Question:
Find the amount of Rs 4096 for 18 months at $12 \frac{1}{2} \%$ per annum, the interest being compounded semi-annually.
Solution:
Given:
$\mathrm{P}=\mathrm{Rs} 4,096$
$\mathrm{R}=12.5 \%$ p. a.
$\mathrm{n}=18$ months $=1.5$ years
We have :
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$$=\operatorname{Rs} 4,096\left(1+\frac{12.5}{200}\right)^{3}$
$=\operatorname{Rs} 4,096(1.0625)^{3}$
$=\operatorname{Rs} 4,913$
Thus, the required amount is Rs 4,913 .