Question:
Ramu borrowed Rs 15625 from a finance company to buy a scooter. If the rate of interest be $16 \%$ per annum compounded annually, what payment will he have to make after $2 \frac{1}{4}$ years?
Solution:
Given:
$\mathrm{P}=\mathrm{Rs} 15,625$
$\mathrm{R}=16 \%$ p. a.
$\mathrm{n}=2 \frac{1}{4}$ years
$\therefore$ Amount after $2 \frac{1}{4}$ years $=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{2}\left(1+\frac{\frac{1}{4}(\mathrm{R})}{100}\right)$
$=$ Rs $15,625\left(1+\frac{16}{100}\right)^{2}\left(1+\frac{\frac{16}{4}}{100}\right)$
$=$ Rs $15,625(1.16)^{2}(1.04)$
$=$ Rs 21,866
Thus, the required amount is Rs 21,866 .