Question

quias as taxas de juros
compostos mensal e trimestral equivalentes a 36% a.a ?

Answer 1

A fórmula para encontrar a taxa para períodos maiores:

$taxa\_maior=(1+taxa)^{periodo}-1$

Caso queiramos encontrar a taxa para periodos menores, a fórmula é:

$taxa\_menor=\sqrt[{periodo}]{1+taxa}-1$


Encontrando a taxa mensal relativa a 36% a.a.:

$taxa\ mensal = \sqrt[12]{1+0,36}-1\\\\ taxa\ mensal = \sqrt[12]{1,36}-1\\\\ taxa\ mensal \approx 1,0259548-1\\\\ taxa\ mensal \approx 0,0259548\ (\approx 2,59548\%\ a.m.)$


A partir da taxa mensal, podemos diretamente encontrar a taxa trimestral:

$taxa\ trimestral = (1+0,0259548)^3-1\\\\ taxa\ trimestral = (1,0259548)^3-1\\\\ taxa\ trimestral \approx 1,08-1\\\\ taxa\ trimestral \approx 0,08\ (\approx 8\%\ a.t.)$


Bons estudos!