A sum of money at compound interest amounts to thrice itself

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A sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself ?

1. 9 years
2. 27 years
3. 6 years
4. 3 years

Correct Option: C

Suppose P = ₹ 1, then A = ₹ 3 ,
Using the given formula ,

A = P		1 +	R		^T
			100

According to question ,

⇒ 3 = 1		1 +	R		³
			100

On squaring both sides, we get

⇒ 9 = 1		1 +	R		⁶
			100

∴ Time = 6 years
We can find required answer with the help of given formula :
Here, p = 3, n₁ = 3 , q = 9, n₂ = ?
Using formula ,
p^1/n₁ = q^1/n₂
⇒ (3)^1/3 = (9)^1/n₂
⇒ 3^1/3 = (3²)^1/n₂
⇒ 3^1/3 = 3^2/n₂

⇒	1	=	2
	3		n₂

⇒ n₂ = 6 years