The formula
final = price × (1 − d₁) × (1 − d₂) × …
What it means
Each discount applies to what is left of the previous one, not to the original price, so the percentages do not add. The second 20% of a «30% + extra 20%» is worked out on the 70% that remained, which is why it takes off fourteen points and not twenty. The bigger the discounts, the bigger the gap.
How to work it out by hand
- Turn each discount into the factor it leaves: 30% leaves 0.70
- Multiply the price by the first factor
- Multiply the result by the second, and so on
- For the equivalent discount, compare the final price with the starting one
What is worth knowing
The equivalent single discount is the figure that compares two offers. «40% off» and «30% plus an extra 20%» look the same or better the second way, and in fact the first leaves the item at 60 and the second at 56: the second wins, but by four points, not by ten. It works the same in reverse: chaining a rise with a discount gives the same final price whichever order you use, though plenty of people expect otherwise.