A sum of money placed at compound interest doubles itself

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A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to four times itself ?

1. 12 years
2. 13 years
3. 8 years
4. 16 years

Correct Option: C

As we know that ,

A = P		1 +	R		^T
			100

Let P be ₹ 1, then A = ₹ 2
Here , T = 4 years , Rate = R%

⇒ 2 = 1		1 +	R		⁴
			100

⇒ 2² =		1 +	R		⁸
			100

∴ Time = 8 years
Second Method to solve this question :
Here, p = 2, n₁ = 4 , q = 4, n₂ = ?
Using p^1/n₁ = q^1/n₂
⇒ (2)^1/4 = (4)^1/n₂
⇒ 2^1/4 = (2²)^1/n₂
⇒ 2^1/4 = 2^1/n₂

⇒	1	=	2
	4		n₂

⇒ n₂ = 8 years