Question:
Find the amount and the compound interest on Rs 8000 for $1 \frac{1}{2}$ years at $10 \%$ per annum, compounded half-yearly.
Solution:
Given:
$\mathrm{P}=\mathrm{Rs} 8,000$
$\mathrm{R}=10 \%$ p. a.
$\mathrm{n}=1.5$ years
When compounded half - yearly, we have:
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{2 \mathrm{n}}$
$=\operatorname{Rs} 8,000\left(1+\frac{10}{200}\right)^{3}$
$=\operatorname{Rs} 8,000(1.05)^{3}$
$=\operatorname{Rs} 9,261$
Also,
$\mathrm{CI}=\mathrm{A}-\mathrm{P}$
$=\operatorname{Rs} 9,261-\operatorname{Rs} 8,000$
$=\operatorname{Rs} 1,261$