Black Friday, Cyber Monday, end-of-season sales — discounts are everywhere. But do you really know how much you're saving? Especially when stores stack discounts like "20% off + extra 10% off," the math isn't always what it seems.
The Basic Discount Formula
Savings = Original Price × (Discount% ÷ 100)
Savings = $120 × 0.30 = $36
Sale price = $120 − $36 = $84
Shortcut: $120 × 0.70 = $84 (multiply by what's left: 100% − 30% = 70%)
Why Double Discounts Don't Add Up
This is the most common misunderstanding in retail math. When a store says "20% off + extra 10% off," most people think they're getting 30% off. They're not.
The second discount applies to the already-reduced price, not the original. The discounts compound, they don't add.
What people think: 30% off → $70
What actually happens:
Step 1: $100 × 0.80 = $80 (20% off)
Step 2: $80 × 0.90 = $72 (10% off the $80)
Effective discount: 28%, not 30%
You pay $72, not $70.
The formula for the effective combined discount is: Effective% = 1 − (1 − D₁/100) × (1 − D₂/100). For 20% + 10%: 1 − 0.80 × 0.90 = 1 − 0.72 = 0.28 = 28%.
Finding the Original Price
Sometimes you see a sale tag and want to know the original price. Work backwards by dividing the sale price by (1 minus the discount rate).
$60 ÷ (1 − 0.25) = $60 ÷ 0.75 = $80
Tax After Discount
In most US states, sales tax is calculated on the discounted price, not the original. This means you save on tax too. If a $100 item is 25% off with 8% tax: sale price = $75, tax = $75 × 0.08 = $6, total = $81. Not $108 × 0.75 = $81. Same result in this case, but the principle matters for understanding your receipt.
Is the "Deal" Actually Good?
Retailers frequently inflate original prices before "discounting" them. A $200 jacket "marked down" to $120 (40% off!) might have always been worth $120. Compare prices across multiple retailers before assuming a discount means a deal. Use price tracking tools for online shopping to see historical prices.