Question

Find the amount of Rs 4096 for 18 months at $12\frac{1}{2}\%$ per annum, the interest being compounded semi-annually.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs}4,096 \\ \mathrm{R}=12.5\%\mathrm{p}.\mathrm{a}. \\ \mathrm{n}=18\mathrm{months}=1.5\mathrm{years} \\ \mathrm{We}\mathrm{have}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ \mathrm{When}\mathrm{the}\mathrm{interest}\mathrm{is}\mathrm{compounded}\mathrm{semi}-\mathrm{annually},\mathrm{we}\mathrm{have}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{200}\right)}^{2\mathrm{n}} \\ =\mathrm{Rs}4,096{\left(1+\frac{12.5}{200}\right)}^3 \\ =\mathrm{Rs}4,096{\left(1.0625\right)}^3 \\ =\mathrm{Rs}4,913 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{amount}\mathrm{is}\mathrm{Rs}4,913. \end{gathered}$$