Question

Qual o montante produzido por um capital de R$ 2.000,00, aplicado a juros compostos de 2% ao mês, durante meio ano: M= C + J

Answer 1

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Resposta correta:

• $\large~~{~~\boxed{\boxed{\begin{array}{lr}\displaystyle{\green{~ M \approx 2{.}536{,}48 ~ }}\end{array}}}}$

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$\underline{\underline{\overline{\overline{\begin{gathered}\boxed{\begin{array}{l} \\\sf\begin{gathered}\large\textsf{\textbf{\underline{Calculo:}}}\end{gathered} \\\ ~ \\\ {\Large{\displaystyle{M= C + J \: \rightarrow{\begin{array}{|lll} \\ \text{Capital [c]} &=& 2{.}000{,}00 \\ \text{Taxa [i]} &=& 2\% \: \text{a{.}m{.}} &=& \frac{2}{100} = 0{,}02 \\ \text{Tempo [n]} &=& 1 \: \text{ano} = 12 \: \text{meses}\end{array}}}}} & \\ \\ {\large{\displaystyle{M = C (1+i)^{12}}}} \\ \\ {\large{\displaystyle{M = 2000{,}00 (1 + 0{,}02)^{12} }}} \\ \\{\large{\displaystyle{M = 2000{,}00 \times 1{,}02^{12} }}} \\ \\{\large{\displaystyle{M = 2000{,}00 \times \left(\frac{51}{50} \right)^{12} }}} \\ \\{\large{\displaystyle{M = 2000{,}00 \times \frac{51 \: ^{12}}{50 \: ^{12}} }}} \\ \\{\large{\displaystyle{M = \frac{ 2000{,}00 \times 51 \: ^{12} }{50 \: ^{12} } }}} \\ \\ { \: \: ~ \: \Large{\displaystyle{ = M \approx 2{.}536{,}48}}}\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\end{array}}\end{gathered}}}}}$

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$~~~~~~~~~~~\bf Att.$

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