Question

Tick (✓) the correct answer:
The compound interest on Rs 40000 at 6% per annum for 6 months, compounded quarterly, is
(a) Rs 1209
(b) Rs 1902
(c) Rs 1200
(d) Rs 1306

Answer 1

(a) Rs.1209

$$\begin{gathered} \mathrm{Time}=6\mathrm{months}=2\mathrm{quater}\mathrm{years} \\ \mathrm{Rate}\mathrm{compounded}\mathrm{quarter}\mathrm{yearly}=\frac{6}{4}\%=\frac{3}{2}\% \\ \mathrm{Now},A=P\times {\left(1+\frac{R}{100}\right)}^n \\ =\mathrm{Rs}.40000\times {\left(1+\frac{3}{100\times 2}\right)}^2 \\ =\mathrm{Rs}.40000\times {\left(\frac{203}{200}\right)}^2 \\ =\mathrm{Rs}.40000\times \left(\frac{203}{200}\right)\times \left(\frac{203}{200}\right) \\ =\mathrm{Rs}.\left(203\times 203\right) \\ =\mathrm{Rs}.41209 \\ \therefore \mathrm{Compound}\mathrm{interest}=\mathrm{amount}-\mathrm{principal}=\mathrm{Rs}.41209-\mathrm{Rs}.40000=\mathrm{Rs}.1209 \end{gathered}$$