Question:
Rahman lent Rs 16000 to Rasheed at the rate of $12 \frac{1}{2} \%$ per annum compound interest. Find the amount payable by Rasheed to Rahman after 3 years.
Solution:
Given,
$\mathrm{P}=\mathrm{Rs} 16,000$
$\mathrm{R}=12.5 \%$ p. a
$\mathrm{n}=3$ years
We know that amount $\mathrm{A}$ at the end of $\mathrm{n}$ years at the rate $\mathrm{R} \%$ per annum when the interest is compounded annually is given by $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$.
$\therefore \mathrm{A}=16,000\left(1+\frac{12.5}{100}\right)^{3}$
$=16,000(1.125)^{3}$
$=22,781.25$
Thus, the required amount is Rs $22,781.25$.