How Stacked Discounts Work

Stacked discounts are several decreases applied one after another. Each percent acts on whatever price is left, so the combined effect is a product of pay-factors, not a sum of the badges. The difference is small on a modest stack and enormous when the badges are large. “Up to 70% off” plus an extra “20% off” is a genre of sign that needs a calculator more than it needs excitement.

Multiply the pay factors

Pay factor for a discount d is (1 − d/100). Two discounts:

combined pay factor = factor₁ × factor₂

total percent off = (1 − combined pay factor) × 100

20% then 10%. Factors 0.80 and 0.90. Product 0.72. You pay 72% and save 28%, not 30%.

On a €250 jacket: after 20% the price is €200; after 10% it is €180. A naive 30% off would be €175. Five euros, on this jacket, is the entire content of the mistake. On a €2,500 sofa it is €50. The discount calculator used twice — once per step — shows the intermediate price, which is the number a cashier can match to the receipt.

Three discounts feel like they “must” add into something round. 30 + 20 + 10 = 60, and the true discount is just under half. I would rather know I am paying about half than believe I am paying 40%.

Order, coupons, and exclusions

Pure percents commute: 10% then 20% equals 20% then 10%. A €15 voucher does not commute with a percent.

€100 item, 20% off, €15 voucher:

• Percent then voucher: €80 − €15 = €65
• Voucher then percent: (€100 − €15) × 0.80 = €68

The better order for the shopper is percent first, and it is also the order many terms forbid (“voucher valid on full price only”) or require (“applied at checkout after promotions”). Read the exclusion before you multiply. A stacked-discount calculation that ignores “not combinable” is fan fiction.

Free shipping is not a percent of the item. It is a euro amount you would have paid, and only if you would have paid it. Folding a €5 shipping waiver into a “percent off” the product usually flatters the offer.

Tax sits outside the stack

Compute the stacked net price first, then add VAT or sales tax if the price you started from was exclusive. If the shelf price was already inclusive, the stack applies to the gross and you do not add tax again. The failure mode is stacking a percent off the inclusive price and then adding VAT on the result. That taxes a discount and double-counts the original tax.

A receipt check

You should be able to point at three numbers: original, price after the first promotion, price after the second. If the receipt only shows the final discount as one line, reconstruct the factors and see whether the final pay factor matches. If it matches a sum instead of a product, the till added the percents and you were over-discounted — rare, and worth a polite question — or you misread one of the rates.

A till-side example with three numbers

A coat is listed at €180. The seasonal sale is 25% off, and your loyalty code is an extra 15% off the reduced price. Tax is already inside the €180 (the shop is not going to add it again).

1. After 25%: 180 × 0.75 = €135.
2. After 15% of €135: 135 × 0.85 = €114.75.
3. Combined pay factor: 0.75 × 0.85 = 0.6375, so you pay 63.75% of €180 and the true discount is 36.25%, not 40%.

The naive 40% off would have been 180 × 0.60 = €108. The stack costs you €6.75 more than the added-percent fantasy. That is the number to remember when a friend says “it’s basically 40.” It is basically 36, and the basically is doing a few euros of work.

If the loyalty code is “€15 off” instead of 15% off, order matters and the terms matter. Percent then €15: 135 − 15 = €120. €15 then percent: (180 − 15) × 0.75 = €123.75. Three euros, and only if both can be combined. Write the intermediate €135 on the receipt check so a single “discount €65.25” line can be rebuilt. If you cannot rebuild it, ask which rate hit which base before you assume the till added the badges.

When a stack is still worth it

A true 28% off can be a good price. The point of the arithmetic is not to sneer at promotions. It is to stop comparing a stacked offer with a single 30% offer as if the badges were denominators in the same fraction. Compare final prices of the specific items. Use factors when the original is shared and you are choosing which coupon pair to apply. The moment a voucher is a fixed amount, write both orders down. The larger of those two savings is the most the terms can be worth; the terms decide whether you are allowed to take it. The discount calculator is one step at a time, which is the right speed for a stack. One visit with the rates added together is the wrong speed. If a third offer is “an extra 5% off already reduced prices,” fold it in as another factor (× 0.95) and recompute the pay percent from the original. The badge count is not the discount. The product of the factors is.