Question

Arun took a loan of Rs 390625 from Kuber Finance. If the company charges interest at 16% per annum, compounded quarterly, what amount will discharge his debt after one year?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{principal}\mathrm{amount}\mathrm{be}P\mathit{}=\mathrm{Rs}390625. \\ \mathrm{Annual}\mathrm{rate}\mathrm{of}\mathrm{interest},R\mathit{}=16\% \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{a}\mathrm{quarter}\mathrm{year}=\frac{16}{4}\%=4\% \\ \mathrm{Time},\mathit{}n=1\mathrm{year}=4\mathrm{quarter}\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{amount}\mathrm{with}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{given}\mathrm{by} \\ A=\mathrm{Rs}\mathit{.}\mathit{}P\times {\left(1+\frac{R}{100}\right)}^n \\ =\mathrm{Rs}.390625\times {\left(1+\frac{4}{100}\right)}^4 \\ =\mathrm{Rs}.390625\times {\left(\frac{100+4}{100}\right)}^4 \\ =\mathrm{Rs}.390625\times {\left(\frac{104}{100}\right)}^4 \\ =\mathrm{Rs}.390625\times {\left(\frac{26}{25}\right)}^4 \\ =\mathrm{Rs}.390625\times \left(\frac{26}{25}\right)\times \left(\frac{26}{25}\right)\times \left(\frac{26}{25}\right)\times \left(\frac{26}{25}\right) \\ =\mathrm{Rs}.\left(26\times 26\times 26\times 26\right) \\ =\mathrm{Rs}.456976 \\ \mathrm{Therefore},\mathrm{Arun}\mathrm{has}\mathrm{to}\mathrm{pay}\mathrm{Rs}456976\mathrm{after}1\mathrm{year}. \end{gathered}$$