Question

A que taxa mensal de juros compostos devo aplicar, por 63 dias, R$ 40.000,00 para resgatar R$ 52.917,00. *

14,25%a.m.
17,25%a.m.
12,25%a.m.
19,25%a.m.
11,25%a.m. ​

Answer 1

Olá!!

Dados

C = 40000

M = 52917

n = 63 dias

i = ?

Fórmula

M = C (1+i)^t

52917 = 40000 . (1 + i)⁶³ ← Trocando membro

(1 + i)⁶³ = 52917/40000 ← Dividindo e tirando raiz

1 + i = ⁶³√1,322925 ← Fazendo

1 + i = 1,00445 ← Trocando termo

i = 1,00445 - 1 ← Subtraindo

i = 0,00445 = 14,25%am ← Resposta

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{M = C \:.\: (1 + i)^t}\rightarrow\begin{cases}\mathsf{M = montante}\\\mathsf{C = capital}\\\mathsf{i = taxa}\\\mathsf{t = tempo}\end{cases}$

$\mathsf{52.917 = 40.000 \:.\: (1 + i)^{\frac{21}{10}}}$

$\mathsf{(1 + i)^{\frac{21}{10}} = \dfrac{52.917}{40.000}}$

$\mathsf{(1 + i)^{\frac{21}{10}} = 1,322925}$

$\mathsf{1 + i = \sqrt[\textsf{2,1}]{\mathsf{1,322925}}}$

$\mathsf{1 + i = 1,14254}$

$\mathsf{i = 0,14254}$

$\boxed{\boxed{\mathsf{i = 14.25\%\:a.m}}}$