Question

Um capital de R$1500,00 esteve aplicado durante 2 meses produzindo r$ 660,00de juros compostos. Qual foi a taxa efetiva mensal aplicada ?

Answer 1

Legenda:

๏ C: Capital inicial
๏ M: Montante
๏ J: Juros
๏ i: Taxa de juros
๏ t: Tempo de aplicação
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Dados:

๏ C: R$ 1.500,00
๏ J: R$ 660,00
๏ t: 2 meses
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Substituindo na formula:

$\mathsf{M=C+J}\\\mathsf{C\cdot \left(1+i\right)^t=C+J}\\\mathsf{1500\cdot \left(1+i\right)^2=1500+660}\\\mathsf{1500\cdot \left(1+i\right)^2=2160}\\\\\mathsf{\left(1+i\right)^2=\dfrac{2160}{1500}}\\\\\mathsf{\left(1+i\right)^2=1,44}\\\\\mathsf{1+i=\sqrt{1,44}}\\\\\mathsf{1+i=1,2}\\\\\mathsf{i=1,2-1}\\\\\mathsf{i=0,2}\\\\\mathsf{i=\left(0,2\cdot 100\right)\%}\\\\\boxed{\mathsf{i=20\%\:a.m}}$