quias as taxas de juros
compostos mensal e trimestral equivalentes a 36% a.a ?
Soluções para a tarefa
Respondido por
1
A fórmula para encontrar a taxa para períodos maiores:
![taxa\_maior=(1+taxa)^{periodo}-1 taxa\_maior=(1+taxa)^{periodo}-1](https://tex.z-dn.net/?f=taxa%5C_maior%3D%281%2Btaxa%29%5E%7Bperiodo%7D-1)
Caso queiramos encontrar a taxa para periodos menores, a fórmula é:
![taxa\_menor=\sqrt[{periodo}]{1+taxa}-1 taxa\_menor=\sqrt[{periodo}]{1+taxa}-1](https://tex.z-dn.net/?f=taxa%5C_menor%3D%5Csqrt%5B%7Bperiodo%7D%5D%7B1%2Btaxa%7D-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.) 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.)](https://tex.z-dn.net/?f=taxa%5C+mensal+%3D+%5Csqrt%5B12%5D%7B1%2B0%2C36%7D-1%5C%5C%5C%5C%0Ataxa%5C+mensal+%3D+%5Csqrt%5B12%5D%7B1%2C36%7D-1%5C%5C%5C%5C%0Ataxa%5C+mensal+%5Capprox+1%2C0259548-1%5C%5C%5C%5C%0Ataxa%5C+mensal+%5Capprox+0%2C0259548%5C+%28%5Capprox+2%2C59548%5C%25%5C+a.m.%29)
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.) 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.)](https://tex.z-dn.net/?f=taxa%5C+trimestral+%3D+%281%2B0%2C0259548%29%5E3-1%5C%5C%5C%5C%0Ataxa%5C+trimestral+%3D+%281%2C0259548%29%5E3-1%5C%5C%5C%5C%0Ataxa%5C+trimestral+%5Capprox+1%2C08-1%5C%5C%5C%5C%0Ataxa%5C+trimestral+%5Capprox+0%2C08%5C+%28%5Capprox+8%5C%25%5C+a.t.%29)
Bons estudos!
Caso queiramos encontrar a taxa para periodos menores, a fórmula é:
Encontrando a taxa mensal relativa a 36% a.a.:
A partir da taxa mensal, podemos diretamente encontrar a taxa trimestral:
Bons estudos!
Perguntas interessantes