Question

2. Quantas prestações mensais imediatas de R$ 500,00 devem ser colocadas, à taxa de 2% ao mês, a fim de constituir um montante de R$ 6.706,00?

Answer 1

Utilizando sistema Price:

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


Bons estudos!