GCSE Maths Percentage Change Notes
Percentage change covers increases, decreases, profit, loss and interest. The multiplier method makes every version fast and reliable.
Key concepts
- Multiplier
- A decimal you multiply by: 1.2 for +20%, 0.8 for −20%.
- Percentage change
- (change ÷ original) × 100. Always divide by the original amount.
- Compound interest
- Interest earned on interest — apply the multiplier repeatedly using a power.
- Reverse percentage
- Finding the original before a change — divide by the multiplier, do not just subtract.
Key formulas
Percentage change
% change = (change ÷ original) × 100
Compound interest
final = P × (1 + r/100)ⁿ
P = principal, r = rate, n = years.
Worked example
£500 is invested at 3% compound interest for 2 years. Find the value.
- 1Multiplier for +3% is 1.03.
- 2Apply it twice: 500 × 1.03² = 500 × 1.0609.
- 3Calculate: 530.45.
Answer: £530.45
Common mistakes
✗ Dividing by the new amount instead of the original for percentage change.
✓ Always divide the change by the original value.
✗ Doing reverse percentages by subtracting the percentage.
✓ Divide by the multiplier: if 120% = £60, then 100% = 60 ÷ 1.2 = £50.
✗ Calculating simple interest when compound is required.
✓ Compound uses a power (…)ⁿ; simple interest multiplies by the years.
Quick check
Try these, then reveal the answers.
Decrease £80 by 25%.Reveal answer
£60
A price rises from £40 to £50. What is the % increase?Reveal answer
25%
What multiplier increases by 8%?Reveal answer
1.08
Exam tips
- Learn the multiplier method — it handles increase, decrease and compound with one idea.
- For reverse percentage, decide what percentage you are given, then divide to reach 100%.
- Round money to 2 decimal places only at the final step.
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Frequently asked questions
What is the difference between simple and compound interest?+
Simple interest is the same each year on the original amount; compound interest grows because each year's interest earns interest too.
How do I do a reverse percentage?+
Write the given amount as a percentage of the original, then divide by its multiplier to find 100%.
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