Question

A scooter is bought at Rs 56000. Its value depreciates at the rate of 10% per annum. What will be its value after 3 years?

Answer 1

$$\begin{gathered} \mathrm{Initial}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{scooter},P=\mathrm{Rs}56000 \\ \mathrm{Rate}\mathrm{of}\mathrm{depreciation},R=10\% \\ \mathrm{Time},\mathit{}n=3\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{scooter}\mathrm{after}\mathrm{three}\mathrm{years}\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{Value}=P\times {\left(1-\frac{R}{100}\right)}^n \\ =\mathrm{Rs}.56000\times {\left(1-\frac{10}{100}\right)}^3 \\ =\mathrm{Rs}.56000\times {\left(\frac{100-10}{100}\right)}^3 \\ =\mathrm{Rs}.56000\times {\left(\frac{90}{100}\right)}^3 \\ =\mathrm{Rs}.56000\times {\left(\frac{9}{10}\right)}^3 \\ =\mathrm{Rs}.56000\times \left(\frac{9}{10}\right)\times \left(\frac{9}{10}\right)\times \left(\frac{9}{10}\right) \\ =\mathrm{Rs}.\left(56\times 9\times 9\times 9\right) \\ =\mathrm{Rs}.40824 \\ \mathrm{Therefore},\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{scooter}\mathrm{after}\mathrm{three}\mathrm{years}\mathrm{will}\mathrm{be}\mathrm{Rs}.40824. \end{gathered}$$