Question

em quanto tempo um capital de 34.000,00, empregado a uma taxa de 10% ao ano rendeu 13.600,00 de juro ?

Answer 1

Dados:

$\begin{cases}C=34.000\\ i=10\% ~a.a.=10/100=0,1\\ J=13.600\\ M=J+C=13.600+34.000=47.600\\ t=?\end{cases}$

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Juros simples..

$J=Cit\Rightarrow t= \dfrac{J}{Ci}\\\\ t= \dfrac{13.600}{34.000\cdot0,1}= \dfrac{13.600}{3.400}=4~anos$

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Juros Compostos..

$M=C(1+i)^t\\ 47.600=34.000\cdot(1+0,1)^t\\\\ (1,1)^t= \dfrac{47.600}{34.000}\\\\ (1,1)^t=1,4\\ \log(1,1)^t=\log(1,4)\\\\ \log(1,1)=0,0414~~e~~\log(1,4)=0,1461\\\\ t\cdot\log(1,1)=\log(1,4)\\ t\cdot0,0414=0,1461\\\\ t= \dfrac{0,1461}{0,0414}\\\\ \Large\boxed{t\approx3,5~~ou~~3~anos~e~meio}$