6bcdf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.087ex; height:2.509ex;" alt="{\displaystyle _{t}=4}"></span> </td> <td><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+0,01)^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>01</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1+0,01)^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe34b8a136835d9223ed1d185b5b1cdb3b001453" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.388ex; height:3.176ex;" alt="{\displaystyle (1+0,01)^{4}}"></span> </td> <td><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 1,04060401}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>,</mo> <mn>04060401</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1,04060401}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/164d2a4608b6c56aa79399a53e1f58cf2bfdaaf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.496ex; height:2.509ex;" alt="{\displaystyle 1,04060401}"></span> </td></tr> <tr> <td colspan="2"><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 \sum F^{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∑</mo> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum F^{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd0806bf160e8864dc38b46bb35bf41b2177fad9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:6.383ex; height:3.843ex;" alt="{\displaystyle \sum F^{t}}"></span> </td> <td><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 4,10100501}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mo>,</mo> <mn>10100501</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4,10100501}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75bb30429c70911db16b8476c2587649db2d21ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.496ex; height:2.509ex;" alt="{\displaystyle 4,10100501}"></span> </td></tr></tbody></table> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=100\cdot 4,101\approx 410,10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <mn>4</mn> <mo>,</mo> <mn>101</mn> <mo>≈</mo> <mn>410</mn> <mo>,</mo> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=100\cdot 4,101\approx 410,10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/880953d2977218665865cab573d7cf7eccbad781" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.657ex; height:2.509ex;" alt="{\displaystyle R=100\cdot 4,101\approx 410,10}"></span> </p><p>Montante/renda acumulada </p><p>Nessa forma de cálculo, diferentemente da primeira, o valor final é referente à situação 1 mês depois do último depósito. </p> <div class="mw-heading mw-heading3"><h3 id="Taxa_de_juros_continuamente_composta">Taxa de juros continuamente composta</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=7" title="Editar secção: Taxa de juros continuamente composta" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=7" title="Editar código-fonte da secção: Taxa de juros continuamente composta"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O regime de juros compostos também pode ser expresso através da taxa de juros continuamente composta. Apesar de ter o mesmo funcionamento do regime de juros compostos, a taxa de juros continuamente composta apresenta uma fórmula de cálculo diferente: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{f}=V_{p}\cdot e^{r\cdot n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo>⋅</mo> <mi>n</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}=V_{p}\cdot e^{r\cdot n},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e220e80f4ef72c992e9ee27c7527896f85c19f26" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.831ex; height:3.009ex;" alt="{\displaystyle V_{f}=V_{p}\cdot e^{r\cdot n},}"></span> onde </p> <ul><li><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 V_{f}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/102b5ce921c1a2d3110a75d0de32023e797f1471" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.784ex; height:2.843ex;" alt="{\displaystyle V_{f}:}"></span> Valor Futuro</li> <li><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 V_{p}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{p}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b48a4a1a78b56299d7f36ee4c013347d2f9ff746" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.706ex; height:2.843ex;" alt="{\displaystyle V_{p}:}"></span> Valor Presente</li> <li><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:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e953871da035a97eb7aded88277ad1a47205893" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.341ex; height:1.676ex;" alt="{\displaystyle r:}"></span> Taxa de juros continuamente composta</li> <li><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 n:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/caa288b1ace2a3baa0acbf8685c92ec2a534a63a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.687ex; height:1.676ex;" alt="{\displaystyle n:}"></span> Número de períodos</li> <li><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 e:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5911bfbb752c2dc1de26a8a9ac2c0e23f4f5ebc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.375ex; height:1.676ex;" alt="{\displaystyle e:}"></span> <a href="/wiki/N%C3%BAmero_de_Euler" class="mw-redirect" title="Número de Euler">Número de Euler</a>, que é equivalente a 2,718281828459...</li></ul> <p>O valor da taxa de juros <b><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span></b>, que é continuamente composta, possui significado diferente do valor da taxa de juros <b><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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span></b>, usada nas fórmulas anteriores. Porém, como ambas são usadas no regime de juros compostos, existe uma equação para fazer a "tradução" de uma taxa para outra: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j=e^{r}-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j=e^{r}-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8f90a0f35254f983b40324c4dca5fe1e17fb7a1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:10.143ex; height:2.676ex;" alt="{\displaystyle j=e^{r}-1}"></span> </p><p>ou, invertendo os termos, </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=ln(j+1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=ln(j+1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ac37511c270cd60dfc93f88d7efa2c6208edcf4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.005ex; height:2.843ex;" alt="{\displaystyle r=ln(j+1)}"></span> </p><p>Diferente da taxa de juros composta, a taxa de juros continuamente composta pode ser somada. Por exemplo, se a taxa de juros continuamente composta de janeiro é 3% e a de fevereiro é 4%, a taxa desse bimestre é 7% (esse cálculo não pode ser feito com taxas que não são continuamente compostas). Devido a essa propriedade, elas podem ser usadas para facilitar a interpretação e o tratamento de <a href="/wiki/Banco_de_Dados" class="mw-redirect" title="Banco de Dados">bases de dados</a>. Além disso, alguns <a href="/wiki/Modelo_(matem%C3%A1tica)" title="Modelo (matemática)">modelos</a> estatísticos em <a href="/wiki/Finan%C3%A7as" title="Finanças">finanças</a> como <a href="/wiki/Teoria_moderna_do_portf%C3%B3lio" title="Teoria moderna do portfólio">Teoria moderna do portfólio</a>, <a href="/wiki/Black-Scholes" title="Black-Scholes">Black-Scholes</a> e <a href="/wiki/Modelo_de_precifica%C3%A7%C3%A3o_de_ativos_financeiros" title="Modelo de precificação de ativos financeiros">Modelo de precificação de ativos financeiros</a> (CAPM) usam esse conceito de taxa de juros nas suas premissas. </p><p>Apesar dessas vantagens, o uso da taxa continuamente composta está concentrado na área <a href="/wiki/Academia" title="Academia">acadêmica</a> e no <a href="/wiki/Mercado_de_capitais" title="Mercado de capitais">mercado de capitais</a>. Devido à dificuldade de interpretação e cálculo, essa forma de cálculo não é usada para divulgar taxa de empréstimos bancários nem tabelas de rentabilidade de <a href="/wiki/Investimento" title="Investimento">investimentos</a> para o público geral. </p><p><b>Exemplo numérico:</b> </p><p>Uma pessoa toma emprestado $100 (<b><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 V_{p}=100}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{p}=100}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b413df946f4d3d2aa3669f9e44ef7c2e1c406e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9ex; height:2.843ex;" alt="{\displaystyle V_{p}=100}"></span></b>) com taxa de juros continuamente composta de 10% ao mês (<b><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=0,1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=0,1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f212f946824913b4e9e3f7ec300bd86058d09da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.506ex; height:2.509ex;" alt="{\displaystyle r=0,1}"></span></b>). Depois de 2 meses (<b><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 n=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a02c8bd752d2cc859747ca1f3a508281bdbc3b34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=2}"></span></b>) essa pessoa irá pagar $122,14, conforme a fórmula: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}V_{f}&=100\cdot e^{0,1\cdot 2}\\&=100\cdot e^{0,2}\\&=100\cdot 2,718281828459\ldots ^{0,2}\\&=100\cdot 1,2214\\&=122,14\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> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>⋅</mo> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mo>,</mo> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <mn>2</mn> <mo>,</mo> <mn>718281828459</mn> <msup> <mo>…</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mo>,</mo> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>100</mn> <mo>⋅</mo> <mn>1</mn> <mo>,</mo> <mn>2214</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>122</mn> <mo>,</mo> <mn>14</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}V_{f}&=100\cdot e^{0,1\cdot 2}\\&=100\cdot e^{0,2}\\&=100\cdot 2,718281828459\ldots ^{0,2}\\&=100\cdot 1,2214\\&=122,14\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c0b572bae979ae25f7d497f47e03d029b63d9f5" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.338ex; width:33.098ex; height:15.843ex;" alt="{\displaystyle {\begin{aligned}V_{f}&=100\cdot e^{0,1\cdot 2}\\&=100\cdot e^{0,2}\\&=100\cdot 2,718281828459\ldots ^{0,2}\\&=100\cdot 1,2214\\&=122,14\end{aligned}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Juros_simples_vs._compostos">Juros simples vs. compostos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=8" title="Editar secção: Juros simples vs. compostos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=8" title="Editar código-fonte da secção: Juros simples vs. compostos"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Juros_compostos.