Question

Divakaran deposited a sum of Rs 6250 in the Allahabad Bank for 1 year, compounded half-yearly at 8% per annum. Find the compound interest he gets.

Answer 1

$$\begin{gathered} \mathrm{Principal}\mathrm{amount}=\mathrm{Rs}.6250 \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}=8\%\mathrm{per}\mathrm{annum}=4\%\mathrm{for}\mathrm{half}\mathrm{year} \\ \mathrm{Time}=1\mathrm{year}=2\mathrm{half}\mathrm{years} \\ \mathrm{Principal}\mathrm{for}\mathrm{the}\mathrm{first}\mathrm{half}\mathrm{year}=\mathrm{Rs}.6250 \\ \mathrm{Interest}\mathrm{for}\mathrm{the}\mathrm{first}\mathrm{half}\mathrm{year}=\mathrm{Rs}.\left(\frac{6250\times 4\times 1}{100}\right)=\mathrm{Rs}.250 \\ \mathrm{Now},\mathrm{amount}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{half}\mathrm{year}=\mathrm{Rs}.(6250+250)=\mathrm{Rs}.6500 \\ \mathrm{Principal}\mathrm{for}\mathrm{the}\mathrm{second}\mathrm{half}\mathrm{year}=\mathrm{Rs}.6500 \\ \mathrm{Interest}\mathrm{for}\mathrm{the}\mathrm{second}\mathrm{half}\mathrm{year}=\mathrm{Rs}.\left(\frac{6500\times 4\times 1}{100}\right)=\mathrm{Rs}.260 \\ \mathrm{Now},\mathrm{amount}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{the}\mathrm{second}\mathrm{half}\mathrm{year}=\mathrm{Rs}(6500+260)=\mathrm{Rs}.6760 \\ \therefore \mathrm{Compound}\mathrm{interest}=\mathrm{Rs}\left(6760-6250\right)=\mathrm{Rs}510 \\ \mathrm{Hence},\mathrm{Divakaran}\mathrm{gets}\mathrm{a}\mathrm{compound}\mathrm{interest}\mathrm{of}\mathrm{Rs}510. \end{gathered}$$