Question

Tick (✓) the correct answer:
The compound interest on Rs 10000 at 12% per annum for $1\frac{1}{2}$ years, compounded annually, is
(a) Rs 1872
(b) Rs 1720
(c) Rs 1910.16
(d) Rs 1782

Answer 1

(a) Rs 1872

$$\begin{gathered} \mathrm{Here},A=P\times {\left(1+\frac{R}{100}\right)}^1\times \left(1+\frac{{\displaystyle \frac{1}{2}}R}{100}\right) \\ =\mathrm{Rs}10000\times \left(1+\frac{12}{100}\right)\times \left(1+\frac{{\displaystyle \frac{1}{2}}\times 12}{100}\right) \\ =\mathrm{Rs}10000\times \left(\frac{100+12}{100}\right)\times \left(\frac{100+6}{100}\right) \\ =\mathrm{Rs}10000\times \left(\frac{112}{100}\right)\times \left(\frac{106}{100}\right) \\ =\mathrm{Rs}10000\times \left(\frac{28}{25}\right)\times \left(\frac{53}{50}\right) \\ =\mathrm{Rs}\left(8\times 28\times 53\right) \\ =\mathrm{Rs}11872 \\ \therefore \mathrm{Compound}\mathrm{interest}=\mathrm{amount}-\mathrm{principal}=\mathrm{Rs}(11872-10000)=\mathrm{Rs}1872 \end{gathered}$$