Question

A sum of money invested at compound interest amount to Rs.800 in 3 years to Rs. 840 in 4 years. Find the rate of interest per annum.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{P}\mathrm{be}\mathrm{the}\mathrm{sum}\mathrm{and}\mathrm{R}\mathrm{be}\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{interest}\mathrm{per}\mathrm{annum}. \\ \mathbf{Case}\mathbf{}\mathbf{1}\mathbf{}\mathbf{:} \\ \mathrm{Amount},\mathrm{A}=\mathrm{Rs}800;\mathrm{Time},\mathrm{n}=3\mathrm{yrs} \\ \mathrm{So},\mathrm{A}=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^{\mathrm{n}} \\ \Rightarrow 800=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^3......\left(1\right) \\ \mathbf{Case}\mathbf{}\mathbf{2}\mathbf{}: \\ \mathrm{Amount},\mathrm{A}=\mathrm{Rs}840;\mathrm{Time},\mathrm{n}=4\mathrm{yrs} \\ \mathrm{So},\mathrm{A}=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^{\mathrm{n}} \\ \Rightarrow 840=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^4......\left(2\right) \\ \mathrm{Dividing}\left(2\right)\mathrm{by}\left(1\right),\mathrm{we}\mathrm{get} \\ \frac{840}{800}=1+\frac{\mathrm{R}}{100} \\ \Rightarrow \frac{\mathrm{R}}{100}=\frac{40}{800} \\ \Rightarrow \mathrm{R}=5 \\ \mathrm{So},\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{interest}=5\%\mathrm{p}.\mathrm{a}. \end{gathered}$$