Discount and final price
Apply one or two discounts in sequence, then tax, and see the true effective markdown. The point of the page is the gap between the advertised percentages and the discount you actually receive.
| Step | Amount | Change |
|---|---|---|
| List price | $120.00 | — |
| After 20% off | $96.00 | −$24.00 |
| After extra 10% off | $86.40 | −$9.60 |
| Total saved | $33.60 | 28.00% of list |
| Sales tax | $7.13 | 8.250% of the reduced price |
| Payable | $93.53 | Discounted price + tax |
Adding the two rates would suggest 30.0% off. Stacking gives 28.00% — the second discount applies to a smaller base.
P₁ = P(1 − d₁) · applied to list price
P₂ = P₁(1 − d₂) · applied to the reduced price
1 − (1−d₁)(1−d₂) · always below d₁ + d₂
P₂(1 + t) · tax is charged on the discounted price
A clear path from inputs to results.
Retailers advertise discounts that stack, and stacked percentages do not add. Twenty percent followed by ten is 28% off, not 30%. This engine applies each discount to the already-reduced price and reports the true markdown.
How to use
- Enter the list price.
- Set the first discount — the headline percentage.
- Set the second discount if the offer is “extra X% off reduced prices”.
- Add the sales tax rate so the payable amount is correct.
- Compare the effective discount with the sum of the two rates.
The formula
Reference: Standard retail markdown arithmetic (Horngren et al., Cost Accounting).
Worked example
$120 with 20% then a further 10%, plus 8.25% tax
- List price $120.
- First discount 20%, second discount 10%.
- Sales tax 8.25%.
- 1
After the first discount: 120 × 0.80 = $96.
- 2
After the second: 96 × 0.90 = $86.40.
- 3
Total saved: $33.60, which is 28.0% of list — not 30%.
- 4
Tax on the reduced price: 86.40 × 0.0825 = $7.13.
- 5
Payable: $93.53.
$86.40 before tax · 28.0% effective discount · $93.53 payable.
Interpreting the result
The shortfall from 30% to 28% comes from the second discount applying to a base that has already shrunk. The gap grows with the size of the discounts: 50% then 50% is 75% off, not 100%. Any offer above two stacked percentages should be checked this way before you believe the headline.
Assumptions & limitations
- Both discounts are percentages, so their order does not matter. Fixed-dollar coupons do not commute with percentages.
- Tax applies to the discounted price, which is the rule in most jurisdictions.
- No minimum spend, membership tier or excluded-brand conditions are modelled.
- The list price is the genuine pre-discount price, not an inflated reference.
Frequently asked questions
Why is 20% + 10% only 28%?
Because the second 10% applies to the already-discounted price. Algebraically 1 − (1−0.2)(1−0.1) = 0.28. The rates multiply as survival factors, not add.
Is tax charged before or after the discount?
After, in most jurisdictions. Tax is due on the price actually paid, so the discount reduces the taxable amount.
Does the order of discounts matter?
Not for percentage discounts — multiplication is commutative. It matters for fixed-dollar coupons: a $20 coupon before 20% off is worth more than the same coupon after.
How do I compare a percentage-off offer with a fixed-dollar one?
Convert both to the same basis: compute the final price under each and compare. A $30 coupon beats 20% off a $120 item ($24) but loses to 20% off a $200 item ($40).
Methodology last reviewed 2026-10-18. Results are informational and not financial or engineering advice — see our disclaimer.