A car depreciates in value by 15% per year. If it is worth $20,000 now, what will it be worth in 3 years? - High Altitude Science

Understanding the Context

What Is Car Depreciation?

Car depreciation refers to the decline in a vehicle’s market value as it ages and accumulates mileage. Unlike some assets, cars lose a significant portion of their value soon after purchase—often starting with 20-30% in the first year. Even after that, annual depreciation continues at a steady pace, averaging 15% per year for many vehicles.

How Depreciation Works: The 15% Annual Rate

Key Insights

Depreciation of 15% per year means that each year, the car’s value is multiplied by 0.85 (which equals 100% – 15% = 85%). This compound effect turns out to significantly reduce value over time.

Let’s calculate the value step by step for 3 years.

Year 1:

Initial value: $20,000
Depreciation: $20,000 × 15% = $3,000
New value: $20,000 – $3,000 = $17,000

Year 2:

Value at start: $17,000
Depreciation: $17,000 × 15% = $2,550
New value: $17,000 – $2,550 = $14,450

Year 3:

Value at start: $14,450
Depreciation: $14,450 × 15% = $2,167.50
Final value after Year 3: $14,450 – $2,167.50 = $12,282.50

Final Thoughts

Summary Table: Value Over 3 Years

| Year | Starting Value | Depreciation (15%) | Ending Value |
|------|----------------|--------------------|---------------|
| 0 | $20,000 | – | $20,000 |
| 1 | $20,000 | $3,000 | $17,000 |
| 2 | $17,000 | $2,550 | $14,450 |
| 3 | $14,450 | $2,167.50 | $12,282.50 |

Why Depreciation Matters

Even though depreciation is inevitable, understanding the 15% per year rate helps you manage expectations: