Question

A taxa mensal de 3% equivale a que taxa anual composta? Escolha uma: a. 42,58% b. 13,28% c. 43,67% d. 37,15% e. 28,3%

Answer 1

Resposta:

Alternativa A.

A taxa anual equivalente é de 42,576088685%.

Explicação passo-a-passo:

Para resolver o exercício devemos utilizar a fórmula de taxa equivalente.

$T_{Quero}= \left(\left\{\left(1+\dfrac{T_{Tenho}}{100}\right)^{\left[\dfrac{Prazo_{\ quero}}{Prazo_{\ tenho}}\right]}\right\}-1\right)\times100\\\\\\T_{Anual}= \left(\left\{\left(1+\dfrac{T_{Mensal}}{100}\right)^{\left[\dfrac{Prazo_{\ ano}}{Prazo_{\ m\^{e}s}}\right]}\right\}-1\right)\times100\\\\\\T_{Anual}= \left(\left\{\left(1+\dfrac{3}{100}\right)^{\left[\dfrac{12}{1}\right]}\right\}-1\right)\times100\\\\\\T_{Anual}= \left(\left\{\left(1+0,03\right)^{12}\right\}-1\right)\times100$

$T_{Anual}= \left(\left\{(1,03)^{12}\right\}-1\right)\times100\\\\T_{Anual}= (1,42576088685-1)\times100\\\\T_{Anual}= 0,42576088685\times100\\\\\boxed{\bf{T_{Anual}= 42,576088685\%}}$

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Answer 2

Resposta:

42,58%

Explicação passo-a-passo:

i efe = ( 1 + i ) n - 1

i efe = ( 1 + 0,03) 12 - 1

i efe = 1.42576088685 - 1

i efe = 0,42576088685

0,42576088685 x 100 = 42,58%