The sum of money which when given on compound interest at

The sum of money which when given on compound interest at 18% per annum would fetch Rs. 960 more when the interest is payable half yearly than when it was payable annually for 2 years is :

As per the given in question ,
When the interest is payable half yearly,
Rate = 9% per half annum , Time = 4 half years
Let the principal be Rs. P.

∴ C.I. = P			1 +	R		^T	− 1
				100

C.I. = P			1 +	9		⁴	− 1
				100

C.I. = P[(1.09)⁴ − 1]
C.I. = P [1.4116 – 1] = Rs. 0.4116 P
According to the question,

= P			1 +	18		²	− 1
				100

= P[(1.18)² − 1]
= P (1.3924 – 1) = Rs. 0.3924 P
According to the question,
0.4116P – 0.3924P = 960
⇒ 0.0192P = 960

⇒ P =	960
	0.0192

P =	960 × 10000	= Rs. 50000
	192