Question

Durante quanto tempo um capital de 9300 reais deve ficar aplicado a uma taxa de 1,5% ao mes para que resulte em um montante de 12090 reais

Answer 1

J = c. i . n
12,090 = 93000 . 0,015 . n
12,090 = 13,95 n
13,95 n = 12,090
n = 12,090 / 13,95
n = 8 meses e 6 dias.

Answer 2

Ae,

temos que..

$\begin{cases}C=9.300\\ taxa~i=1,5\%~a.m.=0,015\\ M=12.090\\ t=?\end{cases}$

Por juro simples temos que..

$M=C[1+(it)]\\ \dfrac{M}{C}=[1+(it)]\\\\ it= \dfrac{M}{C}-1\\\\ t= \left(\dfrac{M}{C}-1\right)\div i\\\\\\ t=\left( \dfrac{12.090}{9.300}-1\right)\div0,015\\\\ t=(1,3-1)\div0,015\\ t=0,3\div0,015\\\\ \large\boxed{t=20~meses~~ou~~1~ano~e~8~meses}$

Por juros compostos..

$M=C(1+i)^t\\ 9.300\cdot(1+0,015)^t=12.090\\\\ (1,015)^t= \dfrac{12.090}{9.300}\\\\ (1,015)^t=1,3\\ \log(1,015)^t=\log(1,3)\\ t\cdot\log(1,015)=\log(1,3)\\\\ \log(1,015)\approx0,006 ~~e~~\log(1,3)\approx0,11\\\\ t\cdot0,006=0,11\\\\ t\approx \dfrac{0,11}{0,006}\approx18,33~meses\\\\\\ \large\boxed{\approx12+6+0,33\approx1~ano~6~meses~e~10~dias}$