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Juros_compostos.png/350px-Juros_compostos.png" decoding="async" width="350" height="232" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Juros_compostos.png/525px-Juros_compostos.png 1.5x, //upload.wikimedia.org/wikipedia/commons/1/15/Juros_compostos.png 2x" data-file-width="684" data-file-height="454" /></a><figcaption>Comportamento de juros compostos, num empréstimo de 100$ com taxa de juro anual de 5%. Ao final de 40 anos, o devedor deve cerca de sete vezes mais em comparação com o capital pedido inicialmente</figcaption></figure> <p>A tabela abaixo mostra os valores de um empréstimo de 100 (Euros ou Reais) com taxa de juros de 10% ao período sob o regime de juros simples e juros compostos. Note que essa tabela apresenta três momentos diferentes: </p> <ul><li>Para períodos inferiores a 1 (<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 n<1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n<1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dffd3f7a2c3b20dc8e615dfd85f820287a8fc06b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n<1}"></span>), o regime de juros simples apresenta valores superiores ao regime de juros compostos.</li> <li>No período 1, o valor é igual para ambos regimes.</li> <li>Para mais de um período, o regime de juros compostos apresenta valores superiores ao regime de juros simples.</li></ul> <table class="wikitable" style="text-align: center;"> <tbody><tr> <th><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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span></th> <th>Juros Simples</th> <th>Juros Compostos </th></tr> <tr> <td>0,00</td> <td>100,00</td> <td>100,00 </td></tr> <tr> <td>0,25</td> <td>102,50</td> <td>102,41 </td></tr> <tr> <td>0,50</td> <td>105,00</td> <td>104,88 </td></tr> <tr> <td>0,75</td> <td>107,50</td> <td>107,41 </td></tr> <tr> <td>1,00</td> <td>110,00</td> <td>110,00 </td></tr> <tr> <td>1,25</td> <td>112,50</td> <td>112,65 </td></tr> <tr> <td>1,50</td> <td>115,00</td> <td>115,37 </td></tr> <tr> <td>1,75</td> <td>117,50</td> <td>118,15 </td></tr> <tr> <td>2,00</td> <td>120,00</td> <td>121,00 </td></tr> <tr> <td>2,25</td> <td>122,50</td> <td>123,92 </td></tr></tbody></table> <p>Enquanto que o juro simples obedece a uma <a href="/wiki/Progress%C3%A3o_aritm%C3%A9tica" title="Progressão aritmética">progressão aritmética</a>, que para o caso da tabela acima o capital devido é dado por: </p><p><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 V_{f}=100\times \left(1+j\times n\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> <mo>×</mo> <mi>n</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}=100\times \left(1+j\times n\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71be5bdbb6fb282241ef8a4a596dad77acde5ebc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.923ex; height:3.009ex;" alt="{\displaystyle V_{f}=100\times \left(1+j\times n\right)}"></span> </p><p>já o juro composto obedece a uma <a href="/wiki/Progress%C3%A3o_geom%C3%A9trica" title="Progressão geométrica">progressão geométrica</a>, que para a tabela acima, o capital devido é: </p><p><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 V_{f}=100\times \left(1+j\right)^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> <mo>×</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{f}=100\times \left(1+j\right)^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9165df63ae04d28b90191503542cbee1461e265" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.907ex; height:3.176ex;" alt="{\displaystyle V_{f}=100\times \left(1+j\right)^{n}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Taxa_nominal_vs._taxa_real">Taxa nominal vs. taxa real</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=9" title="Editar secção: Taxa nominal vs. taxa real" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=9" title="Editar código-fonte da secção: Taxa nominal vs. taxa real"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A taxa de juros nominal é remuneração do empréstimo como foi explicado até este ponto. A taxa de juro real leva em consideração a variação verificada no índice de preços, reflectindo a alteração no poder de compra do dinheiro. O seu cálculo advém da <a href="/wiki/Equa%C3%A7%C3%A3o_de_Fisher" title="Equação de Fisher">equação de Fisher</a>: </p><p><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+i_{r}={\frac {1+i_{n}}{1+\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>π</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+i_{r}={\frac {1+i_{n}}{1+\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69b0fbe74ae602b61588ccf988185f36199ac595" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.737ex; height:5.343ex;" alt="{\displaystyle 1+i_{r}={\frac {1+i_{n}}{1+\pi }}}"></span> </p> <ul><li><b><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}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i_{r}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb684b2bbf7e821cf5badd7505714dff0de81470" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.068ex; height:2.509ex;" alt="{\displaystyle i_{r}:}"></span></b> Taxa de juros real</li> <li><b><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_{n}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i_{n}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eefb76bd2ec19e5e106cad2d275eae436ea202ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.313ex; height:2.509ex;" alt="{\displaystyle i_{n}:}"></span></b> Taxa de juros nominal</li> <li><b><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 \pi :}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi :}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08e6f1d7ecc994ec947971981fff0091c45552ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.624ex; height:1.676ex;" alt="{\displaystyle \pi :}"></span></b> Taxa de inflação</li></ul> <p><b>Exemplo numérico:</b> </p><p>Durante um ano, uma pessoa contrai um empréstimo com uma taxa de juro nominal de 10% (<b><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_{n}=0,1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i_{n}=0,1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86499aed698c683e46bfdbbe794c3cca8ece8aad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.478ex; height:2.509ex;" alt="{\displaystyle i_{n}=0,1}"></span></b>), e durante o mesmo período o índice de preços cresce 5% - ou seja, a inflação é de 5% (<b><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 \pi =0,05}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>05</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi =0,05}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b920d274e6ddc813e2650f7c3f9de81d381d7bd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.952ex; height:2.509ex;" alt="{\displaystyle \pi =0,05}"></span></b>). A taxa de juros real nesse caso é de 4,76%, conforme a fórmula: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}1+i_{r}&={\frac {1+0,1}{1+0,05}}\\1+i_{r}&={\frac {1,1}{1,05}}\\i_{r}&=1,0476-1\\i_{r}&=0,0476\\i_{r}&=4,76\%\\\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> <mn>1</mn> <mo>+</mo> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mn>0</mn> <mo>,</mo> <mn>05</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> <mo>+</mo> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mn>1</mn> <mo>,</mo> <mn>05</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>0476</mn> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>0476</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>4</mn> <mo>,</mo> <mn>76</mn> <mi mathvariant="normal">%</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}1+i_{r}&={\frac {1+0,1}{1+0,05}}\\1+i_{r}&={\frac {1,1}{1,05}}\\i_{r}&=1,0476-1\\i_{r}&=0,0476\\i_{r}&=4,76\%\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52d1095315289e3cf138969f71e8715135054ab8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.838ex; width:20.478ex; height:20.843ex;" alt="{\displaystyle {\begin{aligned}1+i_{r}&={\frac {1+0,1}{1+0,05}}\\1+i_{r}&={\frac {1,1}{1,05}}\\i_{r}&=1,0476-1\\i_{r}&=0,0476\\i_{r}&=4,76\%\\\end{aligned}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Taxa_de_juros_natural">Taxa de juros natural</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=10" title="Editar secção: Taxa de juros natural" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=10" title="Editar código-fonte da secção: Taxa de juros natural"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A taxa de juros natural é a taxa de juros de equilíbrio entre poupança e investimento no <a href="/wiki/Pleno_emprego" title="Pleno emprego">pleno emprego</a> da economia. Trata-se de uma variável não observável, mas existem alguns métodos para estimá-la: </p> <ol><li>o estatístico, no qual se utiliza algum ﬁltro da taxa de juros real para extrair o componente de tendência, que é identiﬁcado com a taxa natural;</li> <li>do modelo do agente representativo, que se baseia na teoria econômica, que entende que taxa de juros natural depende de três parâmetros, a taxa de preferência, a elasticidade de substituição do consumo e a taxa prevista do crescimento da produtividade da mão de obra. A utilização desse método não é adequado em pequenas economias abertas;</li> <li>segundo os modelos de <a href="/wiki/Modelo_Mundell-Fleming" title="Modelo Mundell-Fleming">Mundell-Fleming</a> e de Gerações Superpostas,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span>[</span>7<span>]</span></a></sup> a taxa natural de uma economia aberta pequena é igual a taxa de juros real internacional, sendo que em países nos quais existem restrições a mobilidade de capital deve-se adicionar os prêmios de risco apropriados.