Question

Find the amount and the compound interest on Rs 31250 for $1\frac{1}{2}$ years at 8% per annum, compounded half-yearly.

Answer 1

$$\begin{gathered} \mathrm{Principal},P\mathit{}=\mathrm{Rs}.31250 \\ \mathrm{Annual}\mathrm{rate}\mathrm{of}\mathrm{interest},R\mathit{}=8\% \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{a}\mathrm{half}\mathrm{year}=\frac{1}{2}\times 8\%=4\% \\ \mathrm{Time},\mathit{}n=1\frac{1}{2}\mathrm{years}=3\mathrm{half}\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{amount}\mathrm{with}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{A}=P\times {\left(1+\frac{R}{100}\right)}^n \\ =31250\times {\left(1+\frac{{\displaystyle 4}}{100}\right)}^3 \\ =31250\times {\left(1+\frac{1}{25}\right)}^3 \\ =31250\times {\left(\frac{25+1}{25}\right)}^3 \\ =31250\times {\left(\frac{26}{25}\right)}^3 \\ =31250\times \left(\frac{26}{25}\right)\times \left(\frac{26}{25}\right)\times \left(\frac{26}{25}\right) \\ =\mathrm{Rs}2\times 17576 \\ =\mathrm{Rs}35152 \\ \mathrm{Therefore},\mathrm{compound}\mathrm{interest}=\mathrm{amount}-\mathrm{principal}=\mathrm{Rs}(35152-31250)=\mathrm{Rs}3902 \end{gathered}$$