Stacked Discounts

What two discounts in a row really come to, because they cannot be added.

Formula

How the calculation works

The second discount comes off the already-reduced price, not the original, so the two rates multiply instead of adding. 20% off 1,000 leaves 800, and 10% off 800 leaves 720: 280 saved, which is 28% of the original, not the 30% the two rates suggest. The general rule is that a% then b% leaves (1-a)(1-b) of the price, and the single rate matching it is 1 minus that.

Because multiplication commutes, order makes no difference to what you pay. Taking 10% then 20% also lands on 720, exactly the same as 20% then 10%. What changes with order is only the intermediate number, the amount standing after the first cut, which is why a shop advertising 20 then 10 and one advertising 10 then 20 are offering the same deal.

The gap between the added rates and the real discount widens as the rates grow. 20% then 20% is 36%, not 40%: the four points are the second rate failing to touch the 20% already gone. Two small discounts of 5% and 5% come to 9.75%, barely a quarter point off, but 50% then 50% is 75%, a full twenty-five points short of the 100% the naive sum promises.

Common mistakes

• Adding the rates: 20 + 20 read as 40% off when the price actually falls 36%. The error always flatters the shopper, so the total at the till comes out higher than expected.
• Applying the second rate to the original price. 20% then 10% off 1,000 is 700 if you subtract 30% from the original, but the till charges 720.
• Reading a stacked 20+10 tag as 30% when comparing it with a rival's flat 28%: the flat discount is the smaller number and the better deal.

When to use it

• Use it when a sale stacks one discount on another, to get the price you will really pay and the single rate that matches it, so you can compare it against a rival's flat offer.
• It is the wrong tool for a single discount, and it does not model tax added afterwards or a minimum spend, so a stacked rate on a total that then attracts sales tax is not the final figure.

Worked example

1,000 at 20% then 10% looks like 30% but is really 28%, leaving 720 to pay.

Common questions

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Last updated: 2026-09-29