A certain amount, when put at a compound rate of interest, becomes double in 5 years. In how many years will the amount become eight times?

15 years

The correct answer is Option (4) → 15 years

Let the principal be $P$ and rate be $r$.

• After 5 years, amount doubles:

$P(1+r)^5 = 2P \Rightarrow (1+r)^5 = 2$

• To become eight times the principal:

$P(1+r)^t = 8P \Rightarrow (1+r)^t = 8$

Solve for $t$:

$(1+r)^t = 8$

But $8 = 2^3$, and $(1+r)^5 = 2$

$(1+r)^t = ((1+r)^5)^3 \Rightarrow t = 5 \times 3 = 15 \text{ years}$