Values change
- Depreciation: value falls (cars, phones, equipment).
- Appreciation: value rises (some homes, land, collectibles, investments).
Straight-line depreciation
The item loses the same dollar amount each year.
Annual depreciation = (cost − salvage value) ÷ useful life
Example: A $12,000 machine with a salvage value of $2,000 after 5 years.
(12,000 − 2,000)/5 = $2,000 per year
| Year | Value |
|---|---|
| 0 | $12,000 |
| 1 | $10,000 |
| 2 | $8,000 |
| 5 | $2,000 |
Graph: a straight line sloping down (linear).
Declining-balance depreciation
The item loses the same percent of its value each year.
V = P(1 − r)ᵗ
Example: A $30,000 car depreciates 15% per year.
| Year | Value |
|---|---|
| 0 | $30,000 |
| 1 | $25,500 |
| 2 | $21,675 |
| 5 | ≈ $13,311 |
Graph: an exponential decay curve. Losses are biggest in the early years.
Appreciation
V = P(1 + r)ᵗ
Example: A $400,000 home appreciates 3% per year. After 10 years:
400,000 × 1.03¹⁰ ≈ $537,567
Appreciation isn’t guaranteed: home prices can fall.
Comparing methods
| Straight-line | Declining-balance | |
|---|---|---|
| Each year loses | same $ | same % |
| Model type | linear | exponential |
| Common for | accounting, equipment | vehicles, electronics |
Finding the rate
Example: A laptop drops from $1,500 to $600 in 4 years. Annual depreciation rate?
- (1 − r)⁴ = 0.4 → 1 − r = 0.4^(1/4) ≈ 0.795 → r ≈ 20.5%
Market value
The market value is what something would sell for now. Formulas estimate it; real prices depend on condition, demand and the economy.
Worked examples
Example 1: A $2,400 computer, straight-line over 4 years to $400 salvage. Annual depreciation? $500.
Example 2: $18,000 car, 20% per year. Value after 2 years? 18,000 × 0.8² = $11,520.
Example 3: A painting bought for $5,000 appreciates 6% per year. Value after 8 years? ≈ $7,969.
Common mistakes
- Subtracting the percent of the original value every year (that’s straight-line, not declining-balance).
- Using 1 + r for depreciation.
- Assuming appreciation is certain.
Try it yourself
- $8,000 equipment, $1,000 salvage, 7 years. Straight-line annual depreciation?
- $1,200 phone loses 30% per year. Value after 2 years?
- $250,000 land appreciates 4% per year. Value after 5 years?
- Which method gives a straight-line graph?
Answers: 1) $1,000 2) $588 3) ≈ $304,163 4) straight-line depreciation
Quick recap
- Depreciation lowers value; appreciation raises it.
- Straight-line depreciation: same $ each year (linear).
- Declining-balance depreciation: same % each year (exponential).