Question

Two years ago, Rajani purchased a machine for Rs 75,000. If its value falls by 4% every year, what is the value of the machine today?

Answer 1

Price of the machine two years ago, P = Rs 75,000
Rate (R) = −4% p.a.
Number of years (N) = 2 years
Value of the machine today $=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =75000{\left(1+\frac{-4}{100}\right)}^2 \\ =75000{\left(1-\frac{4}{100}\right)}^2 \\ =75000{\left(1-\frac{1}{25}\right)}^2 \\ =75000{\left(\frac{24}{25}\right)}^2 \\ =75000\times \frac{24}{25}\times \frac{24}{25} \\ =\mathrm{Rs}69120 \end{gathered}$$

The depreciated value is Rs 69120.
∴ The value of the machine today = Rs 69120.