At a certain rate per annum, the simple interest on a sum

At a certain rate per annum, the simple interest on a sum of money for one year is ₹ 260 and the compound interest on the same sum for two years is ₹ 540.80. The rate of interest per annum is

Here , Simple interest for 1 year = ₹ 260 , Compound interest for 2 year = ₹ 540.80
Let the principal be P and rate of interest be r% per annum.

Now, S.I. =	Principal × Time × Rate
	100

260 =	P × r × 1	....(i)
	100

C.I.= P			1 +	R		^T	− 1
				100

540.80 = P			1 +	r		²	− 1
				100

⇒ 540.80 = P		1 +	2r	+	r²	− 1
			100		10000

⇒ 540.80 =	2Pr	+	Pr²
	100		10000

⇒ 540.80 = 2 × 260 +	260.r
	100

⇒ 260r = 54080 – 52000
⇒ 260r = 2080

⇒ r =	2080	= 8%
	260