Question

um capital de 1,000 e aplicado a juros mensais de 4% ao mes, gerando um montante de R$ 1.665,07. determine o tempo de aplicacao desse capital

Answer 1

C = 1.000
i = 4% a m = 4/100 = 0.04
M = C + j = 1.665.07
j = 1.665.07 - 1.000 = 665.07

1665.07 =  1000 ( 1 + 0,04)ⁿ
1665.07  = 1.000 . 1,04ⁿ
1,04ⁿ = 1.665,07/1000
1,04ⁿ =1,66507
n * log 1,04 = log 1,66507
n = 0,2214324/0,01703333
n =12,99  ou 13 m 

Answer 2

$P_f=P_i(1+x\%)^t\\\\1665.07=1000(1+4\%)^t\\\\ 1.66507=(1.04)^t\\\\\ln(1.66507)=t\ln(1.04)\\\\t=\dfrac{\ln(1.66507)}{\ln(1.04)}=12.999\approx13\ meses$