Question

Find the amount and the compound interest on Rs 8000 for 1 year at 10% per annum, compounded half-yearly.

Answer 1

$$\begin{gathered} \mathrm{Principal},P=\mathrm{Rs}.8000 \\ \mathrm{Time},\mathit{}n\mathit{}=1\mathrm{year}=2\mathrm{half}\mathrm{years} \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{per}\mathrm{annum}=10\% \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{half}\mathrm{year},R\mathit{}=\frac{10\%}{2}=5\% \\ \mathrm{The}\mathrm{amount}\mathrm{with}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{Amount}=\mathrm{Rs}.P\times {\left(1+\frac{R}{100}\right)}^2 \\ =\mathrm{Rs}.8000\times {\left(1+\frac{5}{100}\right)}^2 \\ =\mathrm{Rs}.8000\times {\left(\frac{105}{100}\right)}^2 \\ =\mathrm{Rs}.8000\times {\left(\frac{21}{20}\right)}^2 \\ =\mathrm{Rs}.8000\times \left(\frac{21}{20}\right)\times \left(\frac{21}{20}\right) \\ =\mathrm{Rs}.\left(20\times 21\times 21\right) \\ =\mathrm{Rs}.8820 \\ \therefore \mathrm{Compound}\mathrm{interest}=\mathrm{amount}-\mathrm{principal}=\mathrm{Rs}.(8820-8000)=\mathrm{Rs}.820 \end{gathered}$$