Calculate the depreciated value of an asset over time using both the straight-line and declining balance methods, and compare their effects on asset value.
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The moment you drive a new car off the lot, it loses roughly 10–15% of its value. By the end of the first year, it might be worth 20% less than you paid. This isn't damage — it's depreciation, the natural loss of value that almost every physical asset experiences over time. Businesses track depreciation because it affects how much their equipment and vehicles are worth on paper, which matters for tax and accounting. But here's the interesting question: does an asset lose the same dollar amount each year, or the same percentage? The answer depends on which depreciation method you use — and the two methods give very different results over time.
Apply $S = V_0 - Dn$ to calculate salvage value and depreciation amount under straight-line method
Apply $S = V_0(1-r)^n$ to calculate salvage value under the declining balance method
Compare both methods for the same asset and identify which produces a higher salvage value
Calculate total depreciation as $V_0 - S$ and solve for unknown values using either formula
Declining balance depreciates faster in early years; straight-line is constant. After 4 years both end near the same value for these parameters.
Wrong: Depreciation increases the value of an asset over time.
Right: Depreciation decreases the value of an asset due to wear, tear, or obsolescence. Methods include straight-line (constant amount) and declining-balance (constant percentage).
Straight-line depreciation reduces an asset's value by the same fixed dollar amount each period, producing a linear decrease in value over time.
In straight-line (or flat-rate) depreciation, the asset loses the same dollar amount $D$ every year. The formula $S = V_0 - Dn$ gives the salvage value after $n$ periods. For example, a machine worth $24,000 that depreciates by $3,000 per year will be worth $24,000 − ($3,000 × 5) = $9,000 after 5 years. An asset depreciated to zero is "fully depreciated."
If the initial value, final salvage value, and time are all known, calculate $D = (V_0 - S_n) \div n$.
Declining balance depreciation reduces the asset's value by a fixed percentage of its current value each period — so the dollar amount of depreciation decreases as the asset becomes worth less.
The formula $S = V_0(1 - r)^n$ mirrors the compound interest formula structurally — except instead of multiplying by $(1 + r)$ to grow, we multiply by $(1 - r)$ to shrink. For example, a vehicle purchased for $32,000 depreciating at 18% per annum declining balance after 4 years: $S = \$32{,}000 \times (0.82)^4 = \$32{,}000 \times 0.45212 = \$14{,}468$.
Declining balance depreciation depreciates assets more rapidly in early years and more slowly later — this better reflects the real-world loss of value for vehicles and technology.
When comparing depreciation methods, calculate the salvage value under each method for the same asset and time period, then find the difference.
HSC questions frequently ask you to:
Most depreciation mistakes happen because the wrong model is chosen before the calculation even starts, so the first job is to identify whether the change is a fixed dollar amount or a fixed percentage.
| If the question says... | Use... |
|---|---|
| "depreciates by $2,400 per year" | Straight-line: $S = V_0 - Dn$ |
| "depreciates at 18% per annum" | Declining balance: $S = V_0(1-r)^n$ |
| "same amount each year" | Straight-line |
| "same percentage each year" | Declining balance |
| "total depreciation" | Use $V_0 - S$ after finding the salvage value |
A piece of industrial equipment was purchased for $85,000. It depreciates by $7,400 per year using the straight-line method. (a) What is its value after 6 years? (b) After how many complete years will its value first fall below $30,000?
$$S = V_0 - Dn = \$85{,}000 - (\$7{,}400 \times 6) = \$85{,}000 - \$44{,}400 = \$40{,}600$$
Substitute directly into the straight-line formula.
A car is purchased new for $38,500 and depreciates at 22% per annum declining balance. Calculate: (a) its value after 3 years, and (b) the total depreciation over this period.
$r = 0.22$, so $(1 - r) = 0.78$.
$$S = V_0(1 - r)^n = \$38{,}500 \times (0.78)^3$$
$$(0.78)^3 = 0.474552 \quad \text{(calculator)}$$
$$\therefore S = \$38{,}500 \times 0.474552 = \$18{,}270.25$$
Convert 22% to decimal, subtract from 1 to get the multiplier, raise to power 3, then multiply by the initial value.
Office furniture is purchased for $16,000. Method A: straight-line depreciation of $1,800 per year. Method B: declining balance at 14% per annum. (a) Find the value under each method after 5 years. (b) Which method gives a higher salvage value after 5 years, and by how much?
$$S_A = \$16{,}000 - (\$1{,}800 \times 5) = \$16{,}000 - \$9{,}000 = \$7{,}000.00$$
Fixed dollar amount: $1,800 per year × 5 years = $9,000 total depreciation.
A machine was purchased for $28,000 and is worth $15,950 after 4 years under declining balance depreciation.
Find the annual depreciation rate, correct to two decimal places.
$$S = V_0(1-r)^n$$
$$15{,}950 = 28{,}000(1-r)^4$$
Start with the declining balance formula and substitute the known values.
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
5 random questions from a replayable lesson bank — feedback shown immediately
A vehicle worth $45,000 depreciates at 25% per annum declining balance. What is its value after 2 years?
An asset is purchased for $50,000 and has a salvage value of $18,000 after 8 years of straight-line depreciation. What is the annual depreciation amount?
An asset depreciates at 18% per annum declining balance. What multiplier should be used each year?
These questions focus on choosing the correct depreciation model first, then setting out the substitution clearly.
A printer costing $6,200 depreciates by $540 per year using straight-line depreciation. Find its value after 5 years.
A boat was purchased for $64,000 and depreciates at 12% per annum declining balance. Find its value after 3 years.
An asset was bought for $24,000. Under straight-line depreciation it loses $2,200 per year. Under declining balance it depreciates at 10% per annum. Compare the salvage value after 4 years.
Defend your ship by blasting the correct answers for Depreciation. Scores count toward the Asteroid Blaster leaderboard.
Play Asteroid Blaster →Use this as a quick recognition drill: decide which model fits the wording before calculating.
Which description matches straight-line depreciation?
For declining balance depreciation at 12% per annum, what is the yearly multiplier?
If a question asks for total depreciation, what is the safest method after finding the salvage value?
Which phrase most strongly signals declining balance depreciation?