The difference between the compound interest (compounded

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The difference between the compound interest (compounded annually) and the simple interest on a sum of ₹ 1000 at a certain rate of interest for 2 years is ₹ 10. The rate of interest per annum is :

1. 5%
2. 6%
3. 10%
4. 12%

Correct Option: D

Given that , Difference between C.I. and S.I. = ₹ 10 , sum ( P ) = ₹ 1000 , Time = 2 years , Rate = r%
When difference between the compound interest and simple interest on a certain sum of money for 2 years at r% rate is x, then

Difference between C.I. and S.I. = Sum		r		²
		100

⇒ 10 = 1000		r		²
		100

⇒		r		²	=	10
		100				100

⇒	r	=	√	1	=	1
	100			100		10

⇒ r =	100	= 10%
	10

Second Method :
Here, C.I. – S.I. = Rs. 10, R = ?, T= 2 years, P = Rs. 1000

C.I. − S.I. = P		R		²
		100

10 = 1000		R		²
		100

10 = 1000 ×	R	×	R
	100		100

⇒ R² = 100
⇒ R = √100 = 10%