Question

Qual a taxa que deverá ser aplicada a quantia de R$3000,00 para em 5 meses, a juros compostos, o montante seja de R$4500,00? A) 6% a.m. B) 6,98%a.m. C) 7,2%a.m. D) 8,45%a.m. E) 9,4%a.m.

Answer 1

Explicação passo-a-passo:

Juros Compostos

$\sf{ M~=~ C*(1 + i)^t }$

$\sf{ 45\cancel{00}~=~30\cancel{00}*(1 + i)^5 }$

$\sf{ (1 + i)^5~=~ \dfrac{45}{30} }$

$\sf{ (1 + i)^5~=~\dfrac{3}{2} }$

$\sf{ 5\log(1 + i)~=~\log(1,5) }$

$\sf{ \log(1 + i)~=~ \dfrac{0,1760}{5}~=~0,0352 }$

$\sf{ 10^{0,352}~=~1 + i }$

$\sf{ 1 + i~=~1,0845 }$

$\sf{ i ~=~1,0845 - 1~=~0,0845 }$ multiplicar por: 100%

$\sf{ i~=~ 0,0845 * 100\% }$

$\pink{ \boxed{ \sf{ i~=~8,45\% a.m} } }$

Alternativa D)