Question

Harpreet borrowed Rs 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.

Answer 1

$$\begin{gathered} \mathrm{Principal}\mathrm{amount}=\mathrm{Rs}.20000 \\ \mathrm{Simple}\mathrm{interest}=\mathrm{Rs}.\left(\frac{20000\times 2\times 12}{100}\right)=\mathrm{Rs}.4800 \\ \mathrm{The}\mathrm{compound}\mathrm{interest}\mathrm{can}\mathrm{be}\mathrm{calculated}\mathrm{as}\mathrm{follows}: \\ \mathrm{Principal}\mathrm{for}\mathrm{the}\mathrm{first}\mathrm{year}=\mathrm{Rs}.20000 \\ \mathrm{Interest}\mathrm{for}\mathrm{the}\mathrm{first}\mathrm{year}=\mathrm{Rs}.\left(\frac{20000\times 12\times 1}{100}\right)=\mathrm{Rs}.2400 \\ \mathrm{Now},\mathrm{amount}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{year}=\mathrm{Rs}.(20000+2400)=\mathrm{Rs}.22400 \\ \mathrm{Principal}\mathrm{for}\mathrm{the}\mathrm{second}\mathrm{year}=\mathrm{Rs}.22400 \\ \mathrm{Interest}\mathrm{for}\mathrm{the}\mathrm{second}\mathrm{year}=\mathrm{Rs}.\left(\frac{22400\times 12\times 1}{100}\right)=\mathrm{Rs}.2688 \\ \mathrm{Now},\mathrm{amount}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{the}\mathrm{second}\mathrm{year}=\mathrm{Rs}.(22400+2688)=\mathrm{Rs}.25088 \\ \mathrm{Hence},\mathrm{compound}\mathrm{interest}=\mathrm{Rs}.\left(25088-20000\right)=\mathrm{Rs}.5088 \\ \mathrm{Now},\mathrm{CI}-\mathrm{SI}=\mathrm{Rs}.\left(5088-4800\right)=\mathrm{Rs}.288 \\ \therefore \mathrm{The}\mathrm{amount}\mathrm{of}\mathrm{money}\mathrm{Harpreet}\mathrm{will}\mathrm{gain}\mathrm{after}\mathrm{two}\mathrm{years}\mathrm{is}\mathrm{Rs}288. \end{gathered}$$