Question

A sum of money doubles itself in 15 years with compound interest. It will become 8 times in
1. 30 years
2. 40 years
3. 45 years
4. 60 years

Answer 1

Correct Answer - Option 3 : 45 years

Given

A sum of money doubles itself in 15 years with compound interest

Formula used

1) Amount(A) = Principal(P) × [1 + r/100]ⁿ where r = rate of interest  and n = time period

2) (a^m)ⁿ = a^{m × n}

Calculation

A sum of money doubles itself in 15 years

⇒ Amount = 2P

2P = P × (1 + r/100)¹⁵

⇒ 2 = (1 + r/100)¹⁵

On cubing both sides, we get

2³ = [(1 + r/100)¹⁵]³

⇒ 8 = (1 + r/100)⁴⁵

⇒ 8P = P × (1 + r/100)⁴⁵

∴ The sum of money becomes 8 times in 45 years