On a certain sum of money, the difference between the compound

On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is ₹ 180. If the rate of interest in both the cases is 10%, then the sum is

If the interest is compounded half yearly,
Time = 2 years , Rate = 5% half yearly
Using the given formula ,

C.I. = P			1 +	R		^T	− 1
				100

C.I. = P			1 +	5		²	− 1
				100

C.I. = P			21		²	− 1
			20

C.I. =	41P
	400

S.I. =	P × R × T
	100

S.I. =	P × 10	=	P
	100		10

According to question ,
∴ C.I. - S.I. = 180

⇒	41P	−	P	= 180
	400		10

⇒	41 − 40P	= 180
	400

⇒	P	= 180
	400

⇒ P = ₹ 72000
Second Method to solve this question :
Here, C.I. – S.I. = ₹ 180
Interest is compounded half yearly ,

R =	10	= 5%, T = 2 years
	5

C.I. − S.I. = P		R		²
		100

⇒ 180 = P		5		²
		100

⇒ P = 180 × 20 × 20
P = ₹ 72000