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- Reverse percentages, compound interest and decay
Reverse percentages, compound interest and decay
Some percentage questions run backwards, and some repeat year after year. Multipliers handle both.
Reverse percentages
After a 20% rise, a price is £96. Find the original.
The multiplier was 1.2, so original = 96 ÷ 1.2 = £80.
Never take 20% off the new price.
The multiplier was 1.2, so original = 96 ÷ 1.2 = £80.
Never take 20% off the new price.
Compound interest
Interest is added each year, then the next year's interest is on the new total.
amount = original × (multiplier)n
£500 at 4% for 3 years: 500 × 1.043 = £562.43
amount = original × (multiplier)n
£500 at 4% for 3 years: 500 × 1.043 = £562.43
Depreciation and decay
A car losing 15% a year: multiplier 0.85.
Value after n years = original × 0.85n.
Value after n years = original × 0.85n.
A bike costs £180 in a 25% off sale. What was the original price?
- The sale price is 75% of the original, multiplier 0.75.
- 180 ÷ 0.75
- = £240
Answer: £240
Reverse percentage: divide by the multiplier. Compound change: multiply by the multiplier to the power of the number of years.
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