Successive discounts multiply

When two discounts are applied to a price in sequence, the temptation is to add the percentages. This is a mistake: discounts do not add up, their factors are multiplied.

Example — Seasonal sales

A garment costing $80$ EUR is discounted by $30\%$, then a further promotion applies a second discount of $10\%$ on the already-reduced price.

• After the first discount: $80\cdot 0{,}70 = 56$ EUR.
• After the second: $56\cdot 0{,}90 = \boxed{50{,}40}$ EUR.

Overall discount: $(80-50{,}40)/80 = 37{,}0\%$ (not $40\%$: discounts do not add up, their factors $0{,}7\cdot 0{,}9 = 0{,}63$ are multiplied).

The overall factor $0{,}7\cdot 0{,}9 = 0{,}63$ corresponds to a single discount of $37\%$, not $40\%$. Adding the percentages always overestimates the real discount.

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Topics: Percentages
Concepts: Discount
Methods: Discount percentage
Skills: Calculating