Question

a sum of money invested @ compund interest doubles itself in 15 years.. find number of years it will become 8 times?

Answer 1

$A = P (1 + \frac{r}{100} )^{t} \\ \\ 2P = P (1 + \frac{r}{100} )^{15} ...(1)\\ \\ 8P = P (1 + \frac{r}{100} )^{T} ...(2)$

take log of both the equations
$log_e2 = 15 * log_e(1 + \frac{r}{100}) ...(3) \\ \\ log_e8 = T * log_e(1 + \frac{r}{100}) \\ 3log_e2 = T * log_e(1 + \frac{r}{100}) ...(4)$

Divide eq.(4) by eq.(3)
$3 = \frac{T}{15}$ -> T = 45

Answer
45 years

Answer 2

 2 P  = P ( 1 + r )^15

(1+r)^15 = 2            take cube on both sides

(1=r)^45 = 2³ = 8
So  P (1 - r)^45  = 8 P

SO  Principal amounts to 8 times original amount in 45 years