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 5 years. In how many years, it would amount to eight times of itself at the same rate of interest ?

1. 10 years
2. 15 years
3. 7 years
4. 20 years

Correct Option: B

Let the Principal be P and rate of interest be r%.

∴ 2 P = P		1 +	r		²
			100

⇒ 2 =		1 +	r		⁵	...(i)
			100

On cubing both sides, we get

8 =		1 +	r		¹⁵
			100

On multiplying by P both sides ,

8P = P		1 +	r		¹⁵
			100

∴ The sum will be 8 times in 15 years. i.e., Time = 15 years
We can find required answer with the help of given formula :
Here, m = 2, t = 5 years
It becomes 8 times = 2³ times
in t × n = 5 × 3 = 15 years