Question

By using the formula, find the amount and compound interest on:
Rs 9000 for 2 years 4 months at 10% per annum compounded annually.

Answer 1

$$\begin{gathered} \mathrm{Principal}\mathrm{amount},P=\mathrm{Rs}.9000 \\ \mathrm{Rate}\mathrm{of}\mathrm{interest},R=10\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Time},n=2\mathrm{years}4\mathrm{months}=2\frac{1}{3}\mathrm{years}=\frac{7}{3}\mathrm{years} \\ \mathrm{The}\mathrm{formula}\mathrm{for}the\mathrm{amount}\mathrm{including}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{given}\mathrm{below}: \\ A=\mathrm{Rs}.P\times {\left(1+\frac{R}{100}\right)}^{\mathrm{n}} \\ =\mathrm{Rs}.\left(9000\times {\left(1+\frac{10}{100}\right)}^2\times \left(1+\frac{{\displaystyle \frac{1}{3}}\times 10}{100}\right)\right) \\ =\mathrm{Rs}.\left(9000\times 1.10\times 1.10\times 1.033\right) \\ =\mathrm{Rs}.11252.9\approx 11253 \\ \mathrm{i}.\mathrm{e}.,\mathrm{the}\mathrm{amount}\mathrm{including}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{Rs}11253. \\ \therefore \mathrm{Compound}\mathrm{interest}=\mathrm{Rs}.\left(11253-9000\right)=\mathrm{Rs}.2253 \end{gathered}$$