Question

Find the difference between the compound interest and simple interest. On a sum of Rs 50,000 at 10% per annum for 2 years.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs}50,000 \\ \mathrm{R}=10\%\mathrm{p}.\mathrm{a}. \\ \mathrm{n}=2\mathrm{years} \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{amount}\mathrm{A}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{n}\mathrm{years}\mathrm{at}\mathrm{the}\mathrm{rate}\mathrm{R}\%\mathrm{per}\mathrm{annum}\mathrm{when}\mathrm{the}\mathrm{interest}\mathrm{is} \\ \mathrm{compounded}\mathrm{annually}\mathrm{is}\mathrm{given}\mathrm{by}\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right). \\ \therefore \mathrm{A}=\mathrm{Rs}50,000{\left(1+\frac{10}{100}\right)}^2 \\ =\mathrm{Rs}50,000{\left(1.1\right)}^2 \\ =\mathrm{Rs}60,500 \\ \mathrm{Also}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}60,500-\mathrm{Rs}50,000 \\ =\mathrm{Rs}10,500 \\ \mathrm{We}\mathrm{know}\mathrm{that}: \\ \mathrm{SI}=\frac{\mathrm{PRT}}{100} \\ =\frac{50,000\times 10\times 2}{100} \\ =\mathrm{Rs}10,000 \\ \therefore \mathrm{Difference}\mathrm{between}\mathrm{CI}\mathrm{and}\mathrm{SI}=\mathrm{Rs}10,500-\mathrm{Rs}10,000 \\ =\mathrm{Rs}500 \end{gathered}$$