With compound change, each new percentage acts on the latest amount. The same percentage change therefore multiplies repeatedly rather than adding the same cash amount each time. A multiplier above 1 gives growth, and one between 0 and 1 gives depreciation. To undo a percentage change, divide by its multiplier or repeated multiplier. Equal percentage increases and decreases do not cancel: the second change uses a different starting amount. Keep extra precision until the final money answer.
Learning objectives
- Apply repeated percentage changes using multipliers.
- Reverse a percentage change when its multiplier is non-zero.
Key ideas
Growth and depreciation use these multipliers.
For depreciation, the percentage lies from zero to one hundred.
After equal periods, raise the multiplier to the number of periods.
To reverse the change, divide by the accumulated non-zero multiplier.
Worked examples
Example 1
An £800 device depreciates by 12% each year. Find its value after two years.
Answer
Example 2
A price is £540 after a 20% increase. Find its original value.
Answer
Question styles to prepare for
Original practice guidance aligned to the specification, not a count of past-paper appearances or a prediction. The AO labels below describe the intended practice focus, not official AQA mark allocations.
AO1 · Methods
Calculate compound growth, depreciation or a reverse percentage.
AO2 · Reasoning
Explain why percentage change must use the appropriate starting value.
AO3 · Problem solving
Compare repeated-change models or work backwards through successive changes.
When a task asks you to explain, include a mathematical reason. When solving a problem, show how the information becomes a calculation, equation or diagram, then interpret your result.
Avoid this mistake
Apply each change to the current amount. A 100% decrease gives zero and cannot be reversed from the final amount alone.
Try it yourself
Attempt each question before opening its answer.
Check 1: A price is £540 after a 20% increase. Find the original price.
Answer: £450
Divide the final price by 1.20: 540/1.2 = 450.
Check 2: £100 grows by 10%, then the result decreases by 10%. Find the final amount.
Answer: £99
100 × 1.10 × 0.90 = 99; the changes act on different amounts.
Explain it in your own words
- Write growth and depreciation multipliers for 7%.
- Explain why compound interest differs from simple interest.
- Show how division reverses three years of compound change.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All higher notes
Specification source
AQA Ratio specification · Assessment objectives. Checked 16 October 2026. Topic references identify related content; these notes do not cover every specification statement.