Question

Um empréstimo com juros compostos de 1,2% ao mês corresponde a uma taxa anual de:

Escolha uma:

g) (1,01212 −1) × 100%

h) (1,001212 −1) × 100%

f) (1,10212 −1) × 100%

i) (1,100212 −1) × 100%

e) (1,1212 −1) × 100%
REPOSTA CORRETA ( E)

Answer 1

Resposta:

Alternativa G.

$\boxed{\bt{T_{Anual}=\left(\left\{\left(1,012\right)^{12}\right\}-1\right)\ .\ 100}}$

Explicação passo-a-passo:

Para resolver vamos utilizar a fórmula de taxa equivalente.

$T_{Quero}= \left(\left\{\left(1+\dfrac{T_{Tenho}}{100}\right)^{\left[\dfrac{Prazo_{\ quero}}{Prazo_{\ tenho}}\right]}\right\}-1\right)\ .\ 100\\\\\\T_{Anual}= \left(\left\{\left(1+\dfrac{T_{Mensal}}{100}\right)^{\left[\dfrac{Prazo_{\ ano}}{Prazo_{\ m\^{e}s}}\right]}\right\}-1\right)\ .\ 100\\\\\\T_{Anual}= \left(\left\{\left(1+\dfrac{1,2}{100}\right)^{\left[\dfrac{12}{1}\right]}\right\}-1\right)\ .\ 100$

$T_{Anual}= \left(\left\{\left(1+0,012\right)^{[12]}\right\}-1\right)\ .\ 100\\\\\\T_{Anual}= \left(\left\{\left(1,012\right)^{12}\right\}-1\right)\ .\ 100\\\\\\\boxed{\bf{T_{Anual}= \left(\left\{\left(1,012\right)^{12}\right\}-1\right)\ .\ 100\\\\}}$

Se resolvermos a expressão encontramos: 15,3894624183% ao ano, ou seja, uma taxa anual de 15,3894624183%.

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