Question

The difference in simple interest and compound interest on a certain sum of money at $6\frac{2}{3}\%$ per annum for 3 years is Rs 46. Determine the sum.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{CI}-\mathrm{SI}=46 \\ \mathrm{P}\left[{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}-1\right]-\frac{\mathrm{PRT}}{100}=46 \\ \mathrm{P}\left[{\left(1+\frac{20}{300}\right)}^3-1\right]-\frac{\mathrm{P}\times 20\times 3}{3\times 100}=46 \\ \frac{4,096}{3,375}\mathrm{P}-\frac{\mathrm{P}}{5}-\mathrm{P}=46 \\ \frac{(4,096-3,375-675)\mathrm{P}}{3,375}=46 \\ \mathrm{P}=46\times \frac{3,375}{46} \\ =3,375 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{sum}\mathrm{is}\mathrm{Rs}3,375. \end{gathered}$$