Question:
Find the compound interest on Rs 1000 at the rate of $8 \%$ per annum for $1 \frac{1}{2}$ years when interest is compounded half-yearly.
Solution:
Given:
$\mathrm{P}=\mathrm{Rs} 1,000$
$\mathrm{R}=8 \%$ p. a.
$\mathrm{n}=1.5$ years
We know that:
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{2 \mathrm{n}}$
$=1,000\left(1+\frac{8}{200}\right)^{3}$
$=1,000(1.04)^{3}$
$=\mathrm{Rs} 1,124.86$
Now,
$\mathrm{CI}=\mathrm{A}-\mathrm{P}$
$=\mathrm{Rs} 1,124.86-\mathrm{Rs} 1,000$
$=\mathrm{Rs} 124.86$