Successive Percentage Decreases and Stacked Discounts
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Direct answer
Successive percentage decreases compound. Multiply the remaining fractions; do not add the rates unless you only want a rough approximation.
Formula and method
Equivalent decrease = [1 − (1 − p1)(1 − p2)…] × 100
The calculation keeps full precision through the formula and rounds only the displayed answer.
Step-by-step calculation
- Convert each rate to a decimal.
- Turn each into a remaining fraction: 1 − p.
- Multiply the remaining fractions.
- Subtract the product from 1 and convert to a percentage.
Worked examples
20% then 10%
0.80 × 0.90 = 0.72, so 72% remains and the total decrease is 28%, not 30%.
Three reductions
5%, 8% and 12% leave 0.95 × 0.92 × 0.88 = 0.76912; total decrease = 23.088%.
Retail
$150 after 20% then 10% becomes $108.
Interpretation and edge cases
- Order does not change the pure multiplication result, but intervening fees or fixed adjustments can make order matter.
- Round after the full chain when possible.
- A discount plus tax is not two decreases.
Frequently asked questions
Do 10% and 10% equal 20%?
No. They leave 0.9 × 0.9 = 81%, a 19% total decrease.
Can I add discount percentages?
Only when they apply to the same unchanged base; sequential discounts apply to changing bases.
How do I find the final amount?
Multiply the original by every remaining fraction.
Sources and transparency
The formulas and examples were evidence-checked on 2026-09-10. This is educational mathematical content. It does not replace a field-specific standard, accounting policy, laboratory method, contractual definition or professional judgment.
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