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?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sum}\mathrm{be}\mathrm{Rs}\mathrm{x}. \\ \mathrm{Given}: \\ \mathrm{A}=\mathrm{Rs}4913 \\ \mathrm{R}=12.5\% \\ \mathrm{n}=18\mathrm{months}=1.5\mathrm{years} \\ \mathrm{We}\mathrm{know}\mathrm{that}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{200}\right)}^{2\mathrm{n}} \\ 4,913=\mathrm{P}{\left(1+\frac{\mathrm{R}}{200}\right)}^{2\mathrm{n}} \\ 4,913=\mathrm{x}{\left(1+\frac{12.5}{200}\right)}^3 \\ 4,913=\mathrm{x}\left[{\left(1.0625\right)}^3\right] \\ \mathrm{x}=\frac{4,913}{1.1995} \\ =4,096 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{sum}\mathrm{is}\mathrm{Rs}4,096. \end{gathered}$$