Question

The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is Rs 360. Find the sum.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sum}\mathrm{be}\mathrm{P}. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{CI}-\mathrm{SI}=360 \\ \left[\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}-\mathrm{P}\right]-\frac{\mathrm{P}\times 7.5\times 2}{100}=360 \\ \mathrm{P}\left[{\left(1+\frac{7.5}{100}\right)}^2-1\right]-\frac{\mathrm{P}\times 7.5\times 2}{100}=360 \\ \mathrm{P}\left[1.155625-1\right]-0.15\mathrm{P}=3600.155625\mathrm{P}-0.15\mathrm{P}=3600.005625\mathrm{P}=360\mathrm{P}=\frac{360}{0.005625}\mathrm{P}=64000\mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{sum}\mathrm{is}\mathrm{Rs}64,000. \end{gathered}$$