Question

Vitória pediu emprestado a sei irmão R$ 2.400,00 a juros simples durante 10 meses. Se neste período o montante chegou a R$ 3.120,00. Qual foi a taxa de juros cobrado pelo irmão de vitória neste período?
A)2%
B)3%
C)4%
D5%

Answer 1

Vamos começar determinando o total de juros cobrados:

$Montante~=~Capital+Juros\\\\\\3120~=~2400+Juros\\\\\\Juros~=~3120-2400\\\\\\\boxed{Juros~=~720}$

Agora sim, podemos determinar a taxa de juros:

$Juros~=~Capital\times Taxa\times Periodo\\\\\\720~=~2400\times Taxa\times 10\\\\\\720~=~24000\times Taxa\\\\\\Taxa~=~\frac{720}{24000}\\\\\\\boxed{Taxa~=~0,03}\\\\\\ou,~percentualmente\\\\\\Taxa(\%)~=~Taxa\times 100\%\\\\\\Taxa(\%)~=~0,03\times 100\%\\\\\\\boxed{Taxa(\%)~=~3\%}$

Poderíamos ainda achado o mesmo resultado de forma mais direta:

$Montante~=~Capital\times (1+Taxa\times Periodo)\\\\\\3120~=~2400\times (1+Taxa\times 10)\\\\\\1+10\times Taxa~=~\frac{3120}{2400}\\\\\\Taxa~=~\dfrac{\frac{3120}{2400}-1}{10}\\\\\\\boxed{Taxa~=~0,03}$