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span>[</span>8<span>]</span></a></sup></li></ol> <div class="mw-heading mw-heading2"><h2 id="Tabela_Financeira">Tabela Financeira</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=11" title="Editar secção: Tabela Financeira" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=11" title="Editar código-fonte da secção: Tabela Financeira"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A tabela financeira apresenta os fatores de juros de taxas, segundo o regime de juros compostos, dado pela fórmula básica. </p><p><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 F_{t}=(1+i)^{t},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>i</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t}=(1+i)^{t},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78ae8e9de6b3d0bffab7f5c722e1d88c2c191bb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.506ex; height:3.009ex;" alt="{\displaystyle F_{t}=(1+i)^{t},}"></span> onde: </p><p><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="{\textstyle i:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>i</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle i:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac204c71703a1cd165aae63c1d74f564a81aa735" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.094ex; height:2.176ex;" alt="{\textstyle i:}"></span> deve ser expresso em forma fracional (<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 {i}{100}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>i</mi> <mn>100</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {i}{100}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/214dc27fa1a360c5651a30ef753cff733ff241e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.323ex; height:5.176ex;" alt="{\displaystyle {\frac {i}{100}}}"></span>). Exemplo: 1% = 0,01 </p><p><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="{\textstyle t:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>t</mi> <mo>:</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle t:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/252b557ff9b83d638697ec87713ad968994a5b10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.132ex; height:2.009ex;" alt="{\textstyle t:}"></span>período de capitalização </p><p>A tabela financeira é muito utilizada para se preestabelecer, por exemplo, como serão considerados os valores decimais de cada taxa, isto é, quantas casas decimais serão acordadas para os cálculos financeiros. </p> <table class="wikitable" style="text-align: right;"> <caption>Tabela financeira </caption> <tbody><tr> <th></th> <th colspan="11">Períodos </th></tr> <tr> <th>%</th> <th>2</th> <th>3</th> <th>4</th> <th>5</th> <th>6</th> <th>7</th> <th>8</th> <th>9</th> <th>10</th> <th>11</th> <th>12 </th></tr> <tr> <td>0,25</td> <td>1,0050</td> <td>1,0075</td> <td>1,0100</td> <td>1,0126</td> <td>1,0151</td> <td>1,0176</td> <td>1,0202</td> <td>1,0227</td> <td>1,0253</td> <td>1,0278</td> <td>1,0304 </td></tr> <tr> <td>0,50</td> <td>1,0100</td> <td>1,0151</td> <td>1,0202</td> <td>1,0253</td> <td>1,0304</td> <td>1,0355</td> <td>1,0407</td> <td>1,0459</td> <td>1,0511</td> <td>1,0564</td> <td>1,0617 </td></tr> <tr> <td>0,75</td> <td>1,0151</td> <td>1,0227</td> <td>1,0303</td> <td>1,0381</td> <td>1,0459</td> <td>1,0537</td> <td>1,0616</td> <td>1,0696</td> <td>1,0776</td> <td>1,0857</td> <td>1,0938 </td></tr> <tr> <td>1,00</td> <td>1,0201</td> <td>1,0303</td> <td>1,0406</td> <td>1,0510</td> <td>1,0615</td> <td>1,0721</td> <td>1,0829</td> <td>1,0937</td> <td>1,1046</td> <td>1,1157</td> <td>1,1268 </td></tr> <tr> <td>1,25</td> <td>1,0252</td> <td>1,0380</td> <td>1,0509</td> <td>1,0641</td> <td>1,0774</td> <td>1,0909</td> <td>1,1045</td> <td>1,1183</td> <td>1,1323</td> <td>1,1464</td> <td>1,1608 </td></tr> <tr> <td>1,50</td> <td>1,0302</td> <td>1,0457</td> <td>1,0614</td> <td>1,0773</td> <td>1,0934</td> <td>1,1098</td> <td>1,1265</td> <td>1,1434</td> <td>1,1605</td> <td>1,1779</td> <td>1,1956 </td></tr> <tr> <td>1,75</td> <td>1,0353</td> <td>1,0534</td> <td>1,0719</td> <td>1,0906</td> <td>1,1097</td> <td>1,1291</td> <td>1,1489</td> <td>1,1690</td> <td>1,1894</td> <td>1,2103</td> <td>1,2314 </td></tr> <tr> <td>2,00</td> <td>1,0404</td> <td>1,0612</td> <td>1,0824</td> <td>1,1041</td> <td>1,1262</td> <td>1,1487</td> <td>1,1717</td> <td>1,1951</td> <td>1,2190</td> <td>1,2434</td> <td>1,2682 </td></tr> <tr> <td>2,25</td> <td>1,0455</td> <td>1,0690</td> <td>1,0931</td> <td>1,1177</td> <td>1,1428</td> <td>1,1685</td> <td>1,1948</td> <td>1,2217</td> <td>1,2492</td> <td>1,2773</td> <td>1,3060 </td></tr> <tr> <td>2,50</td> <td>1,0506</td> <td>1,0769</td> <td>1,1038</td> <td>1,1314</td> <td>1,1597</td> <td>1,1887</td> <td>1,2184</td> <td>1,2489</td> <td>1,2801</td> <td>1,3121</td> <td>1,3449 </td></tr> <tr> <td>2,75</td> <td>1,0558</td> <td>1,0848</td> <td>1,1146</td> <td>1,1453</td> <td>1,1768</td> <td>1,2091</td> <td>1,2424</td> <td>1,2765</td> <td>1,3117</td> <td>1,3477</td> <td>1,3848 </td></tr> <tr> <td>3,00</td> <td>1,0609</td> <td>1,0927</td> <td>1,1255</td> <td>1,1593</td> <td>1,1941</td> <td>1,2299</td> <td>1,2668</td> <td>1,3048</td> <td>1,3439</td> <td>1,3842</td> <td>1,4258 </td></tr> <tr> <td>3,25</td> <td>1,0661</td> <td>1,1007</td> <td>1,1365</td> <td>1,1734</td> <td>1,2115</td> <td>1,2509</td> <td>1,2916</td> <td>1,3336</td> <td>1,3769</td> <td>1,4216</td> <td>1,4678 </td></tr> <tr> <td>3,50</td> <td>1,0712</td> <td>1,1087</td> <td>1,1475</td> <td>1,1877</td> <td>1,2293</td> <td>1,2723</td> <td>1,3168</td> <td>1,3629</td> <td>1,4106</td> <td>1,4600</td> <td>1,5111 </td></tr> <tr> <td>3,75</td> <td>1,0764</td> <td>1,1168</td> <td>1,1587</td> <td>1,2021</td> <td>1,2472</td> <td>1,2939</td> <td>1,3425</td> <td>1,3928</td> <td>1,4450</td> <td>1,4992</td> <td>1,5555 </td></tr> <tr> <td>4,00</td> <td>1,0816</td> <td>1,1249</td> <td>1,1699</td> <td>1,2167</td> <td>1,2653</td> <td>1,3159</td> <td>1,3686</td> <td>1,4233</td> <td>1,4802</td> <td>1,5395</td> <td>1,6010 </td></tr> <tr> <td>4,25</td> <td>1,0868</td> <td>1,1330</td> <td>1,1811</td> <td>1,2313</td> <td>1,2837</td> <td>1,3382</td> <td>1,3951</td> <td>1,4544</td> <td>1,5162</td> <td>1,5807</td> <td>1,6478 </td></tr> <tr> <td>4,50</td> <td>1,0920</td> <td>1,1412</td> <td>1,1925</td> <td>1,2462</td> <td>1,3023</td> <td>1,3609</td> <td>1,4221</td> <td>1,4861</td> <td>1,5530</td> <td>1,6229</td> <td>1,6959 </td></tr> <tr> <td>4,75</td> <td>1,0973</td> <td>1,1494</td> <td>1,2040</td> <td>1,2612</td> <td>1,3211</td> <td>1,3838</td> <td>1,4495</td> <td>1,5184</td> <td>1,5905</td> <td>1,6661</td> <td>1,7452 </td></tr> <tr> <td>5,00</td> <td>1,1025</td> <td>1,1576</td> <td>1,2155</td> <td>1,2763</td> <td>1,3401</td> <td>1,4071</td> <td>1,4775</td> <td>1,5513</td> <td>1,6289</td> <td>1,7103</td> <td>1,7959 </td></tr> <tr> <td>5,25</td> <td>1,1078</td> <td>1,1659</td> <td>1,2271</td> <td>1,2915</td> <td>1,3594</td> <td>1,4307</td> <td>1,5058</td> <td>1,5849</td> <td>1,6681</td> <td>1,7557</td> <td>1,8478 </td></tr> <tr> <td>5,50</td> <td>1,1130</td> <td>1,1742</td> <td>1,2388</td> <td>1,3070</td> <td>1,3788</td> <td>1,4547</td> <td>1,5347</td> <td>1,6191</td> <td>1,7081</td> <td>1,8021</td> <td>1,9012 </td></tr> <tr> <td>5,75</td> <td>1,1183</td> <td>1,1826</td> <td>1,2506</td> <td>1,3225</td> <td>1,3986</td> <td>1,4790</td> <td>1,5640</td> <td>1,6540</td> <td>1,7491</td> <td>1,8496</td> <td>1,9560 </td></tr> <tr> <td>6,00</td> <td>1,1236</td> <td>1,1910</td> <td>1,2625</td> <td>1,3382</td> <td>1,4185</td> <td>1,5036</td> <td>1,5938</td> <td>1,6895</td> <td>1,7908</td> <td>1,8983</td> <td>2,0122 </td></tr> <tr> <td>6,25</td> <td>1,1289</td> <td>1,1995</td> <td>1,2744</td> <td>1,3541</td> <td>1,4387</td> <td>1,5286</td> <td>1,6242</td> <td>1,7257</td> <td>1,8335</td> <td>1,9481</td> <td>2,0699 </td></tr> <tr> <td>6,50</td> <td>1,1342</td> <td>1,2079</td> <td>1,2865</td> <td>1,3701</td> <td>1,4591</td> <td>1,5540</td> <td>1,6550</td> <td>1,7626</td> <td>1,8771</td> <td>1,9992</td> <td>2,1291 </td></tr> <tr> <td>6,75</td> <td>1,1396</td> <td>1,2165</td> <td>1,2986</td> <td>1,3862</td> <td>1,4798</td> <td>1,5797</td> <td>1,6863</td> <td>1,8002</td> <td>1,9217</td> <td>2,0514</td> <td>2,1899 </td></tr> <tr> <td>7,00</td> <td>1,1449</td> <td>1,2250</td> <td>1,3108</td> <td>1,4026</td> <td>1,5007</td> <td>1,6058</td> <td>1,7182</td> <td>1,8385</td> <td>1,9672</td> <td>2,1049</td> <td>2,2522 </td></tr> <tr> <td>7,25</td> <td>1,1503</td> <td>1,2336</td> <td>1,3231</td> <td>1,4190</td> <td>1,5219</td> <td>1,6322</td> <td>1,7506</td> <td>1,8775</td> <td>2,0136</td> <td>2,1596</td> <td>2,3162 </td></tr> <tr> <td>7,50</td> <td>1,1556</td> <td>1,2423</td> <td>1,3355</td> <td>1,4356</td> <td>1,5433</td> <td>1,6590</td> <td>1,7835</td> <td>1,9172</td> <td>2,0610</td> <td>2,2156</td> <td>2,3818 </td></tr> <tr> <td>7,75</td> <td>1,1610</td> <td>1,2510</td> <td>1,3479</td> <td>1,4524</td> <td>1,5650</td> <td>1,6862</td> <td>1,8169</td> <td>1,9577</td> <td>2,1095</td> <td>2,2730</td> <td>2,4491 </td></tr> <tr> <td>8,00</td> <td>1,1664</td> <td>1,2597</td> <td>1,3605</td> <td>1,4693</td> <td>1,5869</td> <td>1,7138</td> <td>1,8509</td> <td>1,9990</td> <td>2,1589</td> <td>2,3316</td> <td>2,5182 </td></tr> <tr> <td>8,25</td> <td>1,1718</td> <td>1,2685</td> <td>1,3731</td> <td>1,4864</td> <td>1,6090</td> <td>1,7418</td> <td>1,8855</td> <td>2,0410</td> <td>2,2094</td> <td>2,3917</td> <td>2,5890 </td></tr> <tr> <td>8,50</td> <td>1,1772</td> <td>1,2773</td> <td>1,3859</td> <td>1,5037</td> <td>1,6315</td> <td>1,7701</td> <td>1,9206</td> <td>2,0839</td> <td>2,2610</td> <td>2,4532</td> <td>2,6617 </td></tr> <tr> <td>8,75</td> <td>1,1827</td> <td>1,2861</td> <td>1,3987</td> <td>1,5211</td> <td>1,6542</td> <td>1,7989</td> <td>1,9563</td> <td>2,1275</td> <td>2,3136</td> <td>2,5161</td> <td>2,7362 </td></tr> <tr> <td>9,00</td> <td>1,1881</td> <td>1,2950</td> <td>1,4116</td> <td>1,5386</td> <td>1,6771</td> <td>1,8280</td> <td>1,9926</td> <td>2,1719</td> <td>2,3674</td> <td>2,5804</td> <td>2,8127 </td></tr> <tr> <td>9,25</td> <td>1,1936</td> <td>1,3040</td> <td>1,4246</td> <td>1,5563</td> <td>1,7003</td> <td>1,8576</td> <td>2,0294</td> <td>2,2171</td> <td>2,4222</td> <td>2,6463</td> <td>2,8911 </td></tr> <tr> <td>9,50</td> <td>1,1990</td> <td>1,3129</td> <td>1,4377</td> <td>1,5742</td> <td>1,7238</td> <td>1,8876</td> <td>2,0669</td> <td>2,2632</td> <td>2,4782</td> <td>2,7137</td> <td>2,9715 </td></tr> <tr> <td>9,75</td> <td>1,2045</td> <td>1,3219</td> <td>1,4508</td> <td>1,5923</td> <td>1,7475</td> <td>1,9179</td> <td>2,1049</td> <td>2,3102</td> <td>2,5354</td> <td>2,7826</td> <td>3,0539 </td></tr> <tr> <td>10,00</td> <td>1,2100</td> <td>1,3310</td> <td>1,4641</td> <td>1,6105</td> <td>1,7716</td> <td>1,9487</td> <td>2,1436</td> <td>2,3579</td> <td>2,5937</td> <td>2,8531</td> <td>3,1384 </td></tr> <tr> <td>10,25</td> <td>1,2155</td> <td>1,3401</td> <td>1,4775</td> <td>1,6289</td> <td>1,7959</td> <td>1,9799</td> <td>2,1829</td> <td>2,4066</td> <td>2,6533</td> <td>2,9253</td> <td>3,2251 </td></tr> <tr> <td>10,50</td> <td>1,2210</td> <td>1,3492</td> <td>1,4909</td> <td>1,6474</td> <td>1,8204</td> <td>2,0116</td> <td>2,2228</td> <td>2,4562</td> <td>2,7141</td> <td>2,9991</td> <td>3,3140 </td></tr> <tr> <td>10,75</td> <td>1,2266</td> <td>1,3584</td> <td>1,5044</td> <td>1,6662</td> <td>1,8453</td> <td>2,0436</td> <td>2,2633</td> <td>2,5066</td> <td>2,7761</td> <td>3,0745</td> <td>3,4051 </td></tr> <tr> <td>11,00</td> <td>1,2321</td> <td>1,3676</td> <td>1,5181</td> <td>1,6851</td> <td>1,8704</td> <td>2,0762</td> <td>2,3045</td> <td>2,5580</td> <td>2,8394</td> <td>3,1518</td> <td>3,4985 </td></tr> <tr> <td>11,25</td> <td>1,2377</td> <td>1,3769</td> <td>1,5318</td> <td>1,7041</td> <td>1,8958</td> <td>2,1091</td> <td>2,3464</td> <td>2,6104</td> <td>2,9040</td> <td>3,2307</td> <td>3,5942 </td></tr> <tr> <td>11,50</td> <td>1,2432</td> <td>1,3862</td> <td>1,5456</td> <td>1,7234</td> <td>1,9215</td> <td>2,1425</td> <td>2,3889</td> <td>2,6636</td> <td>2,9699</td> <td>3,3115</td> <td>3,6923 </td></tr> <tr> <td>11,75</td> <td>1,2488</td> <td>1,3955</td> <td>1,5595</td> <td>1,7428</td> <td>1,9475</td> <td>2,1764</td> <td>2,4321</td> <td>2,7179</td> <td>3,0372</td> <td>3,3941</td> <td>3,7929 </td></tr> <tr> <td>12,00</td> <td>1,2544</td> <td>1,4049</td> <td>1,5735</td> <td>1,7623</td> <td>1,9738</td> <td>2,2107</td> <td>2,4760</td> <td>2,7731</td> <td>3,1058</td> <td>3,4785</td> <td>3,8960 </td></tr> <tr> <td>12,25</td> <td>1,2600</td> <td>1,4144</td> <td>1,5876</td> <td>1,7821</td> <td>2,0004</td> <td>2,2455</td> <td>2,5205</td> <td>2,8293</td> <td>3,1759</td> <td>3,5649</td> <td>4,0016 </td></tr> <tr> <td>12,50</td> <td>1,2656</td> <td>1,4238</td> <td>1,6018</td> <td>1,8020</td> <td>2,0273</td> <td>2,2807</td> <td>2,5658</td> <td>2,8865</td> <td>3,2473</td> <td>3,6532</td> <td>4,1099 </td></tr> <tr> <td>12,75</td> <td>1,2713</td> <td>1,4333</td> <td>1,6161</td> <td>1,8221</td> <td>2,0545</td> <td>2,3164</td> <td>2,6118</td> <td>2,9448</td> <td>3,3202</td> <td>3,7435</td> <td>4,2208 </td></tr> <tr> <td>13,00</td> <td>1,2769</td> <td>1,4429</td> <td>1,6305</td> <td>1,8424</td> <td>2,0820</td> <td>2,3526</td> <td>2,6584</td> <td>3,0040</td> <td>3,3946</td> <td>3,8359</td> <td>4,3345 </td></tr> <tr> <td>13,25</td> <td>1,2826</td> <td>1,4525</td> <td>1,6450</td> <td>1,8629</td> <td>2,1097</td> <td>2,3893</td> <td>2,7059</td> <td>3,0644</td> <td>3,4704</td> <td>3,9303</td> <td>4,4510 </td></tr> <tr> <td>13,50</td> <td>1,2882</td> <td>1,4621</td> <td>1,6595</td> <td>1,8836</td> <td>2,1378</td> <td>2,4264</td> <td>2,7540</td> <td>3,1258</td> <td>3,5478</td> <td>4,0267</td> <td>4,5704 </td></tr> <tr> <td>13,75</td> <td>1,2939</td> <td>1,4718</td> <td>1,6742</td> <td>1,9044</td> <td>2,1662</td> <td>2,4641</td> <td>2,8029</td> <td>3,1883</td> <td>3,6267</td> <td>4,1254</td> <td>4,6926 </td></tr> <tr> <td>14,00</td> <td>1,2996</td> <td>1,4815</td> <td>1,6890</td> <td>1,9254</td> <td>2,1950</td> <td>2,5023</td> <td>2,8526</td> <td>3,2519</td> <td>3,7072</td> <td>4,2262</td> <td>4,8179 </td></tr> <tr> <td>14,25</td> <td>1,3053</td> <td>1,4913</td> <td>1,7038</td> <td>1,9466</td> <td>2,2240</td> <td>2,5409</td> <td>2,9030</td> <td>3,3167</td> <td>3,7893</td> <td>4,3293</td> <td>4,9462 </td></tr> <tr> <td>14,50</td> <td>1,3110</td> <td>1,5011</td> <td>1,7188</td> <td>1,9680</td> <td>2,2534</td> <td>2,5801</td> <td>2,9542</td> <td>3,3826</td> <td>3,8731</td> <td>4,4347</td> <td>5,0777 </td></tr> <tr> <td>14,75</td> <td>1,3168</td> <td>1,5110</td> <td>1,7338</td> <td>1,9896</td> <td>2,2831</td> <td>2,6198</td> <td>3,0062</td> <td>3,4496</td> <td>3,9585</td> <td>4,5423</td> <td>5,2123 </td></tr> <tr> <td>15,00</td> <td>1,3225</td> <td>1,5209</td> <td>1,7490</td> <td>2,0114</td> <td>2,3131</td> <td>2,6600</td> <td>3,0590</td> <td>3,5179</td> <td>4,0456</td> <td>4,6524</td> <td>5,3503 </td></tr> <tr> <td>15,25</td> <td>1,3283</td> <td>1,5308</td> <td>1,7643</td> <td>2,0333</td> <td>2,3434</td> <td>2,7008</td> <td>3,1126</td> <td>3,5873</td> <td>4,1344</td> <td>4,7649</td> <td>5,4915 </td></tr> <tr> <td>15,50</td> <td>1,3340</td> <td>1,5408</td> <td>1,7796</td> <td>2,0555</td> <td>2,3741</td> <td>2,7420</td> <td>3,1671</td> <td>3,6580</td> <td>4,2249</td> <td>4,8798</td> <td>5,6362 </td></tr> <tr> <td>15,75</td> <td>1,3398</td> <td>1,5508</td> <td>1,7951</td> <td>2,0778</td> <td>2,4051</td> <td>2,7839</td> <td>3,2223</td> <td>3,7298</td> <td>4,3173</td> <td>4,9972</td> <td>5,7843 </td></tr> <tr> <td>16,00</td> <td>1,3456</td> <td>1,5609</td> <td>1,8106</td> <td>2,1003</td> <td>2,4364</td> <td>2,8262</td> <td>3,2784</td> <td>3,8030</td> <td>4,4114</td> <td>5,1173</td> <td>5,9360 </td></tr> <tr> <td>16,25</td> <td>1,3514</td> <td>1,5710</td> <td>1,8263</td> <td>2,1231</td> <td>2,4681</td> <td>2,8691</td> <td>3,3354</td> <td>3,8774</td> <td>4,5074</td> <td>5,2399</td> <td>6,0914 </td></tr> <tr> <td>16,50</td> <td>1,3572</td> <td>1,5812</td> <td>1,8421</td> <td>2,1460</td> <td>2,5001</td> <td>2,9126</td> <td>3,3932</td> <td>3,9531</td> <td>4,6053</td> <td>5,3652</td> <td>6,2504 </td></tr> <tr> <td>16,75</td> <td>1,3631</td> <td>1,5914</td> <td>1,8579</td> <td>2,1691</td> <td>2,5325</td> <td>2,9566</td> <td>3,4519</td> <td>4,0301</td> <td>4,7051</td> <td>5,4932</td> <td>6,4133 </td></tr> <tr> <td>17,00</td> <td>1,3689</td> <td>1,6016</td> <td>1,8739</td> <td>2,1924</td> <td>2,5652</td> <td>3,0012</td> <td>3,5115</td> <td>4,1084</td> <td>4,8068</td> <td>5,6240</td> <td>6,5801 </td></tr> <tr> <td>17,25</td> <td>1,3748</td> <td>1,6119</td> <td>1,8900</td> <td>2,2160</td> <td>2,5982</td> <td>3,0464</td> <td>3,5719</td> <td>4,1881</td> <td>4,9105</td> <td>5,7576</td> <td>6,7508 </td></tr> <tr> <td>17,50</td> <td>1,3806</td> <td>1,6222</td> <td>1,9061</td> <td>2,2397</td> <td>2,6316</td> <td>3,0922</td> <td>3,6333</td> <td>4,2691</td> <td>5,0162</td> <td>5,8941</td> <td>6,9256 </td></tr> <tr> <td>17,75</td> <td>1,3865</td> <td>1,6326</td> <td>1,9224</td> <td>2,2636</td> <td>2,6654</td> <td>3,1385</td> <td>3,6956</td> <td>4,3516</td> <td>5,1240</td> <td>6,0335</td> <td>7,1045 </td></tr> <tr> <td>18,00</td> <td>1,3924</td> <td>1,6430</td> <td>1,9388</td> <td>2,2878</td> <td>2,6996</td> <td>3,1855</td> <td>3,7589</td> <td>4,4355</td> <td>5,2338</td> <td>6,1759</td> <td>7,2876 </td></tr> <tr> <td>18,25</td> <td>1,3983</td> <td>1,6535</td> <td>1,9553</td> <td>2,3121</td> <td>2,7341</td> <td>3,2330</td> <td>3,8230</td> <td>4,5207</td> <td>5,3458</td> <td>6,3214</td> <td>7,4750 </td></tr> <tr> <td>18,50</td> <td>1,4042</td> <td>1,6640</td> <td>1,9718</td> <td>2,3366</td> <td>2,7689</td> <td>3,2812</td> <td>3,8882</td> <td>4,6075</td> <td>5,4599</td> <td>6,4700</td> <td>7,6669 </td></tr> <tr> <td>18,75</td> <td>1,4102</td> <td>1,6746</td> <td>1,9885</td> <td>2,3614</td> <td>2,8042</td> <td>3,3299</td> <td>3,9543</td> <td>4,6957</td> <td>5,5762</td> <td>6,6217</td> <td>7,8633 </td></tr> <tr> <td>19,00</td> <td>1,4161</td> <td>1,6852</td> <td>2,0053</td> <td>2,3864</td> <td>2,8398</td> <td>3,3793</td> <td>4,0214</td> <td>4,7854</td> <td>5,6947</td> <td>6,7767</td> <td>8,0642 </td></tr> <tr> <td>19,25</td> <td>1,4221</td> <td>1,6958</td> <td>2,0222</td> <td>2,4115</td> <td>2,8757</td> <td>3,4293</td> <td>4,0895</td> <td>4,8767</td> <td>5,8155</td> <td>6,9349</td> <td>8,2699 </td></tr> <tr> <td>19,50</td> <td>1,4280</td> <td>1,7065</td> <td>2,0393</td> <td>2,4369</td> <td>2,9121</td> <td>3,4800</td> <td>4,1586</td> <td>4,9695</td> <td>5,9385</td> <td>7,0965</td> <td>8,4804 </td></tr> <tr> <td>19,75</td> <td>1,4340</td> <td>1,7172</td> <td>2,0564</td> <td>2,4625</td> <td>2,9489</td> <td>3,5313</td> <td>4,2287</td> <td>5,0638</td> <td>6,0639</td> <td>7,2616</td> <td>8,6957 </td></tr> <tr> <td>20,00</td> <td>1,4400</td> <td>1,7280</td> <td>2,0736</td> <td>2,4883</td> <td>2,9860</td> <td>3,5832</td> <td>4,2998</td> <td>5,1598</td> <td>6,1917</td> <td>7,4301</td> <td>8,9161 </td></tr> <tr> <td>20,25</td> <td>1,4460</td> <td>1,7388</td> <td>2,0909</td> <td>2,5143</td> <td>3,0235</td> <td>3,6358</td> <td>4,3720</td> <td>5,2573</td> <td>6,3219</td> <td>7,6021</td> <td>9,1416 </td></tr> <tr> <td>20,50</td> <td>1,4520</td> <td>1,7497</td> <td>2,1084</td> <td>2,5406</td> <td>3,0614</td> <td>3,6890</td> <td>4,4453</td> <td>5,3565</td> <td>6,4546</td> <td>7,7778</td> <td>9,3723 </td></tr> <tr> <td>20,75</td> <td>1,4581</td> <td>1,7606</td> <td>2,1259</td> <td>2,5671</td> <td>3,0997</td> <td>3,7429</td> <td>4,5196</td> <td>5,4574</td> <td>6,5898</td> <td>7,9572</td> <td>9,6083 </td></tr> <tr> <td>21,00</td> <td>1,4641</td> <td>1,7716</td> <td>2,1436</td> <td>2,5937</td> <td>3,1384</td> <td>3,7975</td> <td>4,5950</td> <td>5,5599</td> <td>6,7275</td> <td>8,1403</td> <td>9,8497 </td></tr> <tr> <td>21,25</td> <td>1,4702</td> <td>1,7826</td> <td>2,1614</td> <td>2,6206</td> <td>3,1775</td> <td>3,8528</td> <td>4,6715</td> <td>5,6642</td> <td>6,8678</td> <td>8,3272</td> <td>10,0967 </td></tr> <tr> <td>21,50</td> <td>1,4762</td> <td>1,7936</td> <td>2,1792</td> <td>2,6478</td> <td>3,2170</td> <td>3,9087</td> <td>4,7491</td> <td>5,7701</td> <td>7,0107</td> <td>8,5180</td> <td>10,3494 </td></tr> <tr> <td>21,75</td> <td>1,4823</td> <td>1,8047</td> <td>2,1972</td> <td>2,6751</td> <td>3,2570</td> <td>3,9654</td> <td>4,8278</td> <td>5,8779</td> <td>7,1563</td> <td>8,7128</td> <td>10,6079 </td></tr> <tr> <td>22,00</td> <td>1,4884</td> <td>1,8158</td> <td>2,2153</td> <td>2,7027</td> <td>3,2973</td> <td>4,0227</td> <td>4,9077</td> <td>5,9874</td> <td>7,3046</td> <td>8,9117</td> <td>10,8722 </td></tr> <tr> <td>22,25</td> <td>1,4945</td> <td>1,8270</td> <td>2,2335</td> <td>2,7305</td> <td>3,3381</td> <td>4,0808</td> <td>4,9887</td> <td>6,0987</td> <td>7,4557</td> <td>9,1146</td> <td>11,1426 </td></tr> <tr> <td>22,50</td> <td>1,5006</td> <td>1,8383</td> <td>2,2519</td> <td>2,7585</td> <td>3,3792</td> <td>4,1395</td> <td>5,0709</td> <td>6,2119</td> <td>7,6096</td> <td>9,3217</td> <td>11,4191 </td></tr> <tr> <td>22,75</td> <td>1,5068</td> <td>1,8495</td> <td>2,2703</td> <td>2,7868</td> <td>3,4208</td> <td>4,1990</td> <td>5,1543</td> <td>6,3269</td> <td>7,7663</td> <td>9,5332</td> <td>11,7019 </td></tr> <tr> <td>23,00</td> <td>1,5129</td> <td>1,8609</td> <td>2,2889</td> <td>2,8153</td> <td>3,4628</td> <td>4,2593</td> <td>5,2389</td> <td>6,4439</td> <td>7,9259</td> <td>9,7489</td> <td>11,9912 </td></tr> <tr> <td>23,25</td> <td>1,5191</td> <td>1,8722</td> <td>2,3075</td> <td>2,8440</td> <td>3,5053</td> <td>4,3202</td> <td>5,3247</td> <td>6,5627</td> <td>8,0885</td> <td>9,9691</td> <td>12,2869 </td></tr> <tr> <td>23,50</td> <td>1,5252</td> <td>1,8837</td> <td>2,3263</td> <td>2,8730</td> <td>3,5481</td> <td>4,3820</td> <td>5,4117</td> <td>6,6835</td> <td>8,2541</td> <td>10,1938</td> <td>12,5894 </td></tr> <tr> <td>23,75</td> <td>1,5314</td> <td>1,8951</td> <td>2,3452</td> <td>2,9022</td> <td>3,5915</td> <td>4,4444</td> <td>5,5000</td> <td>6,8062</td> <td>8,4227</td> <td>10,4231</td> <td>12,8986 </td></tr> <tr> <td>24,00</td> <td>1,5376</td> <td>1,9066</td> <td>2,3642</td> <td>2,9316</td> <td>3,6352</td> <td>4,5077</td> <td>5,5895</td> <td>6,9310</td> <td>8,5944</td> <td>10,6571</td> <td>13,2148 </td></tr> <tr> <td>24,25</td> <td>1,5438</td> <td>1,9182</td> <td>2,3833</td> <td>2,9613</td> <td>3,6794</td> <td>4,5717</td> <td>5,6803</td> <td>7,0578</td> <td>8,7693</td> <td>10,8958</td> <td>13,5381 </td></tr> <tr> <td>24,50</td> <td>1,5500</td> <td>1,9298</td> <td>2,4026</td> <td>2,9912</td> <td>3,7241</td> <td>4,6364</td> <td>5,7724</td> <td>7,1866</td> <td>8,9473</td> <td>11,1394</td> <td>13,8686 </td></tr> <tr> <td>24,75</td> <td>1,5563</td> <td>1,9414</td> <td>2,4219</td> <td>3,0214</td> <td>3,7691</td> <td>4,7020</td> <td>5,8658</td> <td>7,3175</td> <td>9,1286</td> <td>11,3880</td> <td>14,2065 </td></tr> <tr> <td>25,00</td> <td>1,5625</td> <td>1,9531</td> <td>2,4414</td> <td>3,0518</td> <td>3,8147</td> <td>4,7684</td> <td>5,9605</td> <td>7,4506</td> <td>9,3132</td> <td>11,6415</td> <td>14,5519 </td></tr> <tr> <td>25,25</td> <td>1,5688</td> <td>1,9649</td> <td>2,4610</td> <td>3,0824</td> <td>3,8607</td> <td>4,8355</td> <td>6,0565</td> <td>7,5858</td> <td>9,5012</td> <td>11,9002</td> <td>14,9050 </td></tr> <tr> <td>25,50</td> <td>1,5750</td> <td>1,9767</td> <td>2,4807</td> <td>3,1133</td> <td>3,9072</td> <td>4,9035</td> <td>6,1539</td> <td>7,7231</td> <td>9,6925</td> <td>12,1641</td> <td>15,2660 </td></tr> <tr> <td>25,75</td> <td>1,5813</td> <td>1,9885</td> <td>2,5005</td> <td>3,1444</td> <td>3,9541</td> <td>4,9723</td> <td>6,2526</td> <td>7,8627</td> <td>9,8874</td> <td>12,4333</td> <td>15,6349 </td></tr> <tr> <td>26,00</td> <td>1,5876</td> <td>2,0004</td> <td>2,5205</td> <td>3,1758</td> <td>4,0015</td> <td>5,0419</td> <td>6,3528</td> <td>8,0045</td> <td>10,0857</td> <td>12,7080</td> <td>16,0120 </td></tr> <tr> <td>26,25</td> <td>1,5939</td> <td>2,0123</td> <td>2,5405</td> <td>3,2074</td> <td>4,0494</td> <td>5,1123</td> <td>6,4543</td> <td>8,1486</td> <td>10,2876</td> <td>12,9881</td> <td>16,3975 </td></tr> <tr> <td>26,50</td> <td>1,6002</td> <td>2,0243</td> <td>2,5607</td> <td>3,2393</td> <td>4,0977</td> <td>5,1836</td> <td>6,5573</td> <td>8,2950</td> <td>10,4931</td> <td>13,2738</td> <td>16,7914 </td></tr> <tr> <td>26,75</td> <td>1,6066</td> <td>2,0363</td> <td>2,5810</td> <td>3,2714</td> <td>4,1466</td> <td>5,2558</td> <td>6,6617</td> <td>8,4437</td> <td>10,7024</td> <td>13,5652</td> <td>17,1939 </td></tr> <tr> <td>27,00</td> <td>1,6129</td> <td>2,0484</td> <td>2,6014</td> <td>3,3038</td> <td>4,1959</td> <td>5,3288</td> <td>6,7675</td> <td>8,5948</td> <td>10,9153</td> <td>13,8625</td> <td>17,6053 </td></tr> <tr> <td>27,25</td> <td>1,6193</td> <td>2,0605</td> <td>2,6220</td> <td>3,3365</td> <td>4,2457</td> <td>5,4026</td> <td>6,8748</td> <td>8,7482</td> <td>11,1321</td> <td>14,1656</td> <td>18,0258 </td></tr> <tr> <td>27,50</td> <td>1,6256</td> <td>2,0727</td> <td>2,6427</td> <td>3,3694</td> <td>4,2960</td> <td>5,4774</td> <td>6,9836</td> <td>8,9041</td> <td>11,3528</td> <td>14,4748</td> <td>18,4553 </td></tr> <tr> <td>27,75</td> <td>1,6320</td> <td>2,0849</td> <td>2,6634</td> <td>3,4026</td> <td>4,3468</td> <td>5,5530</td> <td>7,0939</td> <td>9,0625</td> <td>11,5773</td> <td>14,7901</td> <td>18,8943 </td></tr> <tr> <td>28,00</td> <td>1,6384</td> <td>2,0972</td> <td>2,6844</td> <td>3,4360</td> <td>4,3980</td> <td>5,6295</td> <td>7,2058</td> <td>9,2234</td> <td>11,8059</td> <td>15,1116</td> <td>19,3428 </td></tr> <tr> <td>28,25</td> <td>1,6448</td> <td>2,1095</td> <td>2,7054</td> <td>3,4697</td> <td>4,4498</td> <td>5,7069</td> <td>7,3191</td> <td>9,3868</td> <td>12,0385</td> <td>15,4394</td> <td>19,8011 </td></tr> <tr> <td>28,50</td> <td>1,6512</td> <td>2,1218</td> <td>2,7265</td> <td>3,5036</td> <td>4,5021</td> <td>5,7852</td> <td>7,4340</td> <td>9,5527</td> <td>12,2753</td> <td>15,7737</td> <td>20,2692 </td></tr> <tr> <td>28,75</td> <td>1,6577</td> <td>2,1342</td> <td>2,7478</td> <td>3,5378</td> <td>4,5549</td> <td>5,8645</td> <td>7,5505</td> <td>9,7213</td> <td>12,5162</td> <td>16,1146</td> <td>20,7476 </td></tr> <tr> <td>29,00</td> <td>1,6641</td> <td>2,1467</td> <td>2,7692</td> <td>3,5723</td> <td>4,6083</td> <td>5,9447</td> <td>7,6686</td> <td>9,8925</td> <td>12,7614</td> <td>16,4622</td> <td>21,2362 </td></tr> <tr> <td>29,25</td> <td>1,6706</td> <td>2,1592</td> <td>2,7908</td> <td>3,6071</td> <td>4,6621</td> <td>6,0258</td> <td>7,7883</td> <td>10,0664</td> <td>13,0108</td> <td>16,8165</td> <td>21,7353 </td></tr> <tr> <td>29,50</td> <td>1,6770</td> <td>2,1717</td> <td>2,8124</td> <td>3,6421</td> <td>4,7165</td> <td>6,1079</td> <td>7,9097</td> <td>10,2430</td> <td>13,2647</td> <td>17,1778</td> <td>22,2452 </td></tr> <tr> <td>29,75</td> <td>1,6835</td> <td>2,1843</td> <td>2,8342</td> <td>3,6774</td> <td>4,7714</td> <td>6,1909</td> <td>8,0327</td> <td>10,4224</td> <td>13,5230</td> <td>17,5461</td> <td>22,7661 </td></tr> <tr> <td>30,00</td> <td>1,6900</td> <td>2,1970</td> <td>2,8561</td> <td>3,7129</td> <td>4,8268</td> <td>6,2749</td> <td>8,1573</td> <td>10,6045</td> <td>13,7858</td> <td>17,9216</td> <td>23,2981 </td></tr> <tr> <td>30,25</td> <td>1,6965</td> <td>2,2097</td> <td>2,8781</td> <td>3,7488</td> <td>4,8828</td> <td>6,3598</td> <td>8,2837</td> <td>10,7895</td> <td>14,0533</td> <td>18,3044</td> <td>23,8415 </td></tr> <tr> <td>30,50</td> <td>1,7030</td> <td>2,2224</td> <td>2,9003</td> <td>3,7849</td> <td>4,9393</td> <td>6,4458</td> <td>8,4117</td> <td>10,9773</td> <td>14,3253</td> <td>18,6946</td> <td>24,3964 </td></tr> <tr> <td>30,75</td> <td>1,7096</td> <td>2,2352</td> <td>2,9226</td> <td>3,8213</td> <td>4,9963</td> <td>6,5327</td> <td>8,5415</td> <td>11,1680</td> <td>14,6022</td> <td>19,0923</td> <td>24,9632 </td></tr> <tr> <td>31,00</td> <td>1,7161</td> <td>2,2481</td> <td>2,9450</td> <td>3,8579</td> <td>5,0539</td> <td>6,6206</td> <td>8,6730</td> <td>11,3617</td> <td>14,8838</td> <td>19,4977</td> <td>25,5420 </td></tr> <tr> <td>31,25</td> <td>1,7227</td> <td>2,2610</td> <td>2,9675</td> <td>3,8949</td> <td>5,1121</td> <td>6,7096</td> <td>8,8063</td> <td>11,5583</td> <td>15,1703</td> <td>19,9110</td> <td>26,1331 </td></tr> <tr> <td>31,50</td> <td>1,7292</td> <td>2,2739</td> <td>2,9902</td> <td>3,9321</td> <td>5,1708</td> <td>6,7996</td> <td>8,9414</td> <td>11,7580</td> <td>15,4617</td> <td>20,3321</td> <td>26,7368 </td></tr> <tr> <td>31,75</td> <td>1,7358</td> <td>2,2869</td> <td>3,0130</td> <td>3,9697</td> <td>5,2300</td> <td>6,8906</td> <td>9,0783</td> <td>11,9607</td> <td>15,7582</td> <td>20,7614</td> <td>27,3532 </td></tr> <tr> <td>32,00</td> <td>1,7424</td> <td>2,3000</td> <td>3,0360</td> <td>4,0075</td> <td>5,2899</td> <td>6,9826</td> <td>9,2170</td> <td>12,1665</td> <td>16,0598</td> <td>21,1989</td> <td>27,9825 </td></tr> <tr> <td>32,25</td> <td>1,7490</td> <td>2,3131</td> <td>3,0590</td> <td>4,0456</td> <td>5,3503</td> <td>7,0757</td> <td>9,3576</td> <td>12,3755</td> <td>16,3665</td> <td>21,6447</td> <td>28,6252 </td></tr> <tr> <td>32,50</td> <td>1,7556</td> <td>2,3262</td> <td>3,0822</td> <td>4,0839</td> <td>5,4112</td> <td>7,1699</td> <td>9,5001</td> <td>12,5876</td> <td>16,6786</td> <td>22,0991</td> <td>29,2813 </td></tr> <tr> <td>32,75</td> <td>1,7623</td> <td>2,3394</td> <td>3,1055</td> <td>4,1226</td> <td>5,4728</td> <td>7,2651</td> <td>9,6444</td> <td>12,8030</td> <td>16,9959</td> <td>22,5621</td> <td>29,9512 </td></tr> <tr> <td>33,00</td> <td>1,7689</td> <td>2,3526</td> <td>3,1290</td> <td>4,1616</td> <td>5,5349</td> <td>7,3614</td> <td>9,7907</td> <td>13,0216</td> <td>17,3187</td> <td>23,0339</td> <td>30,6351 </td></tr> <tr> <td>33,25</td> <td>1,7756</td> <td>2,3659</td> <td>3,1526</td> <td>4,2008</td> <td>5,5976</td> <td>7,4588</td> <td>9,9389</td> <td>13,2436</td> <td>17,6471</td> <td>23,5147</td> <td>31,3333 </td></tr> <tr> <td>33,50</td> <td>1,7822</td> <td>2,3793</td> <td>3,1763</td> <td>4,2404</td> <td>5,6609</td> <td>7,5573</td> <td>10,0890</td> <td>13,4689</td> <td>17,9810</td> <td>24,0046</td> <td>32,0461 </td></tr> <tr> <td>33,75</td> <td>1,7889</td> <td>2,3927</td> <td>3,2002</td> <td>4,2802</td> <td>5,7248</td> <td>7,6570</td> <td>10,2412</td> <td>13,6976</td> <td>18,3205</td> <td>24,5037</td> <td>32,7737 </td></tr> <tr> <td>34,00</td> <td>1,7956</td> <td>2,4061</td> <td>3,2242</td> <td>4,3204</td> <td>5,7893</td> <td>7,7577</td> <td>10,3953</td> <td>13,9297</td> <td>18,6659</td> <td>25,0123</td> <td>33,5164 </td></tr> <tr> <td>34,25</td> <td>1,8023</td> <td>2,4196</td> <td>3,2483</td> <td>4,3609</td> <td>5,8544</td> <td>7,8596</td> <td>10,5515</td> <td>14,1654</td> <td>19,0170</td> <td>25,5304</td> <td>34,2745 </td></tr> <tr> <td>34,50</td> <td>1,8090</td> <td>2,4331</td> <td>3,2726</td> <td>4,4016</td> <td>5,9202</td> <td>7,9626</td> <td>10,7097</td> <td>14,4046</td> <td>19,3742</td> <td>26,0582</td> <td>35,0483 </td></tr> <tr> <td>34,75</td> <td>1,8158</td> <td>2,4467</td> <td>3,2970</td> <td>4,4427</td> <td>5,9865</td> <td>8,0668</td> <td>10,8700</td> <td>14,6473</td> <td>19,7373</td> <td>26,5960</td> <td>35,8381 </td></tr> <tr> <td>35,00</td> <td>1,8225</td> <td>2,4604</td> <td>3,3215</td> <td>4,4840</td> <td>6,0534</td> <td>8,1722</td> <td>11,0324</td> <td>14,8937</td> <td>20,1066</td> <td>27,1439</td> <td>36,6442 </td></tr> <tr> <td>35,25</td> <td>1,8293</td> <td>2,4741</td> <td>3,3462</td> <td>4,5257</td> <td>6,1210</td> <td>8,2787</td> <td>11,1969</td> <td>15,1438</td> <td>20,4820</td> <td>27,7019</td> <td>37,4669 </td></tr> <tr> <td>35,50</td> <td>1,8360</td> <td>2,4878</td> <td>3,3710</td> <td>4,5677</td> <td>6,1892</td> <td>8,3864</td> <td>11,3636</td> <td>15,3976</td> <td>20,8638</td> <td>28,2704</td> <td>38,3064 </td></tr> <tr> <td>35,75</td> <td>1,8428</td> <td>2,5016</td> <td>3,3959</td> <td>4,6100</td> <td>6,2581</td> <td>8,4953</td> <td>11,5324</td> <td>15,6552</td> <td>21,2519</td> <td>28,8495</td> <td>39,1632 </td></tr> <tr> <td>36,00</td> <td>1,8496</td> <td>2,5155</td> <td>3,4210</td> <td>4,6526</td> <td>6,3275</td> <td>8,6054</td> <td>11,7034</td> <td>15,9166</td> <td>21,6466</td> <td>29,4393</td> <td>40,0375 </td></tr> <tr> <td>36,25</td> <td>1,8564</td> <td>2,5294</td> <td>3,4462</td> <td>4,6955</td> <td>6,3976</td> <td>8,7168</td> <td>11,8766</td> <td>16,1819</td> <td>22,0478</td> <td>30,0401</td> <td>40,9297 </td></tr> <tr> <td>36,50</td> <td>1,8632</td> <td>2,5433</td> <td>3,4716</td> <td>4,7387</td> <td>6,4684</td> <td>8,8293</td> <td>12,0521</td> <td>16,4511</td> <td>22,4557</td> <td>30,6520</td> <td>41,8400 </td></tr> <tr> <td>36,75</td> <td>1,8701</td> <td>2,5573</td> <td>3,4971</td> <td>4,7823</td> <td>6,5398</td> <td>8,9432</td> <td>12,2298</td> <td>16,7242</td> <td>22,8704</td> <td>31,2752</td> <td>42,7689 </td></tr> <tr> <td>37,00</td> <td>1,8769</td> <td>2,5714</td> <td>3,5228</td> <td>4,8262</td> <td>6,6119</td> <td>9,0582</td> <td>12,4098</td> <td>17,0014</td> <td>23,2919</td> <td>31,9100</td> <td>43,7166 </td></tr> <tr> <td>37,25</td> <td>1,8838</td> <td>2,5855</td> <td>3,5485</td> <td>4,8704</td> <td>6,6846</td> <td>9,1746</td> <td>12,5921</td> <td>17,2827</td> <td>23,7205</td> <td>32,5564</td> <td>44,6836 </td></tr> <tr> <td>37,50</td> <td>1,8906</td> <td>2,5996</td> <td>3,5745</td> <td>4,9149</td> <td>6,7580</td> <td>9,2922</td> <td>12,7768</td> <td>17,5681</td> <td>24,1561</td> <td>33,2146</td> <td>45,6701 </td></tr> <tr> <td>37,75</td> <td>1,8975</td> <td>2,6138</td> <td>3,6005</td> <td>4,9597</td> <td>6,8320</td> <td>9,4111</td> <td>12,9638</td> <td>17,8577</td> <td>24,5989</td> <td>33,8850</td> <td>46,6766 </td></tr> <tr> <td>38,00</td> <td>1,9044</td> <td>2,6281</td> <td>3,6267</td> <td>5,0049</td> <td>6,9068</td> <td>9,5313</td> <td>13,1532</td> <td>18,1515</td> <td>25,0490</td> <td>34,5677</td> <td>47,7034 </td></tr> <tr> <td>38,25</td> <td>1,9113</td> <td>2,6424</td> <td>3,6531</td> <td>5,0504</td> <td>6,9822</td> <td>9,6529</td> <td>13,3451</td> <td>18,4496</td> <td>25,5065</td> <td>35,2628</td> <td>48,7508 </td></tr> <tr> <td>38,50</td> <td>1,9182</td> <td>2,6567</td> <td>3,6796</td> <td>5,0962</td> <td>7,0583</td> <td>9,7757</td> <td>13,5394</td> <td>18,7520</td> <td>25,9715</td> <td>35,9706</td> <td>49,8193 </td></tr> <tr> <td>38,75</td> <td>1,9252</td> <td>2,6712</td> <td>3,7062</td> <td>5,1424</td> <td>7,1351</td> <td>9,8999</td> <td>13,7361</td> <td>19,0589</td> <td>26,4442</td> <td>36,6913</td> <td>50,9092 </td></tr> <tr> <td>39,00</td> <td>1,9321</td> <td>2,6856</td> <td>3,7330</td> <td>5,1889</td> <td>7,2125</td> <td>10,0254</td> <td>13,9354</td> <td>19,3702</td> <td>26,9245</td> <td>37,4251</td> <td>52,0209 </td></tr> <tr> <td>39,25</td> <td>1,9391</td> <td>2,7001</td> <td>3,7599</td> <td>5,2357</td> <td>7,2907</td> <td>10,1523</td> <td>14,1371</td> <td>19,6860</td> <td>27,4127</td> <td>38,1722</td> <td>53,1548 </td></tr> <tr> <td>39,50</td> <td>1,9460</td> <td>2,7147</td> <td>3,7870</td> <td>5,2829</td> <td>7,3696</td> <td>10,2806</td> <td>14,3415</td> <td>20,0064</td> <td>27,9089</td> <td>38,9329</td> <td>54,3113 </td></tr> <tr> <td>39,75</td> <td>1,9530</td> <td>2,7293</td> <td>3,8142</td> <td>5,3304</td> <td>7,4492</td> <td>10,4103</td> <td>14,5484</td> <td>20,3314</td> <td>28,4131</td> <td>39,7073</td> <td>55,4909 </td></tr> <tr> <td>40,00</td> <td>1,9600</td> <td>2,7440</td> <td>3,8416</td> <td>5,3782</td> <td>7,5295</td> <td>10,5414</td> <td>14,7579</td> <td>20,6610</td> <td>28,9255</td> <td>40,4957</td> <td>56,6939 </td></tr> <tr> <td>40,25</td> <td>1,9670</td> <td>2,7587</td> <td>3,8691</td> <td>5,4264</td> <td>7,6106</td> <td>10,6738</td> <td>14,9700</td> <td>20,9955</td> <td>29,4462</td> <td>41,2982</td> <td>57,9208 </td></tr> <tr> <td>40,50</td> <td>1,9740</td> <td>2,7735</td> <td>3,8968</td> <td>5,4750</td> <td>7,6923</td> <td>10,8077</td> <td>15,1849</td> <td>21,3347</td> <td>29,9753</td> <td>42,1153</td> <td>59,1720 </td></tr> <tr> <td>40,75</td> <td>1,9811</td> <td>2,7883</td> <td>3,9246</td> <td>5,5239</td> <td>7,7748</td> <td>10,9431</td> <td>15,4024</td> <td>21,6788</td> <td>30,5129</td> <td>42,9470</td> <td>60,4478 </td></tr> <tr> <td>41,00</td> <td>1,9881</td> <td>2,8032</td> <td>3,9525</td> <td>5,5731</td> <td>7,8580</td> <td>11,0798</td> <td>15,6226</td> <td>22,0278</td> <td>31,0593</td> <td>43,7936</td> <td>61,7489 </td></tr> <tr> <td>41,25</td> <td>1,9952</td> <td>2,8182</td> <td>3,9806</td> <td>5,6227</td> <td>7,9420</td> <td>11,2181</td> <td>15,8456</td> <td>22,3819</td> <td>31,6144</td> <td>44,6553</td> <td>63,0756 </td></tr> <tr> <td>41,50</td> <td>2,0022</td> <td>2,8331</td> <td>4,0089</td> <td>5,6726</td> <td>8,0267</td> <td>11,3578</td> <td>16,0713</td> <td>22,7409</td> <td>32,1784</td> <td>45,5324</td> <td>64,4284 </td></tr> <tr> <td>41,75</td> <td>2,0093</td> <td>2,8482</td> <td>4,0373</td> <td>5,7229</td> <td>8,1122</td> <td>11,4990</td> <td>16,2999</td> <td>23,1051</td> <td>32,7515</td> <td>46,4252</td> <td>65,8077 </td></tr> <tr> <td>42,00</td> <td>2,0164</td> <td>2,8633</td> <td>4,0659</td> <td>5,7735</td> <td>8,1984</td> <td>11,6418</td> <td>16,5313</td> <td>23,4744</td> <td>33,3337</td> <td>47,3338</td> <td>67,2141 </td></tr> <tr> <td>42,25</td> <td>2,0235</td> <td>2,8784</td> <td>4,0946</td> <td>5,8245</td> <td>8,2854</td> <td>11,7860</td> <td>16,7656</td> <td>23,8490</td> <td>33,9252</td> <td>48,2586</td> <td>68,6479 </td></tr> <tr> <td>42,50</td> <td>2,0306</td> <td>2,8936</td> <td>4,1234</td> <td>5,8759</td> <td>8,3732</td> <td>11,9317</td> <td>17,0027</td> <td>24,2289</td> <td>34,5262</td> <td>49,1998</td> <td>70,1097 </td></tr> <tr> <td>42,75</td> <td>2,0378</td> <td>2,9089</td> <td>4,1525</td> <td>5,9276</td> <td>8,4617</td> <td>12,0791</td> <td>17,2428</td> <td>24,6142</td> <td>35,1367</td> <td>50,1577</td> <td>71,6001 </td></tr> <tr> <td>43,00</td> <td>2,0449</td> <td>2,9242</td> <td>4,1816</td> <td>5,9797</td> <td>8,5510</td> <td>12,2279</td> <td>17,4859</td> <td>25,0049</td> <td>35,7569</td> <td>51,1324</td> <td>73,1194 </td></tr> <tr> <td>43,25</td> <td>2,0521</td> <td>2,9396</td> <td>4,2109</td> <td>6,0322</td> <td>8,6411</td> <td>12,3783</td> <td>17,7320</td> <td>25,4011</td> <td>36,3870</td> <td>52,1244</td> <td>74,6682 </td></tr> <tr> <td>43,50</td> <td>2,0592</td> <td>2,9550</td> <td>4,2404</td> <td>6,0850</td> <td>8,7320</td> <td>12,5304</td> <td>17,9811</td> <td>25,8028</td> <td>37,0270</td> <td>53,1338</td> <td>76,2470 </td></tr> <tr> <td>43,75</td> <td>2,0664</td> <td>2,9705</td> <td>4,2700</td> <td>6,1382</td> <td>8,8236</td> <td>12,6840</td> <td>18,2332</td> <td>26,2102</td> <td>37,6772</td> <td>54,1610</td> <td>77,8564 </td></tr> <tr> <td>44,00</td> <td>2,0736</td> <td>2,9860</td> <td>4,2998</td> <td>6,1917</td> <td>8,9161</td> <td>12,8392</td> <td>18,4884</td> <td>26,6233</td> <td>38,3376</td> <td>55,2061</td> <td>79,4968 </td></tr> <tr> <td>44,25</td> <td>2,0808</td> <td>3,0016</td> <td>4,3298</td> <td>6,2457</td> <td>9,0094</td> <td>12,9960</td> <td>18,7468</td> <td>27,0422</td> <td>39,0084</td> <td>56,2696</td> <td>81,1689 </td></tr> <tr> <td>44,50</td> <td>2,0880</td> <td>3,0172</td> <td>4,3598</td> <td>6,3000</td> <td>9,1035</td> <td>13,1545</td> <td>19,0083</td> <td>27,4670</td> <td>39,6898</td> <td>57,3517</td> <td>82,8732 </td></tr> <tr> <td>44,75</td> <td>2,0953</td> <td>3,0329</td> <td>4,3901</td> <td>6,3547</td> <td>9,1984</td> <td>13,3147</td> <td>19,2730</td> <td>27,8976</td> <td>40,3818</td> <td>58,4527</td> <td>84,6102 </td></tr> <tr> <td>45,00</td> <td>2,1025</td> <td>3,0486</td> <td>4,4205</td> <td>6,4097</td> <td>9,2941</td> <td>13,4765</td> <td>19,5409</td> <td>28,3343</td> <td>41,0847</td> <td>59,5728</td> <td>86,3806 </td></tr> <tr> <td>45,25</td> <td>2,1098</td> <td>3,0644</td> <td>4,4511</td> <td>6,4652</td> <td>9,3907</td> <td>13,6400</td> <td>19,8120</td> <td>28,7770</td> <td>41,7986</td> <td>60,7124</td> <td>88,1848 </td></tr> <tr> <td>45,50</td> <td>2,1170</td> <td>3,0803</td> <td>4,4818</td> <td>6,5210</td> <td>9,4881</td> <td>13,8051</td> <td>20,0865</td> <td>29,2258</td> <td>42,5236</td> <td>61,8718</td> <td>90,0235 </td></tr> <tr> <td>45,75</td> <td>2,1243</td> <td>3,0962</td> <td>4,5127</td> <td>6,5772</td> <td>9,5863</td> <td>13,9720</td> <td>20,3643</td> <td>29,6809</td> <td>43,2599</td> <td>63,0513</td> <td>91,8973 </td></tr> <tr> <td>46,00</td> <td>2,1316</td> <td>3,1121</td> <td>4,5437</td> <td>6,6338</td> <td>9,6854</td> <td>14,1407</td> <td>20,6454</td> <td>30,1423</td> <td>44,0077</td> <td>64,2512</td> <td>93,8068 </td></tr> <tr> <td>46,25</td> <td>2,1389</td> <td>3,1282</td> <td>4,5749</td> <td>6,6908</td> <td>9,7853</td> <td>14,3110</td> <td>20,9299</td> <td>30,6100</td> <td>44,7671</td> <td>65,4719</td> <td>95,7526 </td></tr> <tr> <td>46,50</td> <td>2,1462</td> <td>3,1442</td> <td>4,6063</td> <td>6,7482</td> <td>9,8861</td> <td>14,4832</td> <td>21,2178</td> <td>31,0841</td> <td>45,5382</td> <td>66,7135</td> <td>97,7353 </td></tr> <tr> <td>46,75</td> <td>2,1536</td> <td>3,1603</td> <td>4,6378</td> <td>6,8060</td> <td>9,9878</td> <td>14,6571</td> <td>21,5092</td> <td>31,5648</td> <td>46,3213</td> <td>67,9766</td> <td>99,7556 </td></tr> <tr> <td>47,00</td> <td>2,1609</td> <td>3,1765</td> <td>4,6695</td> <td>6,8641</td> <td>10,0903</td> <td>14,8327</td> <td>21,8041</td> <td>32,0521</td> <td>47,1165</td> <td>69,2613</td> <td>101,8141 </td></tr> <tr> <td>47,25</td> <td>2,1683</td> <td>3,1928</td> <td>4,7013</td> <td>6,9227</td> <td>10,1937</td> <td>15,0102</td> <td>22,1026</td> <td>32,5460</td> <td>47,9240</td> <td>70,5681</td> <td>103,9115 </td></tr> <tr> <td>47,50</td> <td>2,1756</td> <td>3,2090</td> <td>4,7333</td> <td>6,9817</td> <td>10,2980</td> <td>15,1895</td> <td>22,4045</td> <td>33,0467</td> <td>48,7439</td> <td>71,8972</td> <td>106,0484 </td></tr> <tr> <td>47,75</td> <td>2,1830</td> <td>3,2254</td> <td>4,7655</td> <td>7,0411</td> <td>10,4032</td> <td>15,3707</td> <td>22,7101</td> <td>33,5542</td> <td>49,5764</td> <td>73,2491</td> <td>108,2256 </td></tr> <tr> <td>48,00</td> <td>2,1904</td> <td>3,2418</td> <td>4,7979</td> <td>7,1008</td> <td>10,5092</td> <td>15,5536</td> <td>23,0194</td> <td>34,0687</td> <td>50,4217</td> <td>74,6241</td> <td>110,4436 </td></tr> <tr> <td>48,25</td> <td>2,1978</td> <td>3,2582</td> <td>4,8304</td> <td>7,1610</td> <td>10,6162</td> <td>15,7385</td> <td>23,3323</td> <td>34,5901</td> <td>51,2799</td> <td>76,0224</td> <td>112,7032 </td></tr> <tr> <td>48,50</td> <td>2,2052</td> <td>3,2748</td> <td>4,8630</td> <td>7,2216</td> <td>10,7240</td> <td>15,9252</td> <td>23,6489</td> <td>35,1187</td> <td>52,1512</td> <td>77,4446</td> <td>115,0052 </td></tr> <tr> <td>48,75</td> <td>2,2127</td> <td>3,2913</td> <td>4,8958</td> <td>7,2826</td> <td>10,8328</td> <td>16,1138</td> <td>23,9693</td> <td>35,6544</td> <td>53,0359</td> <td>78,8909</td> <td>117,3502 </td></tr> <tr> <td>49,00</td> <td>2,2201</td> <td>3,3079</td> <td>4,9288</td> <td>7,3440</td> <td>10,9425</td> <td>16,3044</td> <td>24,2935</td> <td>36,1973</td> <td>53,9340</td> <td>80,3617</td> <td>119,7389 </td></tr> <tr> <td>49,25</td> <td>2,2276</td> <td>3,3246</td> <td>4,9620</td> <td>7,4058</td> <td>11,0531</td> <td>16,4968</td> <td>24,6215</td> <td>36,7476</td> <td>54,8458</td> <td>81,8574</td> <td>122,1721 </td></tr> <tr> <td>49,50</td> <td>2,2350</td> <td>3,3414</td> <td>4,9953</td> <td>7,4680</td> <td>11,1647</td> <td>16,6912</td> <td>24,9534</td> <td>37,3053</td> <td>55,7714</td> <td>83,3783</td> <td>124,6506 </td></tr> <tr> <td>49,75</td> <td>2,2425</td> <td>3,3582</td> <td>5,0288</td> <td>7,5307</td> <td>11,2772</td> <td>16,8876</td> <td>25,2892</td> <td>37,8705</td> <td>56,7111</td> <td>84,9249</td> <td>127,1751 </td></tr> <tr> <td>50,00</td> <td>2,2500</td> <td>3,3750</td> <td>5,0625</td> <td>7,5938</td> <td>11,3906</td> <td>17,0859</td> <td>25,6289</td> <td>38,4434</td> <td>57,6650</td> <td>86,4976</td> <td>129,7463 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Ver_também"><span id="Ver_tamb.C3.A9m"></span>Ver também</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=12" title="Editar secção: Ver também" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=12" title="Editar código-fonte da secção: Ver também"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Usura" title="Usura">Usura</a></li> <li><a href="/wiki/Economia" title="Economia">Economia</a></li> <li><a href="/wiki/Infla%C3%A7%C3%A3o" title="Inflação">Inflação</a></li> <li><a href="/wiki/Macroeconomia" title="Macroeconomia">Macroeconomia</a></li> <li><a href="/wiki/Matem%C3%A1tica_financeira" title="Matemática financeira">Matemática financeira</a></li> <li><a href="/wiki/Amortiza%C3%A7%C3%A3o" title="Amortização">Amortização</a></li> <li><a href="/wiki/Anatocismo" title="Anatocismo">Anatocismo</a></li> <li><a href="/wiki/Rendimento" class="mw-redirect" title="Rendimento">Rendimento</a></li> <li><a href="/wiki/Seguro" title="Seguro">Seguro</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Ligações_externas"><span id="Liga.C3.A7.C3.B5es_externas"></span>Ligações externas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Juro&veaction=edit&section=13" title="Editar secção: Ligações externas" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Juro&action=edit&section=13" title="Editar código-fonte da secção: Ligações externas"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://juroscompostos.info">Calculadora de juros compostos</a>: Site para cálculo de juros compostos com resultado em formato gráfico e tabulado.</li></ul> <h2 id="Notas_e_referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Notas_e_refer.C3.AAncias"></span>Notas e referências</h2><h3 id="Notas" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso.">Notas</h3> <div class="reflist" style="list-style-type: decimal;"></div> <div class="reflist" style="list-style-type: lower-alpha;"></div> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><a href="/wiki/356_a.C." title="356 a.C.">356 a.C.</a> Tito Lívio dá como cônsules M. Fábio Ambusto e T. Quíncio, e comenta que alguns analistas trocavam T. Quíncio por M. Popílio.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">No período de 1° de julho de 1996 a 4 de março de 1999, o Copom fixava a TBC (Taxa Básica do Banco Central). A partir de 5 de março de 1999, com a extinção da TBC, o Copom passou a divulgar a meta para a taxa Selic - para fins de política monetária. <a rel="nofollow" class="external text" href="http://www4.bcb.gov.br/pec/gci/port/focus/faq%203-copom.pdf">Boletim <i>Copom</i> (com informações até março de 2014)</a>, p. 8, nota 1.</span> </li> </ol></div></div> <div class="reflist" style="list-style-type: lower-alpha;"></div> <div class="reflist" style="list-style-type: decimal;"></div> <div class="reflist" style="list-style-type: lower-alpha;"></div> <h3 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h3> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-livio.7.18-1"><span class="mw-cite-backlink"><a href="#cite_ref-livio.7.18_1-0">↑</a></span> <span class="reference-text"><a href="/wiki/Tito_L%C3%ADvio" title="Tito Lívio">Tito Lívio</a>, <i>História de Roma</i>, vii. 18. <a rel="nofollow" class="external text" href="http://mcadams.posc.mu.edu/txt/ah/Livy/Livy07.html">[em linha]</a></span> </li> <li id="cite_note-livio.7.19-3"><span class="mw-cite-backlink"><a href="#cite_ref-livio.7.19_3-0">↑</a></span> <span class="reference-text"><a href="/wiki/Tito_L%C3%ADvio" title="Tito Lívio">Tito Lívio</a>, <i>História de Roma</i>, vii. 19.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Banco Central do Brasil - SELIC. <a rel="nofollow" class="external autonumber" href="http://www.bcb.gov.br/pt-br/#!/n/selic">[1]</a></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Banco Central do Brasil - COPOM. <a rel="nofollow" class="external autonumber" href="http://www.bcb.gov.br/htms/copom/a-hist.asp">[2]</a></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.assbandf.com.br/glossario_p.htm">Glossário da Associação dos Bancos no Distrito Federal - ASSBAN</a></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.infomoney.com.br/templates/news/view.asp?codigo=1371558&path=/investimentos/">Conheça melhor as taxas Libor e Euribor, referências às operações interbancárias</a>, por Roberto Altenhofen Pires Pereira. <i>Infomoney</i>, 7 de outubro de 2008</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://repositorio.unb.br/handle/10482/31295">IMPACTO DE LONGO PRAZO DE REFORMAS NA PREVIDÊNCIA UTILIZANDO UM MODELO DE GERAÇÕES SOBREPOSTAS</a>, acesso em 19 de abril de 2019.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.scielo.br/scielo.php?pid=S0034-71402016000400399&script=sci_arttext">A Taxa de Juros Natural e a Regra de Taylor no Brasil: 2003-2015</a>, acesso em 19 de abril de 2019.</span> </li> </ol></div></div> <div role="navigation" class="navbox" aria-labelledby="Controle_de_autoridade" style="padding:3px"><table class="nowraplinks hlist navbox-inner" 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style="width:1%;text-align:center;">Sub-disciplinas</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Economia_comportamental" title="Economia comportamental">Comportamental</a></li> <li><a href="/wiki/Economia_do_conhecimento" title="Economia do conhecimento">Conhecimento</a></li> <li><a href="/wiki/Desenvolvimento_econ%C3%B4mico" title="Desenvolvimento econômico">Desenvolvimento</a></li> <li><a href="/wiki/An%C3%A1lise_econ%C3%B4mica_do_direito" title="Análise econômica do direito">Direito e Economia</a></li> <li><a href="/wiki/Engenharia_econ%C3%B3mica" title="Engenharia económica">Engenharia Econômica</a></li> <li><a href="/wiki/Finan%C3%A7as_p%C3%BAblicas" title="Finanças públicas">Finanças públicas</a></li> <li><a href="/wiki/Geografia_econ%C3%B4mica" title="Geografia econômica">Geografia econômica</a></li> <li><a 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econômica</a></li> <li><a href="/wiki/Economia_regional" title="Economia regional">Regional</a></li> <li><a href="/wiki/Sociologia_econ%C3%B4mica" title="Sociologia econômica">Sociologia econômica</a></li> <li><a href="/wiki/Economia_do_trabalho" title="Economia do trabalho">Trabalho</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Escolas_do_pensamento_econ%C3%B4mico" title="Escolas do pensamento econômico">Escolas</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Escola_Austr%C3%ADaca" title="Escola Austríaca">Escola Austríaca</a></li> <li><a href="/wiki/Economia_cl%C3%A1ssica" title="Economia clássica">Economia clássica</a></li> <li><a href="/wiki/Economia_marxiana" title="Economia marxiana">Economia marxiana/marxista</a></li> <li><a href="/wiki/Economia_neocl%C3%A1ssica" title="Economia neoclássica">Economia neoclássica</a></li> <li><a href="/wiki/Escola_keynesiana" title="Escola keynesiana">Escola keynesiana</a></li> <li><a href="/wiki/Nova_economia_keynesiana" title="Nova economia keynesiana">Neo-keynesiana</a></li> <li><a href="/wiki/Escola_de_Chicago_(economia)" title="Escola de Chicago (economia)">Escola de Chicago</a></li> <li><a href="/wiki/Economia_pelo_lado_da_oferta" title="Economia pelo lado da oferta">Supply-side</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Ideologia_econ%C3%B4mica" title="Ideologia econômica">Ideologias</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Economia_anarquista" title="Economia anarquista">Anarquista</a></li> <li><a href="/wiki/Capitalismo" title="Capitalismo">Capitalista</a></li> <li><a href="/wiki/Corporativismo" title="Corporativismo">Corporativista</a></li> <li><a href="/wiki/Georgismo" title="Georgismo">Georgista</a></li> <li><a href="/wiki/Laissez-faire" title="Laissez-faire">Laissez-faire</a></li> <li><a href="/wiki/Mercantilismo" title="Mercantilismo">Mercantilista</a></li> <li><a href="/wiki/Economia_ortodoxa" title="Economia ortodoxa">Ortodoxa</a> e <a href="/wiki/Economia_heterodoxa" title="Economia heterodoxa">Heterodoxa</a></li> <li><a