Question

A car costing $25 000 depreciates 30% of its value each year. What is the book value at the end of 3 years?

Answer 1

To find the book value of a car after 3 years of depreciation, we first need to understand how depreciation works. In this case, the car depreciates by 30% of its value each year.

1. **Initial Cost of the Car**: $25,000

2. **Depreciation Calculation**:
- At the end of Year 1:
\[
\text{Depreciation for Year 1} = 0.30 \times 25,000 = 7,500
\]
\[
\text{Book Value at the End of Year 1} = 25,000 - 7,500 = 17,500
\]

- At the end of Year 2:
\[
\text{Depreciation for Year 2} = 0.30 \times 17,500 = 5,250
\]
\[
\text{Book Value at the End of Year 2} = 17,500 - 5,250 = 12,250
\]

- At the end of Year 3:
\[
\text{Depreciation for Year 3} = 0.30 \times 12,250 = 3,675
\]
\[
\text{Book Value at the End of Year 3} = 12,250 - 3,675 = 8,575
\]

3. **Final Result**:
The book value of the car at the end of 3 years is **$8,575**.