Sudershan deposited Rs 32000 in a bank, where the interest is credited quarterly. If the rate of interest be 5% per annum, what amount will he receive after 6 months?

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{principal}\mathrm{amount}\mathrm{be}P=\mathrm{Rs}32000. \\ \mathrm{Annual}\mathrm{rate}\mathrm{of}\mathrm{interest},\mathit{}R=5\% \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{a}\mathrm{quarter}\mathrm{year}=\frac{5}{4}\% \\ \mathrm{Time},n=6\mathrm{months}=2\mathrm{quarter}\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{amount}\mathrm{with}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{given}\mathrm{by} \\ A=\mathrm{Rs}.\mathit{}P\mathit{}\times {\left(1+\frac{R}{100}\right)}^n \\ =\mathrm{Rs}.32000\times {\left(1+\frac{5}{100\times 4}\right)}^2 \\ =\mathrm{Rs}.32000\times {\left(\frac{400+5}{400}\right)}^2 \\ =\mathrm{Rs}.32000\times {\left(\frac{405}{400}\right)}^2 \\ =\mathrm{Rs}.32000\times {\left(\frac{81}{80}\right)}^2 \\ =\mathrm{Rs}.32000\times \left(\frac{81}{80}\right)\times \left(\frac{81}{80}\right) \\ =\mathrm{Rs}.\left(5\times 81\times 81\right) \\ =\mathrm{Rs}.32805 \\ \mathrm{Therefore},\mathrm{Sudershan}\mathrm{will}\mathrm{receive}\mathrm{an}\mathrm{amount}\mathrm{of}\mathrm{Rs}.32805\mathrm{after}6\mathrm{months}. \end{gathered}$$