Compound & Reverse Percentages — Year 9 Revision Notes
These notes cover percentage multipliers, repeated (compound) percentage change including compound interest, and reverse percentages — all at Year 9 (Stage 9) level.
Percentage multipliers
A multiplier turns a percentage change into a single multiplication. For an increase of 5%, multiply by 1.05; for a decrease of 5%, multiply by 0.95. Multipliers make repeated changes much easier to handle.
Key Facts & Formulas
- Increase 5% → × 1.05
- Decrease 5% → × 0.95
Tips
- Increase multiplier > 1; decrease multiplier < 1.
- Write the multiplier before you start calculating.
Compound change and interest
For repeated percentage change, raise the multiplier to the power of the number of times it happens. $500 at 4% compound interest for 3 years is 500 × 1.04³. This also models depreciation, using a multiplier below 1.
Key Facts & Formulas
- Final = start × (multiplier)ⁿ
- 500 × 1.04³
Tips
- Use a power for repeated change, not repeated addition.
- Depreciation uses a multiplier less than 1.
Reverse percentages
In a reverse percentage problem, the amount you are given is not 100%. Decide what percentage it represents, then divide by the matching multiplier to find the original. If $72 is the price after a 20% discount, then $72 is 80%, so the original is 72 ÷ 0.8 = $90.
Key Facts & Formulas
- Original = amount ÷ multiplier
- 72 ÷ 0.8 = 90
Tips
- The amount given is not the original 100%.
- Divide by the multiplier to reverse the change.
Revision Checklist
- I can write and use percentage multipliers
- I can calculate repeated (compound) percentage change
- I can calculate compound interest over several years
- I can use reverse percentages to find an original amount
Frequently Asked Questions
Why can't I just add 20% then subtract 20% to get back to the start?
Because the two percentages are taken from different amounts. A 20% increase then a 20% decrease does not return to the original, since the decrease is calculated from the larger value. You must use the correct multiplier to reverse a change.
Build strong foundations in Compound & Reverse Percentages
A free trial class with Teacher Rig helps your Year 9 child master Compound & Reverse Percentages now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Compound & Reverse Percentages develops in IGCSE Number (Cambridge 0580) →