A sum of money becomes double in 3 years at compound interest

Home » Aptitude » Compound Interest » Question

A sum of money becomes double in 3 years at compound interest compounded annually. At the same rate, in how many years will it become four times of itself ?

1. 4 years
2. 6 years
3. 6.4 years
4. 7.5 years

Correct Option: B

Given , Time = 3 years , Rate = R%
Let Principal be ₹ P and Amount = ₹ 2P
Using the given formula

A = P		1 +	R		^T
			100

According to question ,

⇒ 2 = 1		1 +	R		³
			100

On squaring both sides and multiplying by P

4P = P		1 +	R		⁶
			100

∴ Time = 6 years
Second Method to solve this question :
Here, p = 2, n₁ = 3
q = 4, n₂ = ?
∴ p^1/n₁ = q^1/n₂
⇒ 2^1/3 = 4^1/n₂
2^1/3 = (2²)^1/n₂
⇒ 2^1/3 = 2^2/n₂
Equating powers of 2 on both sides , we get

1	=	2
3	=	n₂

∴ n₂ = 6 Years