Successive percentage discounts

20% off, then another 10% off: is that 30% in total? Predict the effective discount and compare the same starting price.

Formula and worked example

The base changes

A 20% discount on 100 price units leaves 80. The next 10% is taken from 80, not from the original 100, so it removes 8. The final price is 72 and the total discount is 28%, not 30%.

Multiply what remains

Final price = original price × (1 − a/100) × (1 − b/100). Effective discount = [1 − (1 − a/100)(1 − b/100)] × 100%. The same principle explains why a 20% rise followed by a 20% fall leaves 96% of the starting value.

When does order matter?

For two unrestricted percentage reductions applied in sequence, switching their order gives the same mathematical result. But fixed-amount coupons, caps, minimum spend, shipping and intermediate rounding can change a real checkout. Read the conditions before applying this simple model.

Assumptions and limits

Use the same currency throughout. Prices are displayed to two decimal places; calculations keep the unrounded value. Tax, shipping, fixed-amount coupons and store-specific rounding are excluded. A discount percentage alone does not establish a product’s value.

This is a learning exercise, not a validated assessment.