Question

Tick (✓) the correct answer:
The compound interest on Rs 6250 at 8% per annum for 1 year, compounded half yearly, is
(a) Rs 500
(b) Rs 510
(c) Rs 550
(d) Rs 512.50

Answer 1

(b) Rs. 510

$$\begin{gathered} \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{compounded}\mathrm{half}\mathrm{yearly}=\frac{8}{2}\%=4\% \\ \mathrm{Time}=1\mathrm{year}=2\mathrm{half}\mathrm{years} \\ \mathrm{Now},A=P\times {\left(1+\frac{R}{100}\right)}^n \\ =\mathrm{Rs}.6250\times {\left(1+\frac{4}{100}\right)}^2 \\ =\mathrm{Rs}.6250\times {\left(\frac{104}{100}\right)}^2 \\ =\mathrm{Rs}.6250\times \left(\frac{26}{25}\right)\times \left(\frac{26}{25}\right) \\ =\mathrm{Rs}.\left(10\times 26\times 26\right) \\ =\mathrm{Rs}.6760 \\ \therefore \mathrm{Compound}\mathrm{interest}=\mathrm{amount}-\mathrm{principal}=\mathrm{Rs}.(6760-6250)=\mathrm{Rs}.510 \end{gathered}$$