Question

Find the amount of Rs 8000 for 2 years compounded annually and the rates being 9% per annum during the first year and 10% per annum during the second year.

Answer 1

$$\begin{gathered} \mathrm{Principal}\mathrm{amount},P=\mathrm{Rs}.8000 \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{the}\mathrm{first}\mathrm{year},p=9\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{the}\mathrm{second}\mathrm{year},q=10\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Time},n=2\mathrm{years}. \\ \mathrm{Formula}\mathrm{for}\mathrm{the}\mathrm{amount}\mathrm{including}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{for}\mathrm{the}\mathrm{first}\mathrm{year}: \\ A=\mathrm{Rs}.\left\{\mathrm{P}\times \left(1+\frac{p}{100}\right)\times \left(1+\frac{q}{100}\right)\right\} \\ =\mathrm{Rs}.\left\{8000\times \left(1+\frac{9}{100}\right)\times \left(1+\frac{10}{100}\right)\right\} \\ =\mathrm{Rs}.\left\{8000\times \left({\displaystyle \frac{109}{100}}\right)\times \left({\displaystyle \frac{110}{100}}\right)\right\} \\ =\mathrm{Rs}.\left\{8000\times \left(1.09\right)\times \left(1.1\right)\right\} \\ =\mathrm{Rs}.9592 \\ \mathrm{i}.\mathrm{e}.,\mathrm{the}\mathrm{amount}\mathrm{including}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{for}\mathrm{first}\mathrm{year}\mathrm{is}\mathrm{Rs}9592. \end{gathered}$$