Question

Qual será a taxa equivalente para 1% ao mês para 1 trimestre, 1 semestre e 1 ano a juros compostos?

Answer 1

Resposta:

a) A taxa equivalente é 3,0301% ao trimestre;

b) A taxa equivalente é 6,1520150601% ao semestre; e

c) A taxa equivalente é 12,682503013% ao ano.

Explicação passo-a-passo:

Taxa Equivalente, devemos utilizar a seguinte fórmula:

$T_{Quero}= \left(\left\{\left(1+\dfrac{T_{Tenho}}{100}\right)^{\left[\dfrac{Prazo_{\ quero}}{Prazo_{\ tenho}}\right]}\right\}-1\right)\times100$

1% ao mês -> 1 trimestre (3 meses)

$T_{Trimestre}= \left(\left\{\left(1+\dfrac{T_{M\^{e}s}}{100}\right)^{\left[\dfrac{Prazo_{\ Trimestre}}{Prazo_{\ M\^{e}s}}\right]}\right\}-1\right)\times100\\\\T_{Trimestre}= \left(\left\{\left(1+\dfrac{1}{100}\right)^{\left[\dfrac{3}{1}\right]}\right\}-1\right)\times100\\\\T_{Trimestre}= (\{1,01^{3}\}-1)\times100\\\\T_{Trimestre}= (1,030301-1)\times100\\\\T_{Trimestre}= 0,030301\times100\\\\\boxed{\bf{T_{Trimestre}= 3,0301\%}}$

1% ao mês -> 1 semestre (6 meses)

$T_{Semestre}= \left(\left\{\left(1+\dfrac{T_{M\^{e}s}}{100}\right)^{\left[\dfrac{Prazo_{\ Semestre}}{Prazo_{\ M\^{e}s}}\right]}\right\}-1\right)\times100\\\\T_{Semestre}= \left(\left\{\left(1+\dfrac{1}{100}\right)^{\left[\dfrac{6}{1}\right]}\right\}-1\right)\times100\\\\T_{Semestre}= (\{1,01^{6}\}-1)\times100\\\\T_{Semestre}= (1,061520150601-1)\times100\\\\T_{Semestre}= 0,061520150601\times100\\\\\boxed{\bf{T_{Semestre}=6,1520150601\%}}$

1% ao mês -> 1 ano (12 meses)

$T_{Ano}= \left(\left\{\left(1+\dfrac{T_{M\^{e}s}}{100}\right)^{\left[\dfrac{Prazo_{\ Ano}}{Prazo_{\ M\^{e}s}}\right]}\right\}-1\right)\times100\\\\T_{Ano}= \left(\left\{\left(1+\dfrac{1}{100}\right)^{\left[\dfrac{12}{1}\right]}\right\}-1\right)\times100\\\\T_{Ano}= (\{1,01^{12}\}-1)\times100\\\\T_{Ano}= (1,12682503013-1)\times100\\\\T_{Ano}= 0,12682503013\times100\\\\\boxed{\bf{T_{Ano}=12,682503013\%}}$

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