Question:
Simple interest on a sum of money for 2 years at $6 \frac{1}{2} \%$ per annum is Rs 5200 . What will be the compound interest on the sum at the same rate for the same period?
Solution:
P=\frac{S I \times 100}{R T}
$\therefore P=\frac{5,200 \times 100}{6.5 \times 2}$
= 40,000
Now,
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$
$=40,000\left(1+\frac{6.5}{100}\right)^{2}$
$=40,000(1.065)^{2}$
$=45,369$
Also,
$\mathrm{CI}=\mathrm{A}-\mathrm{P}$
$=45,369-40,000$
$=5,369$
Thus, the required compound interest is Rs 5,369 .