Question

At what rate per cent per annum will Rs 640 amount to Rs 774.40 in 2 years when compounded annually?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{required}\mathrm{rate}\mathrm{be}R\%\mathrm{p}.\mathrm{a}. \\ A\mathit{}=774.40 \\ P=640 \\ \mathrm{n}=2\mathrm{years} \\ Now,A=P{\left(1+\frac{R}{100}\right)}^n \\ \Rightarrow 774.40=640{\left(1+\frac{R}{100}\right)}^2 \\ \Rightarrow \frac{774.40}{640}={\left(1+\frac{R}{100}\right)}^2 \\ \Rightarrow 1.21={\left(1+\frac{R}{100}\right)}^2 \\ \Rightarrow {\left(1.1\right)}^2={\left(1+\frac{R}{100}\right)}^2 \\ \Rightarrow 1.1-1=\frac{R}{100} \\ \Rightarrow 0.1=\frac{R}{100} \\ \Rightarrow R\mathit{}=\left({\displaystyle 0.1\times 100}\right)=10 \\ \mathrm{Hence},\mathrm{the}\mathrm{required}\mathrm{rate}\mathrm{is}10\%\mathrm{p}.\mathrm{a}. \end{gathered}$$