Question

Após quanto tempo, à taxa de 4% a.m., a aplicação de R$1000,00 renderá juros de R$ 170,00 no sistema de juros compostos ? Dados : log 1,170 =0,068 e log 1,04 = 0,0170 R= 4 meses

Answer 1

Explicação passo-a-passo:

C= 1 000

j = 170

M = C + j = 1 000 + 170 = 1 170 >>>

i = 4% a m = 4 /100 = 0,04

M = C * ( 1 + i)^t

1170 = 1 000 ( 1 + 0,04 )^t

1 170 = 1 000 * 1,04^t

1170/1000 = 1,04^t

1,17 = 1,04^t

t * log 1,04 = log 1,17

t * 0,0170 = 0,068

t = 0,068 / 0,0170

t = 4meses >>>>resposta

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

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

$\mathsf{1.170 = 1.000 \times (1 + 0,04)^{t}}$

$\mathsf{1.170 = 1.000 \times (1,04)^{t}}$

$\mathsf{(1,04)^{t} = \dfrac{1.170}{1.000}}$

$\mathsf{(1,04)^{t} = 1,17}$

$\mathsf{log\:(1,04)^{t} = log\:1,17}$

$\mathsf{t\: log\:1,04 = log\:1,17}$

$\mathsf{t = \dfrac{log\:1,17}{log\:1,04}}$

$\mathsf{t = \dfrac{0.0681858}{0.0170333}}$

$\boxed{\boxed{\mathsf{t = 4}}}\leftarrow\textsf{meses}$