What is the compound interest on a sum of ₹7500 for $$2\frac{3}{4}$$years at 8% p.a., the interest being compounded yearly? (nearest to an integer)

Principal sum $$P$$ = Rs. 7500

Rate of interest = $$r=8\%$$ and time period = $$t=2\frac{3}{4}$$ years

Amount when compounded annually (time in fraction) = $$P\times(1+\frac{r}{100})^t\times(1+\frac{\frac{3}{4}r}{100})$$     {$$\because$$ time in mixed fraction is $$\frac{3}{4}$$}

= $$7500\times(1+\frac{8}{100})^2\times(1+\frac{3\times8}{400})$$

= $$7500\times(\frac{729}{625})\times(\frac{53}{50})$$

= $$12\times729\times\frac{53}{50}=9272.88$$

$$\therefore$$ Compound interest = $$9272.88-7500=1772.88\approx Rs.$$ $$1773$$

=> Ans - (B)