Question

Calcule a taxa i de juro composto aplicado quando tem um capital de R$450,00 e gera um montante de R$506,48 durante 4 meses

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{M = C \times (1 + i)^t}\rightarrow\begin{cases}\mathsf{M = montante}\\\mathsf{C = capital}\\\mathsf{i = taxa}\\\mathsf{t = tempo}\end{cases}$

$\mathsf{506,48 = 450 \times (1 + i)^4}$

$\mathsf{(1 + i)^4 = \dfrac{506,48}{450}}$

$\mathsf{(1 + i)^4 = 1,12551}$

$\mathsf{1 + i = \sqrt[\mathsf{4}]{\mathsf{1,12551}}}$

$\mathsf{1 + i = 1,03}$

$\mathsf{i = 0,03}$

$\boxed{\boxed{\mathsf{i = 3\%\:a.m}}}$

Answer 2

$m = c.(1 + i) {}^{t}$

$506.48 = 450.(1 + i) {}^{4}$

$(1 + i) {}^{4} = \frac{506.48}{450}$

$(1 + i) {}^{4} = 1.1255111...$

$(1 + i) = \sqrt[4]{1.1255111}$

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$(1 + i) = 1.03$

$i = 1.03 - 1$

$i = 0.3 = 3\%$

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