In short
Multiply the starting value by 0.85 for each year. After six years that is 30,000 × 0.85⁶, about $11,314.
The idea
Reducing balance means the loss each year is a percentage of what is left, not of the original price. So the loss shrinks as the value shrinks.
Losing 15% means keeping 85%. The multiplier each year is 0.85.
The formula
V = P × (1 − r)ⁿ
Here P = 30,000, r = 0.15 and n = 6.
Year by year
| Year | Value at start | Loss (15%) | Value at end |
|---|---|---|---|
| 1 | $30,000.00 | $4,500.00 | $25,500.00 |
| 2 | $25,500.00 | $3,825.00 | $21,675.00 |
| 3 | $21,675.00 | $3,251.25 | $18,423.75 |
| 4 | $18,423.75 | $2,763.56 | $15,660.19 |
| 5 | $15,660.19 | $2,349.03 | $13,311.16 |
| 6 | $13,311.16 | $1,996.67 | $11,314.49 |
Check with the formula: 0.85⁶ ≈ 0.3771, and 30,000 × 0.3771 ≈ $11,314.
The common mistake
Try it: a $12,000 laptop loses 20% each year. What is it worth after 3 years? Answer: 12,000 × 0.8³ = $6,144.
AI explanations can contain mistakes. Check important answers with your teacher.
AI explanations can contain mistakes. Check important answers with your teacher.