Straight-Line Depreciation Revision Notes for HSC SSCE Mathematics Standard

Straight-Line Depreciation

What is straight-line depreciation?

Straight-line depreciation is a method where an asset loses the same fixed amount of value during each time period. This is the simplest form of depreciation and is commonly used for vehicles, equipment, and other assets that lose value over time.

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Understanding straight-line depreciation is easier with a practical example. Let's look at how a car's value changes over time.

For example, imagine you purchase a car for $20,000 that depreciates by $2,000 each year. Using straight-line depreciation:

After one year: $20,000 - $2,000 = $18,000
After two years: $20,000 - $2,000 - $2,000 = $16,000

Notice that the car loses exactly $2,000 in value each year - this consistent decrease is what makes it "straight-line" depreciation.

The straight-line depreciation formula

The formula for calculating straight-line depreciation is:

$S = V_0 - Dn$

Where:

$S$ = Salvage value - the current value of an item (also called book value)
$V_0$ = Purchase price - the original value of the item when $n = 0$
$D$ = Depreciated amount - the amount the item loses in value per time period
$n$ = Number of time periods - how many periods have passed (usually years)

chatImportant

Make sure you identify which value you're solving for. You might need to rearrange the formula to find $D$ or $n$ instead of $S$ . Always isolate the unknown variable before substituting values.

Understanding how straight-line depreciation works

The key feature of straight-line depreciation is that the depreciation amount remains constant over time. Each period, you subtract the same value ( $D$ ) from the remaining worth of the asset.

This method assumes that the asset loses value at a uniform rate, which makes calculations straightforward and predictable. It's particularly useful for budgeting and financial planning because you can easily forecast the future value of an asset.

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Real-world applications:

Straight-line depreciation is commonly used in:

Accounting for company assets
Tax calculations
Budgeting and financial forecasting
Insurance valuations

Worked example 1: Calculating the salvage value

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Worked Example: Finding the Car's Value After Three Years

Problem: A used car is purchased for $14,500 and depreciates by $1,100 each year. What will the car be worth after three years?

Solution:

Step 1: Write the straight-line depreciation formula:

$S = V_0 - Dn$

Step 2: Identify the values from the problem:

$V_0 = 14,500$ (purchase price)

$D = 1,100$ (annual depreciation)

$n = 3$ (number of years)

Step 3: Substitute these values into the formula:

$S = 14,500 - 1,100 \times 3$

Step 4: Calculate the result:

$S = 14,500 - 3,300$

$S = 11,200$

Answer: The value of the car after three years is $11,200.

Worked example 2: Finding the annual depreciation amount

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Worked Example: Calculating Annual Depreciation

Problem: A new car is purchased for $25,800. After 4 years, its salvage value is $15,160. What is the annual amount of depreciation, assuming constant depreciation?

Solution:

Step 1: Write the straight-line depreciation formula:

$S = V_0 - Dn$

Step 2: Identify the known values:

$V_0 = 25,800$ (purchase price)

$S = 15,160$ (salvage value after 4 years)

$n = 4$ (number of years)

Step 3: Substitute into the formula:

$15,160 = 25,800 - D \times 4$

Step 4: Rearrange to solve for $D$ :

$D \times 4 = 25,800 - 15,160$

$D = \frac{25,800 - 15,160}{4}$

Step 5: Calculate:

$D = \frac{10,640}{4}$

$D = 2,660$

Answer: The annual depreciation is $2,660.

Important tip: When solving for $D$ , always rearrange the formula first before substituting values. This helps avoid calculation errors.

Remember!

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Key Points to Remember:

Straight-line depreciation means the asset loses the same amount of value each time period
The formula is $S = V_0 - Dn$ $S = V_{0} - D n$ where:
- $S$ is salvage value
- $V_0$ is purchase price
- $D$ is depreciation per period
- $n$ is number of periods
You can rearrange the formula to find any unknown variable ( $S$ , $D$ , or $n$ )
Always check your answer makes sense - the salvage value should be less than the purchase price
This method is most accurate when an asset loses value at a constant rate over time

Straight-Line Depreciation (HSC SSCE Mathematics Standard): Revision Notes