Why 20% + 10% Off Is Not 30% Off
Stacked discounts are everywhere: “20% off sale, plus an extra 10% for members.” The numbers look like they should add up to 30%, but they don’t. The actual combined saving is only 28%. Here is exactly why.
The maths, step by step
Start with a $100 item.
- Apply 20% discount: $100 × 0.80 = $80
- Apply 10% discount to the new price: $80 × 0.90 = $72
- Total saving: $100 − $72 = $28, which is 28% off the original.
The second discount acts on $80, not $100. That is the key. The base has changed.
The formula
For A = 20 and B = 10: 100 − (0.80 × 0.90) × 100 = 100 − 72 = 28%.
More examples
| First discount | Second discount | Naive sum | True combined |
|---|---|---|---|
| 10% | 10% | 20% | 19% |
| 25% | 25% | 50% | 43.75% |
| 50% | 50% | 100% | 75% |
| 30% | 10% | 40% | 37% |
| 15% | 5% | 20% | 19.25% |
Why retailers love advertising stacked discounts
Advertising “20% + 10%” rather than simply “28% off” creates several psychological advantages:
- Two discounts feel like two acts of generosity, even though the combined saving is mathematically smaller than the sum suggests.
- The first number anchors the value. Customers mentally add 20 + 10 and feel they are getting a great deal.
- Membership exclusivity. Framing the second discount as a loyalty or member benefit increases perceived status even if the extra saving is small.
- Price comparison is harder. A competitor offering a flat 30% is technically better, but shoppers often cannot quickly compare the two.
The investment version: gains and losses
The same maths applies to investment returns, and the asymmetry is even more stark:
- A 50% gain followed by a 50% loss leaves you at 75% of your starting value — a net loss of 25%.
- A 20% gain followed by a 20% loss leaves you at 96% — a 4% net loss.
- To recover from a 50% loss, you need a 100% gain, not 50%.
This is why volatile assets are mathematically harder to profit from than a simple average return suggests.
How to always find the true combined discount
Use the Compound Percentage Calculator to enter any two percentages and instantly see:
- The true combined discount or increase
- The difference from the naive (incorrect) sum
- The final value if you enter an original price
Related articles
- 5 Percentage Mistakes Almost Everyone Makes
- What Is a Good Discount Percentage?
- Discount Calculator — single discount calculator