Question

On what sum will the compound interest at 5% per annum for 2 years compounded annually be Rs 164?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sum}\mathrm{be}\mathrm{Rs}\mathrm{x}. \\ \mathrm{We}\mathrm{know}\mathrm{that}: \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}-\mathrm{P} \\ =\mathrm{P}\left[{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}-1\right] \\ 164=\mathrm{x}\left[{\left(1+\frac{5}{100}\right)}^2-1\right] \\ 164=\mathrm{x}\left[{\left(1.05\right)}^2-1\right] \\ \mathrm{x}=\frac{164}{0.1025} \\ =1,600 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{sum}\mathrm{is}\mathrm{Rs}1,600. \end{gathered}$$