The simple interest on a certain sum for $$3\frac{1}{2}$$ years at 10% per annum is ₹2,940. What will be the compound interest on the same sum for $$2\frac{1}{2}$$ years at the same rate when interest is compounded yearly (nearest to a rupee)?

P = principal amount

R = rate of interest

T = time

The simple interest on a certain sum for $$3\frac{1}{2}$$ years at 10% per annum is ₹2,940.

$$interest=\frac{P\times\ R\times\ T}{100}$$

$$2,940=\frac{P\times10\times3.5}{100}$$

$$2,940=\frac{35P}{100}$$

P = 8400

$$compound\ interest=8400\ of\ (100+10)\%\ of\ (100+10)\%\ of\ (100+5)\% - 8400$$

$$=8400\ of\ 110\%\ of\ 110\%\ of\ 105\% - 8400$$

$$=8400\times1.10\times1.10\ \times1.05 - 8400$$

$$=8400\times1.2705-8400$$

$$=8400\times(1.2705-1)$$

$$=8400\times 0.2705$$

= 2272.2

= ₹2,272