Question

Swati borrowed Rs 40960 from a bank to buy a piece of land. If the bank charges $12\frac{1}{2}\%$ per annum, compounded half-yearly, what amount will she have to pay after $1\frac{1}{2}$ years? Also, find the interest paid by her.

Answer 1

$$\begin{gathered} \mathrm{Principal},P\mathit{}=\mathrm{Rs}.40960 \\ \mathrm{Annual}\mathrm{rate}\mathrm{of}\mathrm{interest},R\mathit{}=\frac{25}{2}\% \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{half}\mathrm{year}=\frac{25}{4}\% \\ \mathrm{Time},n=1\frac{1}{2}\mathrm{years}=3\mathrm{half}\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{amount}\mathrm{with}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{given}\mathrm{by} \\ A=P\times {\left(1+\frac{R}{100}\right)}^n \\ =40960\times {\left(1+\frac{25}{100\times 4}\right)}^3 \\ =40960\times {\left(\frac{400+25}{400}\right)}^3 \\ =40960\times {\left(\frac{425}{400}\right)}^3 \\ =40960\times \left(\frac{17}{16}\right)\times \left(\frac{17}{16}\right)\times \left(\frac{17}{16}\right) \\ =\left(10\times 17\times 17\times 17\right) \\ =\mathrm{Rs}49130 \\ \mathrm{Therefore},\mathrm{compound}\mathrm{interest}=\mathrm{amount}-\mathrm{principal}=\mathrm{Rs}(49130-40960)=\mathrm{Rs}8170 \\ \mathrm{Therefore},\mathrm{Swati}\mathrm{has}\mathrm{to}\mathrm{pay}\mathrm{Rs}.49130,\mathrm{which}\mathrm{includes}\mathrm{an}\mathrm{interest}\mathrm{of}\mathrm{Rs}.8170,\mathrm{to}\mathrm{the}\mathrm{bank}\mathrm{after}1\frac{1}{2}\mathrm{years}. \end{gathered}$$