Question:
Find the amount that David would receive if he invests Rs 8192 for 18 months at $12 \frac{1}{2} \%$ per annum, the interest being compounded half-yearly.
Solution:
Given:
$\mathrm{P}=\mathrm{Rs} 8,192$
$\mathrm{R}=12.5 \%$ p. a.
$\mathrm{n}=1.5$ years
When the interest is compounded half - yearly, we have :
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{2 \mathrm{n}}$
$=\operatorname{Rs} 8,192\left(1+\frac{12.5}{200}\right)^{3}$
$=\operatorname{Rs} 8,192(1.0625)^{3}$
$=\operatorname{Rs} 9,826$
Thus, the required amount is Rs 9,826 .