Question

Quantas parcelas mensais de R$ 500 devem ser depositadas, `a taxa de 2% am, a fim de se constituir o montante de R$ 6706.

Answer 1

Resposta:

begin{gathered}Presta\c{c}\~ao=Montante \times \dfrac{taxa}{(1+taxa)^{periodo}-1}\\\\\\ 500=6.706 \times \dfrac{0,02}{(1+0,02)^{periodo}-1}\\\\\\ (1,02)^{periodo}-1=6.706 \times \dfrac{0,02}{500}\\\\\\ (1,02)^{periodo}=6.706 \times 0,00004+1\\\\\\ (1,02)^{periodo}=0,26824+1\\\\\\ (1,02)^{periodo}=1,26824\\\\\\ periodo = \log_{1,02}1,26824\\\\\\ periodo = \dfrac{\log 1,26824}{\log 1,02}\\\\\\ \boxed{periodo = 12\ meses}\end{gathered}