Compound depreciation
When the value of something—like a car or a piece of equipment—goes down a little more each year based on its current value, that’s called compound depreciation. It’s the flip side of compound interest, and it’s useful in real life when working out how much something will be worth after a few years of wear and tear. Jump to the questions
Practise now
Calculate the final amount after compound depreciation is applied. Since it's money, round your answer to two decimal places!
Topic guide
What this worksheet practises
This worksheet provides practice on compound depreciation. Depreciation occurs when the value of an item (like a car or machinery) decreases over time. Unlike simple depreciation, compound depreciation means the value decreases by a percentage of its current value each year, not its original starting value.
Key method
The most efficient way to calculate compound depreciation is by using a decimal multiplier.
- First, calculate the multiplier. Subtract the percentage decrease from 100%, then divide by 100 to get a decimal.
- Second, identify the number of years (the time period). This will be your power (exponent).
- Third, multiply the starting amount by the multiplier raised to the power of the number of years.
- Finally, round your answer appropriately, usually to 2 decimal places if dealing with money.
Worked example
A car is bought for £15,000. It depreciates by 12% each year. Find its value after 4 years.
Step 1: Find the multiplier. 100% − 12% = 88%. As a decimal, this is 0.88.
Step 2: Set up the calculation.
Value = 15000 × 0.884
Step 3: Calculate the result.
Value = 8995.39968
Step 4: Round to 2 decimal places (for money).
The car's value is £8995.40.
Common mistakes to avoid
A very common error is calculating 12% of £15,000, multiplying it by 4, and subtracting that from the total. That is simple depreciation. Compound depreciation requires a power because the 12% drop is calculated on a newly reduced amount every single year.
How to check your answer
A quick mental check using simple depreciation gives a rough lower bound. 12% of 15,000 is 1,800. Over 4 years, that's 7,200 total loss, leaving 7,800. Because the car loses less value each year (as its total value drops), the true compound answer should be somewhat higher than 7,800. Our answer of 8995.40 fits perfectly.