Question

A car is valued at Rs 4,00,000. If its value falls by 2.5% per year, what will be its value after 3 years?

Answer 1

Price of the car, P = Rs 4,00,000
Rate (R) = −2.5% p.a.
Number of years (N) = 3 years
Depreciated amount$=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =400000{\left(1+\frac{-2.5}{100}\right)}^3 \\ =400000{\left(1-\frac{1}{40}\right)}^3 \\ =400000{\left(\frac{39}{40}\right)}^3 \\ =400000\times \frac{39}{40}\times \frac{39}{40}\times \frac{39}{40} \\ =\mathrm{Rs}3,70,743.75 \end{gathered}$$

The depreciated value is Rs 3, 70,743.75
∴ The price of car after 3 years will be Rs 3,70,743.75