At what rate percent per annum of compound interest, will

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At what rate percent per annum of compound interest, will a sum of money become four times of itself in two years ?

1. 100%
2. 75%
3. 50%
4. 20%

Correct Option: A

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

4P = P		1 +	R		²
			100

⇒ 4 =		1 +	R		²
			100

Taking square root both sides , we get

⇒ 1 +	R	= 2
	100

⇒	R	= 1
	100

⇒ R = 100%
We can find required answer with the help of given formula :
Here, n = 4, t = 2 years
R% = (n^1/t − 1) × 100%
R% = [(4)^1/2 − 1] × 100%
R% = [2 - 1] × 100%
∴ R% = 100%