A sum of money was lent at 10% per annum, compounded annually,

A sum of money was lent at 10% per annum, compounded annually, for 2 years. If the interest was compounded half-yearly, he would have received ₹ 220.25 more. Find the sum.

Let the sum be ₹ P.
Here , R = 10% per annum , Time = 2 years
When compounded yearly,

amount = P		1 +	10		²	=	121	P
			100				100

When compounded half-yearly,

amount = P		1 +	5		⁴	=	194481	P
			100				160000

So, Given difference = ₹ 220.25

⇒		194481	−	121		P = 220.25
		160000		100

⇒	194481 − 193600	P = 220.25
	160000

⇒	881	P = 220.25
	160000

⇒ P =	160000	× 220.25 = ₹ 40,000.
	881