Question

Find the rate percent per annum if Rs 2000 amount to Rs 2662 in $1\frac{1}{2}$ years, interest being compounded half-yearly?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{interest}\mathrm{be}\mathrm{R}\%. \\ \mathrm{Then}, \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ 2,662=2,000{\left(1+\frac{\mathrm{R}}{100}\right)}^3 \\ {\left(1+\frac{\mathrm{R}}{100}\right)}^3=\frac{2,662}{2,000} \\ {\left(1+\frac{\mathrm{R}}{100}\right)}^3=1.331 \\ {\left(1+\frac{\mathrm{R}}{100}\right)}^3={\left(1.1\right)}^3 \\ \left(1+\frac{\mathrm{R}}{100}\right)=1.1 \\ \frac{\mathrm{R}}{100}=0.1 \\ \mathrm{R}=10 \\ \mathrm{Because}\mathrm{the}\mathrm{interest}\mathrm{rate}\mathrm{is}\mathrm{being}\mathrm{compounded}\mathrm{half}-\mathrm{yearly},\mathrm{it}\mathrm{is}20\%\mathrm{per}\mathrm{annum}. \end{gathered}$$