Question

Qual será o montante de R$30.000, a juros compostos de 47% ao ano, durante 4 anos e 3 meses?

Answer 1

O total de meses referente ao investimento é de:

$periodo = (4 \times 12) + 3\\\\ periodo = 48 + 3\\\\ periodo = 51\ meses$


Encontrando a taxa de juros referente a um mês:

$(1+taxa\_mensal)^{periodo}-1=taxa\_anual\\\\ (1+taxa\_mensal)^{12}-1=0,47\\\\ (1+taxa\_mensal)^{12}=0,47+1\\\\ (1+taxa\_mensal)^{12}=1,47\\\\ 1+taxa\_mensal=\sqrt[12]{1,47}\\\\ taxa\_mensal=\sqrt[12]{1,47}-1\\\\ taxa\_mensal \approx 1,032626132-1\\\\ taxa\_mensal \approx 0,032626132\ (\ \approx 3,2626132\%\ a.m.\ )$


Agora vamos encontrar o montante relativo aos 51 meses com taxa mensal de 3,2626132%:

$F\'ormula\ Juros\ Compostos:\\\\ Montante = Capital \times ( 1 + taxa )^{periodo}\\\\ Teremos:\\\\ Montante = 30000 \times ( 1 + 0,0326261 )^{51}\\\\ Montante = 30000 \times ( 1,03263 )^{51}\\\\ Montante = 30000 \times 5,1416\\\\ \boxed{Montante = R\ \ 154.248,15}$


Bons estudos!