href="/wiki/Protecionismo" title="Protecionismo">Protecionista</a></li> <li><a href="/wiki/Sindicalismo" title="Sindicalismo">Sindicalista</a></li> <li><a href="/wiki/Economia_socialista" title="Economia socialista">Socialista</a></li> <li><a href="/wiki/Socialismo_de_mercado" title="Socialismo de mercado">Socialismo de mercado</a></li> <li><a href="/wiki/Terceira_via" title="Terceira via">Terceira via</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Economista" title="Economista">Economistas</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Adam_Smith" title="Adam Smith">Adam Smith</a></li> <li><a href="/wiki/David_Ricardo" title="David Ricardo">David Ricardo</a></li> <li><a href="/wiki/Friedrich_Hayek" title="Friedrich Hayek">Friedrich Hayek</a></li> <li><a href="/wiki/Henry_George" title="Henry George">Henry George</a></li> <li><a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">John Maynard Keynes</a></li> <li><a href="/wiki/Karl_Marx" title="Karl Marx">Karl Marx</a></li> <li><a href="/wiki/Ludwig_von_Mises" title="Ludwig von Mises">Ludwig von Mises</a></li> <li><a href="/wiki/Milton_Friedman" title="Milton Friedman">Milton Friedman</a></li> <li><a href="/wiki/Paul_Samuelson" title="Paul Samuelson">Paul Samuelson</a></li> <li><i><a href="/wiki/Categoria:Economistas" title="Categoria:Economistas">outros</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Relacionados</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Austeridade" title="Austeridade">Austeridade</a></li> <li><a href="/wiki/Economia_da_ci%C3%AAncia" title="Economia da ciência">Economia da ciência</a></li> <li><a href="/wiki/Economia_da_paz" title="Economia da paz">Economia da paz</a></li> <li><a href="/wiki/Economia_na_religi%C3%A3o" title="Economia na religião">Economia na religião</a></li> <li><a href="/wiki/%C3%89tica_econ%C3%B4mica" title="Ética econômica">Ética econômica</a></li> <li><a href="/wiki/Guerra_econ%C3%B4mica" title="Guerra econômica">Guerra econômica</a></li> <li><a href="/wiki/Hist%C3%B3ria_do_pensamento_econ%C3%B3mico" title="História do 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/32px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Economy" class="extiw" title="commons:Category:Economy">Commons</a></b></li></ul> </div></td></tr></tbody></table></div> <div role="navigation" class="navbox" aria-labelledby="Macroeconomia" style="padding:3px"><table class="nowraplinks hlist collapsible collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="plainlinks hlist navbar mini"><ul><li class="nv-ver"><a href="/wiki/Predefini%C3%A7%C3%A3o:Macroeconomia" title="Predefinição:Macroeconomia"><abbr title="Ver esta predefinição" style=";;background:none 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class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Economia_marxiana" title="Economia marxiana">Escola Marxiana</a></li> <li><a href="/wiki/Escola_Austr%C3%ADaca" title="Escola Austríaca">Escola Austríaca</a></li> <li><a href="/wiki/Escola_keynesiana" title="Escola keynesiana">Escola keynesiana</a></li> <li><a href="/wiki/Escola_de_Chicago_(economia)" title="Escola de Chicago (economia)">Escola de Chicago</a></li> <li><a href="/wiki/Nova_economia_keynesiana" title="Nova economia keynesiana">Neo-keynesiana</a></li> <li><a href="/wiki/Economia_neocl%C3%A1ssica" title="Economia neoclássica">Neoclássica</a></li> <li><a href="/wiki/Economia_pelo_lado_da_oferta" title="Economia pelo lado da oferta">Supply-side</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Campos</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Crescimento_econ%C3%B4mico" title="Crescimento econômico">Crescimento econômico</a></li> <li><a href="/wiki/Economia_do_desenvolvimento" title="Economia do desenvolvimento">Economia do desenvolvimento</a></li> <li><a href="/wiki/Economia_monet%C3%A1ria" title="Economia monetária">Economia monetária</a></li> <li><a href="/wiki/Economia_pol%C3%ADtica" title="Economia política">Economia política</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Conceitos</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Balan%C3%A7o_de_pagamentos" class="mw-redirect" title="Balanço de pagamentos">Balanço de pagamentos</a></li> <li><a href="/wiki/Capitalismo" title="Capitalismo">Capitalismo</a></li> <li><a href="/wiki/Choque_de_oferta" title="Choque de oferta">Choque de oferta</a></li> <li><a href="/wiki/Contabilidade_nacional" class="mw-redirect" title="Contabilidade nacional">Contabilidade nacional</a></li> <li><a href="/wiki/Dinheiro" title="Dinheiro">Dinheiro</a></li> <li><a href="/wiki/Desemprego" title="Desemprego">Desemprego</a></li> <li><a href="/wiki/Equival%C3%AAncia_ricardiana" title="Equivalência ricardiana">Equivalência ricardiana</a></li> <li><a href="/wiki/Expectativas_adaptativas" title="Expectativas adaptativas">Expectativas adaptativas</a></li> <li><a href="/wiki/Expectativas_racionais" title="Expectativas racionais">Expectativas racionais</a></li> <li><a href="/wiki/%C3%8Dndice_de_pre%C3%A7os" title="Índice de preços">Índice de preços</a></li> <li><a href="/wiki/Infla%C3%A7%C3%A3o" title="Inflação">Inflação</a></li> <li><a href="/wiki/Economia_pelo_lado_da_oferta" title="Economia pelo lado da oferta">Lado da oferta</a></li> <li><a href="/wiki/Lei_de_Gresham" title="Lei de Gresham">Lei de Gresham</a></li> <li><a href="/wiki/Metas_de_infla%C3%A7%C3%A3o" title="Metas de inflação">Metas de inflação</a></li> <li><a href="/wiki/Moeda" title="Moeda">Moeda</a></li> <li><a href="/wiki/Monetarismo" title="Monetarismo">Monetarismo</a></li> <li><a href="/wiki/Nova_economia_cl%C3%A1ssica" title="Nova economia clássica">Nova economia clássica</a></li> <li><a href="/wiki/Nova_economia_keynesiana" title="Nova economia keynesiana">Nova economia keynesiana</a></li> <li><a href="/wiki/Padr%C3%A3o-ouro" title="Padrão-ouro">Padrão-ouro</a></li> <li><a href="/wiki/Paridade_do_poder_de_compra" title="Paridade do poder de compra">Paridade do poder de compra</a></li> <li><a href="/wiki/Propens%C3%A3o_marginal_a_consumir" title="Propensão marginal a consumir">Propensão marginal a consumir</a></li> <li><a href="/wiki/Reaganomics" title="Reaganomics">Reaganomics</a></li> <li><a href="/wiki/Recess%C3%A3o" title="Recessão">Recessão</a></li> <li><a class="mw-selflink selflink">Taxa de Juros</a></li> <li><a href="/wiki/Socialismo" title="Socialismo">Socialismo</a></li> <li><a href="/wiki/Mais-valia" title="Mais-valia">Mais-valia</a></li> <li><a href="/wiki/Fetichismo_da_mercadoria" title="Fetichismo da mercadoria">Fetichismo da mercadoria</a></li> <li><a href="/wiki/Mais-trabalho" title="Mais-trabalho">Mais-trabalho</a></li> <li><a href="/wiki/Acumula%C3%A7%C3%A3o_de_capital" title="Acumulação de capital">Acumulação de capital</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Pol%C3%ADtica_econ%C3%B4mica" title="Política econômica">Políticas</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Banco_central" title="Banco central">Banco central</a></li> <li><a href="/wiki/Pol%C3%ADtica_cambial" title="Política cambial">Política cambial</a></li> <li><a href="/wiki/Pol%C3%ADtica_comercial" title="Política comercial">Política comercial</a></li> <li><a href="/wiki/Pol%C3%ADtica_or%C3%A7amental" title="Política orçamental">Política Fiscal</a></li> <li><a href="/wiki/Pol%C3%ADtica_monet%C3%A1ria" title="Política monetária">Política monetária</a></li> <li><a href="/wiki/Pol%C3%ADtica_de_rendas" title="Política de rendas">Política de rendas</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modelo_macroecon%C3%B3mico" title="Modelo macroeconómico">Modelos</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Cruz_Keynesiana" title="Cruz Keynesiana">Cruz Keynesiana</a></li> <li><a href="/wiki/Curva_de_Phillips" title="Curva de Phillips">Curva de Phillips</a></li> <li><a href="/wiki/DSGE" title="DSGE">DSGE</a></li> <li><a href="/wiki/Modelo_Arrow%E2%80%93Debreu" class="mw-redirect" title="Modelo Arrow–Debreu">Modelo Arrow–Debreu</a></li> <li><a href="/wiki/Modelo_Harrod-Domar" title="Modelo Harrod-Domar">Modelo Harrod-Domar</a></li> <li><a href="/wiki/Modelo_Mundell-Fleming" title="Modelo Mundell-Fleming">Modelo Mundell-Fleming</a></li> <li><a href="/wiki/Modelo_de_gera%C3%A7%C3%B5es_sobrepostas" title="Modelo de gerações sobrepostas">Modelo de gerações sobrepostas</a></li> <li><a href="/wiki/Modelo_de_Ramsey-Cass-Koopmans" title="Modelo de Ramsey-Cass-Koopmans">Modelo de Ramsey-Cass-Koopmans</a></li> <li><a href="/wiki/Modelo_de_Solow" title="Modelo de Solow">Modelo de Solow</a></li> <li><a href="/wiki/Modelo_IS/LM" title="Modelo IS/LM">Modelo IS/LM</a></li> <li><a href="/wiki/Modelo_OA/DA" title="Modelo OA/DA">Modelo OA/DA</a></li> <li><a href="/wiki/NAIRU" title="NAIRU">NAIRU</a></li> <li><a href="/wiki/Overshooting" title="Overshooting">Overshooting</a></li> <li><a href="/wiki/Teoria_do_ajuste" title="Teoria do ajuste">Teoria do ajuste</a></li> <li><a href="/wiki/Teoria_do_crescimento_end%C3%B3geno" title="Teoria do crescimento endógeno">Teoria do crescimento endógeno</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Teóricos</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Adam_Smith" title="Adam Smith">Adam Smith</a></li> <li><a href="/wiki/Edmund_Phelps" title="Edmund Phelps">Edmund Phelps</a></li> <li><a href="/wiki/Edward_C._Prescott" class="mw-redirect" title="Edward C. Prescott">Edward C. Prescott</a></li> <li><a href="/wiki/Friedrich_Hayek" title="Friedrich Hayek">Friedrich Hayek</a></li> <li><a href="/wiki/Joan_Robinson" title="Joan Robinson">Joan Robinson</a></li> <li><a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">John Maynard Keynes</a></li> <li><a href="/wiki/Knut_Wicksell" title="Knut Wicksell">Knut Wicksell</a></li> <li><a href="/wiki/Lawrence_Klein" class="mw-redirect" title="Lawrence Klein">Lawrence Klein</a></li> <li><a href="/wiki/Karl_Marx" title="Karl Marx">Karl Marx</a></li> <li><a href="/wiki/Martin_Feldstein" title="Martin Feldstein">Martin Feldstein</a></li> <li><a href="/wiki/Micha%C5%82_Kalecki" class="mw-redirect" title="Michał Kalecki">Michał Kalecki</a></li> <li><a href="/wiki/Milton_Friedman" title="Milton Friedman">Milton Friedman</a></li> <li><a href="/wiki/N._Gregory_Mankiw" class="mw-redirect" title="N. Gregory Mankiw">N. 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