Why 40% Off Plus 15% Off Is Not 55% Off
A sign says 40% off. Your coupon says an extra 15% off. It is tempting to add them and expect 55% off. The real figure is 49%.
The second discount applies to a smaller price
Percentage discounts are applied one after the other. The coupon takes 15% off the sale price, not the original price.
On a $120.00 item:
- 40% off $120.00 leaves $72.00.
- 15% off $72.00 leaves $61.20.
You saved $58.80, which is 49% of the original price. If the discounts had simply added up, the price would have been $54.00.
The shortcut
Multiply what you keep each time. 40% off means you pay 60%. 15% off means you pay 85%.
0.60 × 0.85 = 0.51, so you pay 51% and save 49%.
| First discount | Extra discount | Looks like | Actually is |
|---|---|---|---|
| 20% | 10% | 30% | 28% |
| 25% | 15% | 40% | 36.3% |
| 30% | 20% | 50% | 44% |
| 40% | 15% | 55% | 49% |
| 50% | 20% | 70% | 60% |
| 50% | 50% | 100% | 75% |
Notice the last row: 50% off plus another 50% off is 75% off, not free.
Does the order matter?
Not for two percentage discounts. 0.60 × 0.85 is the same as 0.85 × 0.60.
It does matter when one discount is a fixed dollar amount. On a $100.00 item with $20.00 off and 25% off:
- Dollars first: ($100.00 − $20.00) × 0.75 = $60.00
- Percent first: $100.00 × 0.75 − $20.00 = $55.00
Taking the percentage first gives the lower price. Check the coupon terms to see which order a store uses.
Then sales tax
In almost every state, store discounts reduce the taxable price, so sales tax is charged on the discounted amount. At 7.25%, the $61.20 item above costs $65.64 at the register.
This article is general information, not tax, legal or financial advice. See our disclaimer.