Question:
What sum will amount to Rs 4913 in 18 months, if the rate of interest is $12 \frac{1}{2} \%$ per annum, compounded half-yearly?
Solution:
Let the sum be Rs $\mathrm{x}$.
Given:
$\mathrm{A}=\mathrm{Rs} 4913$
$\mathrm{R}=12.5 \%$
$\mathrm{n}=18$ months $=1.5$ years
We know that:
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{2 \mathrm{n}}$
$4,913=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{2 \mathrm{n}}$
$4,913=\mathrm{x}\left(1+\frac{12.5}{200}\right)^{3}$
$4,913=\mathrm{x}\left[(1.0625)^{3}\right]$
$\mathrm{x}=\frac{4,913}{1.1995}$
$=4,096$
Thus, the required sum is Rs 4,096 .