Question

Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in an year and a half, interest being compounded six monthly.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{rate}\mathrm{percent}\mathrm{per}\mathrm{annum}\mathrm{be}\mathrm{R}. \\ \mathrm{Because}\mathrm{interest}\mathrm{is}\mathrm{compounded}\mathrm{every}\mathrm{six}\mathrm{months},\mathrm{n}\mathrm{will}\mathrm{be}3\mathrm{for}1.5\mathrm{years}. \\ \mathrm{Now}, \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{200}\right)}^{\mathrm{n}} \\ 2,315.25=2,000{\left(1+\frac{\mathrm{R}}{200}\right)}^3 \\ {\left(1+\frac{\mathrm{R}}{200}\right)}^3=\frac{2,315.25}{2,000} \\ {\left(1+\frac{\mathrm{R}}{200}\right)}^3=1.157625 \\ {\left(1+\frac{\mathrm{R}}{200}\right)}^3={\left(1.05\right)}^3 \\ 1+\frac{\mathrm{R}}{200}=1.05 \\ \frac{\mathrm{R}}{200}=0.05 \\ =10 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{rate}\mathrm{is}10\%\mathrm{per}\mathrm{annum}. \end{gathered}$$