Depreciation

Learn about how the value of an asset decreases over time due to wear and tear, and how to calculate depreciation using various methods.

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How to use this guide

Depreciation is the process by which the value of an asset decreases over time. Work through each section and pay close attention to how the depreciation calculations are done.

Big idea: Depreciation reduces the value of an asset over time. We can calculate it using a fixed percentage or other methods.

What is Depreciation?

Depreciation refers to the decrease in the value of an asset over time. It usually applies to physical assets like machines, vehicles, and equipment. Depreciation can occur due to wear and tear or obsolescence.

There are various methods of calculating depreciation, with the most common being **Straight Line Depreciation**.

Depreciation Formula

The general formula for depreciation using **Straight Line Depreciation** is:

\[ \text{Depreciation Value} = \frac{\text{Cost of Asset} \times \text{Depreciation Rate}}{100} \]

Where:

Cost of Asset = The initial value of the asset
Depreciation Rate = The percentage by which the asset’s value decreases each year
Time = The number of years over which the depreciation is calculated

After finding the annual depreciation value, we can subtract this from the cost of the asset to find the asset’s value after a given time.

Depreciation Problem Example

Let's solve an example problem:

Problem: Find the value of a machine costing $5000 after 2 years if it depreciates at 10% per annum.

Step 1: Find the Depreciation Value per Year

\[ \text{Depreciation per Year} = \frac{5000 \times 10}{100} = 500 \]

So, the machine depreciates $500 each year.

Step 2: Calculate Total Depreciation over 2 Years

\[ \text{Total Depreciation} = 500 \times 2 = 1000 \]

Step 3: Subtract Depreciation from Original Cost to Find Value

\[ \text{Value of Machine after 2 years} = 5000 - 1000 = 4000 \]

Answer: After 2 years, the value of the machine is $4000.

Mixed Practice

Find the value of a car that costs $12,000 after 3 years if it depreciates at 8% per annum. Step 1: Find the Depreciation per Year. \[ \text{Depreciation per Year} = \frac{12000 \times 8}{100} = 960 \] Step 2: Calculate Total Depreciation over 3 Years. \[ \text{Total Depreciation} = 960 \times 3 = 2880 \] Step 3: Find the value of the car after 3 years. \[ \text{Value after 3 years} = 12000 - 2880 = 9120 \]

Answer: The value of the car after 3 years is $9120.

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