Question

Simple interest on a sum of money for 2 years at $6\frac{1}{2}\%$ per annum is Rs 5200. What will be the compound interest on the sum at the same rate for the same period?

Answer 1

$$\begin{gathered} \mathrm{P}=\frac{\mathrm{SI}\times 100}{\mathrm{RT}} \\ \therefore \mathrm{P}=\frac{5,200\times 100}{6.5\times 2} \\ =40,000 \\ \mathrm{Now}, \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =40,000{\left(1+\frac{6.5}{100}\right)}^2 \\ =40,000{\left(1.065\right)}^2 \\ =45,369 \\ \mathrm{Also}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =45,369-40,000 \\ =5,369 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{Rs}5,369. \end{gathered}$$