Question

A sum of money invested at compound interest doubles itself in 6 years. at the same rate of interest, it will amount to eight times of itself in.

Answer 1

In 6 year = 2 times
We need 8 times it means 2³ so we will multiply this 3 in the time
6= 2
6*3 = 2³
So in the 18 year it will amount to eight times itself

Answer 2

Answer:

18 years

Step-by-step explanation:

as we know that for time $t_{1}$ money become $n_{1}$. and in time $t_{2}$ it become $n_{2}$.

so relation between them is,

$n_{2} = (n_{1})^{\frac{t_{2}}{t_{1}}}$

so

$8 = (2)^{\frac{t_{2}}{6}} \\\\2^{3}= (2)^{\frac{t_{2}}{6}}$

by comparing we get,

$3=\frac{t_{2}}{6}\\\\t_{2}=18$

it will amount to eight times of itself in 18 years.