Correct Answer - Option 3 : 45 years

**Formula used:**

Amount = Principal × (1 + r/100)^{n}

**Calculation:**

Given that a sum of money doubles itself at compound interest in 15 years.

⇒ 2P = P(1 + r/100)^{15}

⇒ 2 = (1 + r/100)^{15} ----(i)

For Sum to become 8 times

⇒ 8P = P(1 + r/100)^{n}

⇒ 8 = (1 + r/100)^{n}

⇒ (2)^{3} = (1 + r/100)^{n}

⇒ {[1 + r/100]^{15}}^{3} = (1 + r/100)^{n} {From (i)}

⇒ (1 + r/100)^{45} = (1 + r/100)^{n}

⇒ n = 45

∴ Time taken = 45 years