A certain sum, invested at 4% per annum compound interest,

A certain sum, invested at 4% per annum compound interest, compounded halfyearly, amounts to ₹ 7,803 at the end of one year. The sum is

Let the sum be P.
As, the interest is compounded half-yearly,
∴ R = 2%, T = 2 half years , A = ₹ 7,803

∴ A = P		1 +	R		^T
			100

⇒ 7803 = P		1 +	2		²
			100

⇒ 7803 = P		1 +	1		²
			50

⇒ 7803 = P ×	51	×	51
	50		50

⇒ P =	7803 × 50 × 50	= ₹ 7500
	51 × 51