Question

Mark (✓) against the correct answer:
If the simple interest on a sum of money at 10% per annum for 3 years is Rs 1500, then the compound interest on the same sum at the same rate for the same period is
(a) Rs 1655
(b) Rs 1155
(c) Rs 1555
(d) Rs 1855

Answer 1

(a) Rs. 1655

$$\begin{gathered} \mathrm{Here},\mathrm{SI}=\frac{P\mathit{\times }R\mathit{\times }T}{\mathit{100}} \\ \Rightarrow \mathrm{Rs}.1500=\frac{P\times 10\times 3}{100} \\ \Rightarrow P=\frac{1500\times 100}{10\times 3}=\mathrm{Rs}.5000 \\ \mathrm{Now},A\mathit{}=P\times {\left(1+\frac{R}{100}\right)}^n \\ =\mathrm{Rs}.5000\times {\left(1+\frac{10}{100}\right)}^3 \\ =\mathrm{Rs}.5000\times {\left(\frac{110}{100}\right)}^3 \\ =\mathrm{Rs}.5000\times \left(\frac{11}{10}\right)\times \left(\frac{11}{10}\right)\times \left(\frac{11}{10}\right) \\ =\mathrm{Rs}.\left(5\times 11\times 11\times 11\right) \\ =\mathrm{Rs}.6655 \\ \therefore \mathrm{CI}=A-P=\mathrm{Rs}(6655-5000)=\mathrm{Rs}1655 \end{gathered}$$