The compound interest on a sum of ₹15625 for $$2\frac{3}{4}$$ years at 16% per annum, the interest compound annually is :

Principal sum $$P$$ = Rs. 15,625

Rate of interest = $$r=16\%$$ 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 $$\frac{3}{4}$$}

= $$15,625\times(1+\frac{16}{100})^2\times(1+\frac{3\times16}{400})$$

= $$15,625\times(\frac{841}{625})\times(\frac{28}{25})$$

= $$25\times841\times\frac{28}{25}=23,548$$

$$\therefore$$ Compound interest = $$23548-15625=7923$$

=> Ans - (D)