Why two discounts do not add: compare the final price
Calculate successive discounts on the remaining price, check a 20% plus 10% example, and separate savings from tax and shipping.
Method
A second percentage discount usually applies to the amount left after the first reduction. Each percentage therefore has a different base. Adding the advertised rates treats both reductions as percentages of the original price, which overstates the saving. Start with the price of the eligible item and identify the exact order of the offer before calculating.
Turn each discount into a remaining-price multiplier: subtract its decimal rate from one. Multiply the original price by both multipliers. The effective discount is one minus their product. Swapping two unrestricted percentage discounts gives the same result because multiplication commutes. This stops being true when the offer includes a fixed amount, a maximum saving, or an eligibility threshold.
For a teaching example, take an original price of 100 in any one currency. A 20% first reduction removes 20 and leaves 80. The second reduction is 10% of 80, so it removes 8 and leaves 72. Total saving is 28, equivalent to a single 28% discount on the original 100. The second reduction is not 10 currency units.
View data
- Original
- 100 100
- After first discount
- 80 100 × 0.80
- After second discount
- 72 80 × 0.90
Worked example
For a teaching example, take an original price of 100 in any one currency. A 20% first reduction removes 20 and leaves 80. The second reduction is 10% of 80, so it removes 8 and leaves 72. Total saving is 28, equivalent to a single 28% discount on the original 100. The second reduction is not 10 currency units.
You can check the result by comparing the two routes. Sequential pricing gives 100 × 0.80 × 0.90 = 72; equivalent pricing gives 100 × (1 − 0.28) = 72. A competing offer of 30% off would leave 70 before any other costs. Use the final payable total, including separately calculated delivery and tax, when comparing actual offers.
100 × 0.80 × 0.90 = 72
100 − 72 = 28
28 / 100 × 100 = 28%
The calculator models two percentage reductions on the remaining price. It does not establish a seller’s coupon policy, tax treatment, minimum spend, eligible items or rounding method. Check those terms on the actual order. Keep intermediate values unrounded and round only as the seller’s billing rules require. A 100% reduction leaves zero in this model; no price becomes negative.
View data
- Original price
- 100
- First multiplier
- × 0.80
- Second multiplier
- × 0.90
Checks and limits
The calculator models two percentage reductions on the remaining price. It does not establish a seller’s coupon policy, tax treatment, minimum spend, eligible items or rounding method. Check those terms on the actual order. Keep intermediate values unrounded and round only as the seller’s billing rules require. A 100% reduction leaves zero in this model; no price becomes negative.
Related calculators
Sources: OpenStax — Understand Percent