A sum of money at compound interest doubles itself in 15

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A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in

1. 45 years
2. 48 years
3. 54 years
4. 60 years

Correct Option: A

Suppose the Principal be P and rate of interest be R%.
According to question ,

2P = P		1 +	R		¹⁵
			100

2 =		1 +	R		¹⁵
			100

Cubing on both sides, we have

8 = 1		1 +	R		⁴⁵
			100

On Multiplying by P both sides ,

8P = P		1 +	R		⁴⁵
			100

Required time = 45 years
We can find required answer with the help of given formula :
Here, m = 2, t = 15 years
It becomes 8 times = 2³ times
in t × n years= 15 × 3 = 45 years