Depreciation

Depreciation is the process of reducing the value of an asset (like a car, machine, or computer) over time. This usually happens because the asset is being used and is getting older, which makes it less valuable. Understanding depreciation is important because it helps you figure out how much an item is worth after it has been used for a while.

Key Terms You Need to Know:

Asset: The item that is losing value over time (e.g., a car, equipment, etc.).
Depreciation Rate ( $i$ ): The percentage by which the value of the asset decreases each year.
Initial Value ( $P$ ): The original value or cost of the asset when it was new.
Final Value ( $F$ ): The value of the asset after a certain number of years, after depreciation has been applied.

How to Calculate Depreciation Using the Formula

To calculate how much an asset will be worth after it has depreciated over time, we use a formula. This formula assumes that the depreciation rate stays the same each year, which is often the case with what's known as straight-line depreciation.

The formula is: $F = P(1 - i)^t$

$F$ is the final value of the asset after depreciation.
$P$ is the initial value (the starting value of the asset).
$i$ is the depreciation rate as a decimal (e.g., $10$ % becomes $0.10$ ).
$t$ is the time in years over which the asset depreciates.

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Exam Tip:

This formula is also in your Formulae and Tables book, so make sure you know where to find it. You don't need to memorise it—just be familiar with how to use it during your exam!

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Step-by-Step Example Using the Formula

Let's say you bought a car for $€20,000$ and it depreciates at a rate of $15$ % per year. You want to know what the car will be worth after $3$ years.

Step 1: Convert the Depreciation Rate to a Decimal

Depreciation rates are usually given as percentages, but for the formula, we need to convert the percentage to a decimal.
$15$ % becomes $0.15$ (just divide by $100$ ).

Step 2: Substitute the Values into the Formula

Plug the values into the formula: $F = 20,000(1 - 0.15)^3$

Step 3: Subtract the Depreciation Rate from $1$

Inside the brackets, subtract the depreciation rate $i$ from $1$ : $1 - 0.15 = 0.85$

Step 4: Raise This Number to the Power of the Number of Years

Now, raise $0.85$ to the power of $3$ (because we're calculating the value after $3$ years): $0.85^3 = 0.614125$

Step 5: Multiply by the Initial Value

Finally, multiply the result by the initial value ( $€20,000$ ): $F = 20,000 \times 0.614125 = €12,282.50$ Final Answer:
After $3$ years, the car will be worth $€12,282.50$ .

Explanation of Each Step:

Why convert the depreciation rate to a decimal? The formula requires the rate as a decimal to correctly calculate how much value is lost each year.
Why subtract the rate from 1? Subtracting the rate from 1 shows how much of the asset's value remains each year after depreciation.
Why raise it to the power of the number of years? Raising this number to the power of the number of years calculates how the asset's value decreases over time.
Why multiply by the initial value? This step gives the final value of the asset after the depreciation has been applied over the specified number of years.

Depreciation Simplified Revision Notes for Junior Cycle Mathematics