Juros simples, compostos e cont\303\255nuos Conceito Principal
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Os juros s\303\243o o pre\303\247o pago pelo benef\303\255cio do empr\303\251stimo de dinheiro por um determinado per\303\255odo de tempo. Normalmente, o valor dos juros \303\251 expresso como uma determinada fra\303\247\303\243o ou porcentagem do valor principal do dinheiro emprestado. Quando a quantidade de tempo em que o principal \303\251 emprestado n\303\243o \303\251 conhecida com anteced\303\252ncia, os juros s\303\243o normalmente acordados para serem calculados como o produto de uma taxa de juros e o per\303\255odo de tempo, onde a taxa de juros \303\251 expressa como uma certa fra\303\247\303\243o ou porcentagem de o valor principal, por unidade de tempo.</Font></Text-field> <Text-field style="Text" layout="Normal"></Text-field> <Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Existem tr\303\252s m\303\251todos principais de cobran\303\247a de juros. Quando os juros s\303\243o pagos apenas no final do per\303\255odo do empr\303\251stimo, s\303\243o chamados de juros simples. \303\200s vezes, no entanto, os juros s\303\243o cobrados periodicamente, sempre que passa um determinado intervalo de tempo. Se os juros forem cobrados e n\303\243o pagos, aumentam efetivamente o valor do principal devido, portanto, para o pr\303\263ximo intervalo de tempo, ser\303\243o cobrados juros sobre os juros do \303\272ltimo intervalo de tempo. Esse m\303\251todo \303\251 chamado de juros compostos. Finalmente, os juros cont\303\255nuos ocorrem quando os juros s\303\243o cobrados continuamente (e constantemente adicionados ao principal).</Font></Text-field> <Text-field style="Text" layout="Normal"></Text-field> <Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Os exemplos a seguir e a demonstra\303\247\303\243o ilustram diferentes tipos de interesse e como eles podem ser \303\272teis (ou prejudiciais) para os investidores.</Font></Text-field> <Text-field bookmark="bkmrk0" style="Heading 4" layout="Heading 4"><Font bold="true" size="14">Examplo 1: Simples Juros</Font></Text-field> Suponha que Alice queira emprestar $ 1000 de um banco por um ano. O banco concorda em emprestar o dinheiro a ela, desde que ela concorde em pagar o valor original mais 10% de juros no pr\303\263ximo ano. Isso significa que ela ter\303\241 que pagar $ 1000 + (10%) \303\227 ($ 1000) = $ 1000 + $ 100 = $ 1100 no pr\303\263ximo ano. A f\303\263rmula para o valor futuro S de algum investimento com juros simples \303\251: 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 onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn\303\251 o valor principal, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn\303\251 a taxa de juros, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn \303\251 o per\303\255odo de tempo do investimento. Para este exemplo, significa: "P = $ 1000", r = 0,10 por ano e t = 1 ano. Notar que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn est\303\241 na forma decimal em vez da forma percentual. 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
<Text-field bookmark="bkmrk1" style="Heading 4" layout="Heading 4"><Font bold="true" size="14">Examplo 2: Simples Juros</Font></Text-field> Suponha que Alice queira tomar emprestado $ 1.000 por 2 anos \303\240 mesma taxa de juros simples de 10% ao ano. Aqui, "P = $ 1000", r = 0,10 por ano e agora t = 2 anos. Portanto, ao final dos 2 anos ela dever\303\241: 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
<Text-field bookmark="bkmrk2" style="Heading 4" layout="Heading 4"><Font bold="true" size="14">Examplo 3: Juros compostos</Font></Text-field> Considere o mesmo problema de Alice querendo emprestar $ 1000 do banco por 2 anos com juros de 10% ao ano. Em vez de cobrar juros simples sobre o empr\303\251stimo, o banco pode usar uma forma de c\303\241lculo de juros mais amplamente usada, os juros compostos. Juros compostos s\303\243o os juros que s\303\243o adicionados ao principal de um empr\303\251stimo, de forma que os juros adicionados tamb\303\251m rendem juros. O acr\303\251scimo de juros ao valor principal \303\251 denominado composi\303\247\303\243o. Isso significa que, no primeiro ano, voc\303\252 pode emprestar $ 1.000 e, somando os juros do primeiro ano, significa que deve ao banco $ 1.000 * (1 + 0,10) = $ 1100 no final do ano. 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JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ent\303\243o, no segundo ano, o principal devido \303\251 de $ 1100 e, subsequentemente, voc\303\252 deve ao banco juros sobre esse valor no final do prazo. 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Usando juros compostos, o banco recebe $ 10 a mais do que com juros simples. Os juros compostos tamb\303\251m podem ser usados a seu favor. A compra de certificados de investimento garantidos (GICs) ou t\303\255tulos do governo pode fazer o banco pagar juros. Os GICs pagam juros compostos, o que, como voc\303\252 ver\303\241, \303\251 muito melhor do que juros simples para investimentos.
