Question

A machine is purchased for Rs 625000. Its value depreciates at the rate of 8% per annum. What will be its value after 2 years?

Answer 1

$$\begin{gathered} \mathrm{Initial}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{machine},P\mathit{=}\mathrm{Rs}625000 \\ \mathrm{Rate}\mathrm{of}\mathrm{depreciation},R=8\% \\ \mathrm{Time},\mathit{}n=2\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{machine}\mathrm{after}\mathrm{two}\mathrm{years}\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{Value}=\mathit{}P\times {\left(1-\frac{R}{100}\right)}^n \\ =\mathrm{Rs}625000\times {\left(1-\frac{8}{100}\right)}^2 \\ =\mathrm{Rs}625000\times {\left(\frac{100-8}{100}\right)}^2 \\ =\mathrm{Rs}625000\times {\left(\frac{92}{100}\right)}^2 \\ =\mathrm{Rs}625000\times {\left(\frac{23}{25}\right)}^2 \\ =\mathrm{Rs}625000\times \left(\frac{23}{25}\right)\times \left(\frac{23}{25}\right) \\ =\mathrm{Rs}\left(1000\times 23\times 23\right) \\ =\mathrm{Rs}529000 \\ \mathrm{Therefore},\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{machine}\mathrm{after}\mathrm{two}\mathrm{years}\mathrm{will}\mathrm{be}\mathrm{Rs}.529000. \end{gathered}$$