A machine depreciates at the rate of 10% of its value at the beginning of a year. If the present value of a machine is ₹ 8,000, its value after 3 years will be:

1. ₹ 5,382

2. ₹ 5,832

3. ₹ 5,238

4. ₹ 5,638

Given,

V = ₹ 8,000

n = 3 years

R = 10%

Value of machine after n years = $\Big[V \times \Big(1 - \dfrac{r}{100}\Big)^n \Big]$

$\text{Value of machine after 3 years }= 8000 \Big(1 - \dfrac{10}{100}\Big)^{3} \\[1em] = 8000 \Big(\dfrac{100 - 10}{100}\Big)^3 \\[1em] = 8000 \Big(\dfrac{90}{100}\Big)^3 \\[1em] = 8000 (0.9)^3 \\[1em] = 8000 \times 0.729 \\[1em] = ₹ 5,832.$

Value of machine after 3 years = ₹ 5,832

Hence, option 2 is correct option.