<Text-field bookmark="bkmrk3" style="Heading 4" layout="Heading 4"><Font bold="true" size="14">Examplo 4: Juros compostos</Font></Text-field> Suponha que Bob compre um GIC do banco no valor de $ 1000 com juros de 2,5% compostos anualmente por um per\303\255odo de 12 anos. Ap\303\263s o primeiro ano, seu investimento valer\303\241: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaLUZHNi5RIn5GJ0Y1RkFGSkZMRk5GUEZSRlRGVi9GWVEmMC4wZW1GJy9GZm5GW28tRkc2LlEiJEYnRjVGQUZKRkxGTkZQRlJGVEZWRmpuRlxvLUY+NiVRJTEwMDBGJ0Y1RkFGZ24tSShtZmVuY2VkR0YkNiUtRiM2KkY9RmduLUZHNi5RIitGJ0Y1RkFGSkZMRk5GUEZSRlRGVi9GWVEsMC4yMjIyMjIyZW1GJy9GZm5GXHBGZ25GZ24tRj42JVEmMC4wMjVGJ0Y1RkFGNUZBRjVGQUZGRmduRl1vLUY+NiVRJTEwMjVGJ0Y1RkFGNUZB No pr\303\263ximo ano ele ter\303\241 2,5% de juros sobre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1RkE=, ent\303\243o: 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 A diferen\303\247a entre juros compostos e simples \303\251 de apenas $ 0,63 ap\303\263s 2 anos. Depois de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbW5HRiQ2JVEjMTJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbWlHRiQ2JlEjdGhGJy8lJ2l0YWxpY0dGNEYyRjVGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YyRjU= ano no entanto, seu investimento inicial cresceu para: 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 A f\303\263rmula geral para juros compostos ap\303\263s n per\303\255odos compostos \303\251: 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 onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn\303\251 o valor principal do dinheiro (investimento inicial) e r \303\251 a taxa de juros para cada per\303\255odo de capitaliza\303\247\303\243o na forma decimal. Isso pode ser generalizado para quaisquer per\303\255odos de tempo pagando r taxa de juros por ano da seguinte forma: 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 onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EibUYnLyUlc2l6ZUdRIzExRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNS9GOVEnbm9ybWFsRic= \303\251 o n\303\272mero de vezes que os juros s\303\243o compostos por ano.
<Text-field bookmark="bkmrk4" style="Heading 4" layout="Heading 4"><Font bold="true" size="14">Examplo 5: Composto vs. Juros Simples</Font></Text-field> Suponha que Bob compre dois GICs do banco no valor de $ 5.000 cada. Ambos ter\303\243o dura\303\247\303\243o de 3 anos e taxa de juros de 2,5% ao ano; no entanto, um paga juros simples e o outro \303\251 composto mensalmente. Ap\303\263s 3 anos, os juros simples que GIC pagar\303\241 a Bob: 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 Em contraste, os juros compostos que o GIC pagar\303\241 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 que \303\251 mais do que simples juros GIC.
<Text-field bookmark="bkmrk5" style="Heading 4" layout="Heading 4"><Font bold="true" encoding="UTF-8" size="14">Examplo 6: Juro Cont\303\255nuo </Font><Font bold="true" italic="false" size="14"> </Font></Text-field> \303\211 claro que quanto mais frequentes os per\303\255odos de capitaliza\303\247\303\243o, mais r\303\241pido crescer\303\241 o investimento. Se voc\303\252 pegar o limite quando a frequ\303\252ncia vai para o infinito (ou, de forma equivalente, como a dura\303\247\303\243o do per\303\255odo de composi\303\247\303\243o vai para zero), voc\303\252 chega a juros cont\303\255nuos. O retorno dos juros compostos continuamente \303\251 dado pela f\303\263rmula: 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 onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn \303\251 a dura\303\247\303\243o do investimento, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn \303\251 o valor principal, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn \303\251 a taxa de juros. Agora, compare os juros compostos continuamente com os juros compostos semestrais (duas vezes por ano). Suponha que a taxa de juros anual seja 5% e o valor principal seja $ 5000. Ao longo de 10 anos, os juros compostos dar\303\243o um retorno de: 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 Considerando que os juros compostos continuamente far\303\243o: 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbW5HRiQ2JVEoODI0My42MUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEifkYnRi9GMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGNUY1RjVGNUY1Ri9GMg== A composi\303\247\303\243o cont\303\255nua sempre gera mais juros do que a composi\303\247\303\243o discreta. Alguns empr\303\251stimos exigem juros cont\303\255nuos, o que os torna especialmente dif\303\255ceis de pagar se ficarem crescendo por muito tempo.
Altere os valores na tabela abaixo para comparar o quanto os v\303\241rios tipos de juros alteram o valor total ganho (ou pago) ao longo da vida do empr\303\251stimo.
Valor Principal CompoundInterest:-Slide("Principal"); $CompoundInterest:-DoPlot(); Taxa de juros anual CompoundInterest:-Slide("Rate"); CompoundInterest:-DoPlot();% Frequ\303\252ncia de composi\303\247\303\243o CompoundInterest:-Slide("Freq"); CompoundInterest:-DoPlot(); time(s) per year Dura\303\247\303\243o do Investimento CompoundInterest:-Slide("Length"); CompoundInterest:-DoPlot(); years
Final Values with: Juros Simples Juros Composo Juros Cont\303\255nuo
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