Question

Find the amount and the compound interest on Rs 12800 for 1 year at $7\frac{1}{2}\%$ per annum, compounded semi-annually.

Answer 1

$$\begin{gathered} \mathrm{Principal},P\mathit{}=\mathrm{Rs}.12800 \\ \mathrm{Annual}\mathrm{rate}\mathrm{of}\mathrm{interest},R=\frac{15}{2}\% \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{a}\mathrm{half}\mathrm{year}=\frac{1}{2}\left(\frac{15}{2}\right)\%=\frac{15}{4}\% \\ \mathrm{Time},\mathit{}n=1\mathrm{year}=2\mathrm{half}\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{amount}\mathrm{with}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{given}\mathrm{by} \\ A=P\times {\left(1+\frac{R}{100}\right)}^n \\ =12800\times {\left(1+\frac{{\displaystyle \frac{15}{4}}}{100}\right)}^2 \\ =12800\times {\left(1+\frac{15}{100\times 4}\right)}^2 \\ =12800\times {\left(\frac{400+15}{400}\right)}^2 \\ =12800\times {\left(\frac{415}{400}\right)}^2 \\ =12800\times \left(\frac{83}{80}\right)\times \left(\frac{83}{80}\right) \\ =\left(2\times 83\times 83\right) \\ =\mathrm{Rs}13778 \\ \mathrm{Therefore},\mathrm{compound}\mathrm{interest}=\mathrm{amount}-\mathrm{principal}=\mathrm{Rs}(13778-12800)=\mathrm{Rs}978 \end{gathered}$$