Question

Determinar a taxa mensal equivalente a uma taxa de 60% a.t. a. 16,96%a.m. b. 3,096%a.m. c. 21,37%a.m. d. 20%a.m. e. 3,91%a.m.

Answer 1

Resposta:

Alternativa A.

A taxa mensal equivalente é 16,960709529%.

Explicação passo-a-passo:

Vamos utilizar a fórmula de taxa equivalente:

$T_{Quero}= \left(\left\{\left(1+\dfrac{T_{Tenho}}{100}\right)^{\left[\dfrac{Prazo_{\ quero}}{Prazo_{\ tenho}}\right]}\right\}-1\right)\times100\\\\\\T_{Mensal}= \left(\left\{\left(1+\dfrac{T_{trimestral}}{100}\right)^{\left[\dfrac{Prazo_{\ m\^{e}s}}{Prazo_{\ trimestre}}\right]}\right\}-1\right)\times100\\\\\\T_{Mensal}= \left(\left\{\left(1+\dfrac{60}{100}\right)^{\left[\dfrac{1}{3}\right]}\right\}-1\right)\times100$

$T_{Mensal}= \left(\left\{(1+0,60)^{\left[\dfrac{1}{3}\right]}\right\}-1\right)\times100\\\\\\T_{Mensal}= \left(\left\{(1,60)^{\left[\dfrac{1}{3}\right]}\right\}-1\right)\times100\\\\\\T_{Mensal}= (1,16960709529-1)\times100\\\\T_{Mensal}= 0,16960709529\times100\\\\\boxed{\bf{T_{Mensal}= 16,960709529\%}}$

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