Question

Tick (✓) the correct answer:
The compound interest on Rs 4000 at 10% per annum for 2 years 3 months, compounded annually, is
(a) Rs 916
(b) Rs 900
(c) Rs 961
(d) Rs 896

Answer 1

(c) Rs 961

$$\begin{gathered} \mathrm{Here},A\mathit{}=P\mathit{}\times {\left(1+\frac{R}{100}\right)}^2\times \left(1+\frac{{\displaystyle \frac{1}{4}}R}{100}\right) \\ =\mathrm{Rs}.4000\times {\left(1+\frac{10}{100}\right)}^2\times \left(1+\frac{{\displaystyle \frac{1}{4}}\times 10}{100}\right) \\ =\mathrm{Rs}.4000\times {\left(\frac{100+10}{100}\right)}^2\times \left(\frac{40+1}{40}\right) \\ =\mathrm{Rs}.4000\times {\left(\frac{110}{100}\right)}^2\times \left(\frac{41}{40}\right) \\ =\mathrm{Rs}.4000\times \left(\frac{11}{10}\right)\times \left(\frac{11}{10}\right)\times \left(\frac{41}{40}\right) \\ =\mathrm{Rs}.\left(11\times 11\times 41\right) \\ =\mathrm{Rs}.4961 \\ \therefore \mathrm{Compound}\mathrm{interest}=\mathrm{amount}-\mathrm{principal}=\mathrm{Rs}(4961-4000)=\mathrm{Rs}961 \end{gathered}$$