When you can combine a 20% off coupon with a 10% discount, the result is 28% off — not 30%. Here's why and how to think about it.
People assume 20% off + 10% off = 30% off. They don’t. The second discount is applied to the already-discounted price.
Take a $100 item with two stackable discounts: 20% and 10%.
$100 × (1 − 0.20) = $80 (first discount)
$80 × (1 − 0.10) = $72 (second discount)Total savings: $28, or 28% off — not 30%.
For any two stacked discounts P1 and P2:
combined factor = (1 − P1/100) × (1 − P2/100)
total discount = 1 − combined factorFor 20% and 10%: 0.80 × 0.90 = 0.72, so total discount = 28%.
| Discount 1 | Discount 2 | Actual total | vs. sum |
|---|---|---|---|
| 10% | 10% | 19% | 1pp lost |
| 20% | 10% | 28% | 2pp lost |
| 25% | 15% | 36.25% | 3.75pp lost |
| 30% | 20% | 44% | 6pp lost |
| 50% | 50% | 75% | 25pp lost |
The larger the discounts, the bigger the gap between the sum and the actual combined total.
Multiply each “keep” factor: (1 − P1) × (1 − P2) × (1 − P3). Combining 20%, 10%, and 5%: 0.80 × 0.90 × 0.95 = 0.684, so total discount = 31.6%.
20% then 10% gives the same final price as 10% then 20%. But retailers sometimes specify the order in their terms — when in doubt, check whether your loyalty discount applies before or after a promotional coupon.
No. The second discount applies to the already-reduced price, so the combined discount is always slightly less than the sum. 20% + 10% = 28%, not 30%.
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