Question

The present value of a machine is ₹ 24000. If its value decreases 20% every year, find its value:

1. 2 years ago
2. After 2 years

Answer 1

Given:

• Present value of the machine, (V₀ = ₹ 24000)
• Rate of depreciation each year, (r = 20%)

Formulas used:

Value (n) years ago: `V_(-n) = V_0/(1 - r/100)^n`

Value after (n) years: `V_(n) = V_0 xx (1 - r/100)^n`

Step-wise calculation:

Step i: Value 2 years ago

`V_(-2) = 24000/(1 - 20/100)^2`

`V_(-2) = 24000/(0.8)^2`

`V_(-2) = 24000/0.64`

V_–2 = ₹ 37500

Step ii: Value after 2 years

`V_2 = 24000 xx (1 - 20/100)^2`

V₂ = 24000 × (0.8)²

V₂ = 24000 × 0.64

V₂ = ₹ 15360

The value of the machine 2 years ago was ₹ 37,500.

The value of the machine after 2 years will be ₹ 15,360.