Question

The present value of a car is ₹ 525000. Its value depreciates at the rate of 10% in the first year and then 6% every year. Find its value after 3 years.

Answer 1

Given:

• Present value (V₀ = ₹ 525000)
• Depreciation first year = 10%
• Depreciation subsequent years = 6%
• Find value after 3 years

Step-wise calculation:

1. After first year (10% depreciation):

V₁ = 525000 × (1 – 0.10)

V₁ = 525000 × 0.90

V₁ = ₹ 472500

2. After second year (6% depreciation):

V₂ = 472500 × 0.94

V₂ = 472500 × (1 – 0.06)

V₂ = ₹ 444150

3. After third year (6% depreciation):

V₃ = 444150 × 0.94

V₃ = ₹ 417501

Thus, the final value after 3 years is ₹ 417501, which matches the textbook answer.

The difference in your earlier answer (₹ 416655) arose from using 0.94 approximately as 0.94 but with slightly different values or rounding off earlier.

The value after 3 years is ₹417,501 using precise sequential depreciation calculation.