A man invested a sum of money at compound interest. It amounted

A man invested a sum of money at compound interest. It amounted to Rs. 2420 in 2 years and to Rs. 2662 in 3 years. Find the sum.

Given that , A₁ = Rs. 2420 , T₁ = 2 years and A₂ = Rs. 2662 , T₂ = 3 years

A = P		1 +	R		^T
			100

∴ 2420 = P		1 +	R		²	.... (i)
			100

and, 2662 = P		1 +	R		³	.... (ii)
			100

By equation (ii) ÷ (i)

2662	= 1 +	R
2420	= 1 +	100

⇒	R	=	2662	− 1
	100		2420

⇒	R	=	2662 - 2420
	100		2420

⇒	R	=	242	=	1
	100		2420		10

⇒ R = 10% per annum.
From equation (i),

2420 = P		1 +	10		²
			100

⇒ 2420 = P		11		²
		10

⇒ 2420 = P ×	121
	100

⇒ P =	2420 × 100	= Rs. 2000
	121