A sum of money is invested at 20% compound interest (compounded

A sum of money is invested at 20% compound interest (compounded annually). It would fetch Rs. 723 more in 2 years if interest is compounded half yearly. The sum is

Let the principal be Rs. P.
When the interest is compounded annually,

C.I. = P			1 +	R		^T	− 1
				100

C.I. = P			1 +	20		²	− 1
				100

C.I. = P			6		²	− 1
			5

C.I. = P		36	− 1
		25

C.I. = Rs.	11P
	25

When the interest is compounded half–yearly,

C.I. = P			1 +	10		⁴	− 1
				100

C.I. = P			11		⁴	− 1
			10

C.I. = P		14641	− 1
		10000

C.I. = Rs.	4641P
	10000

From the question ,

∴	4641P	−	11P	= 723
	10000		25

⇒	4641P − 4400P	= 723
	10000

⇒	241P	= 723
	10000

⇒ P =	723 × 10000	= Rs. 30000
	241