Question

Find the principal if the interest compounded annually at the rate of 10% for two years is Rs 210.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sum}\mathrm{be}\mathrm{Rs}\mathrm{x}. \\ \mathrm{We}\mathrm{know}\mathrm{that}: \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}-\mathrm{P} \\ =\mathrm{P}\left[{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}-1\right] \\ 210=\mathrm{x}\left[{\left(1+\frac{10}{100}\right)}^2-1\right] \\ 210=\mathrm{x}\left[{\left(1.10\right)}^2-1\right] \\ \mathrm{x}=\frac{210}{0.21} \\ =1,000 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{sum}\mathrm{is}\mathrm{Rs}1,000. \end{gathered}$$