Black Friday. Sign says: "50% OFF + Take an additional 20% off at checkout!" My friend was ecstatic. "$100 jacket for $30!" I pulled out my phone calculator. "Actually, $40." She looked confused. "50 plus 20 is 70. 70% off = $30." Nope. Sequential discounts multiply, they don't add. 50% off = $50. Then 20% off of $50 = $10 more off = final price $40. Retailers know this. Most shoppers don't.
The Sequential Discount Formula
When you see "X% off, then Y% off," here's what actually happens:
Total discount = X% + Y%
Final price = Original × (1 - Total discount)
Example: $100, 50% + 20%
Total discount = 50% + 20% = 70%
Final price = $100 × (1 - 0.70) = $30 ❌
CORRECT (how it actually works):
After first discount: Original × (1 - X%)
After second discount: [Original × (1 - X%)] × (1 - Y%)
Example: $100, 50% then 20%
After 50% off: $100 × 0.50 = $50
After 20% off: $50 × 0.80 = $40 ✅
Combined formula:
Final = Original × (1 - X%) × (1 - Y%)
Final = $100 × 0.50 × 0.80 = $40
You thought you'd save $70. You only save $60. That's a $10 difference—not trivial on larger purchases.
Real Store Examples
Let's run the numbers on common retail discount scenarios:
| Original Price | Discount Offer | What People Think | Actual Price | Difference |
|---|---|---|---|---|
| $100 | 50% + 20% | $30 (70% off) | $40 | +$10 |
| $200 | 40% + 30% | $60 (70% off) | $84 | +$24 |
| $500 | 30% + 25% | $225 (55% off) | $262.50 | +$37.50 |
| $1,000 | 60% + 10% | $300 (70% off) | $360 | +$60 |
On a $1,000 purchase, the difference between what you expect to pay ($300) and what you actually pay ($360) is $60.
Why Retailers Love This Confusion
Stores intentionally phrase discounts to maximize perceived savings while minimizing actual discounts.
Tactic #1: "Additional" Language
"Take an additional 20% off sale prices!"
Sale items already marked down 30%. "Additional 20%" sounds like 50% total. It's not.
After 30% sale: $70
"Additional 20%" off $70: $70 × 0.80 = $56
Total discount: 44%, not 50%
You pay $56, not $50
Tactic #2: Large First Number
"60% off everything + extra 15% off clearance!"
Your brain anchors on the 60%. Adding 15% feels like 75% total.
$100 × 0.40 (after 60% off) × 0.85 (after 15% off) = $34
Total discount: 66%, not 75%
Tactic #3: Coupon Stacking
"Use code SAVE20 for 20% off, plus member discount of 10%!"
Sounds like 30% total. Nope.
Total discount: 28%, not 30%
💡 Rule of Thumb: Sequential Discounts
To calculate combined discount from two sequential discounts:
Combined % = X + Y - (X × Y)
Example: 50% + 20%
Combined = 50 + 20 - (50 × 20 ÷ 100)
Combined = 50 + 20 - 10 = 60% total
NOT 70%
The Markup/Discount Asymmetry
Here's another percentage trick retailers use: markup percentages don't equal discount percentages.
Markup from cost:
($100 - $50) ÷ $50 = 100% markup
If they "50% off" the retail price:
$100 × 0.50 = $50 final price
They broke even (selling at cost).
100% markup ≠ 50% discount in dollar terms
This is why "50% off" sales can still be profitable. If the markup was 200%, a 50% discount still nets them a profit.
Real Example: Mattress Store
List price: $1,600 (300% markup)
"50% OFF SALE!" → $800
Store's profit: $800 - $400 = $400 (100% markup still)
You think you got 50% off. They still doubled their money.
Percentage Increase vs. Decrease (Non-Symmetrical)
A 50% increase doesn't undo a 50% decrease. The math is not reversible.
Decrease by 50%:
$100 × 0.50 = $50
Increase by 50%:
$50 × 1.50 = $75
You're NOT back to $100. You're at $75.
You lost $25 (25% of original)
Stock market example:
- Stock drops 50%: $100 → $50
- To get back to $100, it needs to gain 100% (not 50%)
- $50 × 2.00 = $100
This is why market crashes are so devastating. A 50% drop requires a 100% gain to recover.
🔢 Calculate Real Discounts
See what sequential discounts, markups, and percentage changes actually mean in dollars.
Try Percentage Calculator →The "Up To" Scam
"Save up to 70%!"
Technically true if ONE item in the entire store is 70% off. Everything else could be 10% off.
"Up to" is marketing language for "probably not, but legally we're covered."
Real Data from a 2019 Study (CouponFollow):
- Stores advertising "up to 70% off" had an average discount of 22%
- Only 3% of items hit the advertised maximum
- 87% of shoppers overestimated savings based on the "up to" number
Percentage Points vs Percentages (Different Things)
This confuses even smart people.
Change in percentage POINTS: 1 percentage point
(6% - 5% = 1 point difference)
Change in PERCENT: 20%
(1 ÷ 5 × 100 = 20% increase)
News headline: "Rates up 20%!" (scary)
Reality: "Rates up 1 percentage point" (less scary, same thing)
Why it matters: Media uses whichever sounds more dramatic.
The Tax Confusion
Sales tax percentage is calculated on AFTER-discount price, not original price.
Discount: 40%
Sales tax: 8%
WRONG calculation:
Discount: $100 × 0.40 = $40 off
Tax: $100 × 0.08 = $8
Total: $100 - $40 + $8 = $68 ❌
CORRECT calculation:
After discount: $100 × 0.60 = $60
Tax on $60: $60 × 0.08 = $4.80
Total: $60 + $4.80 = $64.80 ✅
The difference is small on one purchase, but adds up over time if you're budgeting.
How to Actually Calculate Best Deals
Don't trust percentage marketing. Calculate final dollar price.
Strategy: Work Backwards
$100 × 0.60 × 0.80 = $48
Offer B: "Buy one, get one 50% off" (for 2 items)
Item 1: $100 × 1.00 = $100
Item 2: $100 × 0.50 = $50
Total for 2: $150
Average per item: $75
Offer A is better ($48 vs $75 per item)
The Subscription Trap
"Get 20% off your first month, then 10% off forever!"
Sounds generous. Let's calculate 12 months:
Month 1: $50 × 0.80 = $40
Months 2-12: $50 × 0.90 × 11 = $495
Year 1 total: $535
Average monthly cost: $535 ÷ 12 = $44.58
You're paying 89.2% of full price, not 80-90%
The big first-month discount creates the perception of ongoing savings greater than reality.
Final Thoughts
Percentage math is intentionally confusing in retail/marketing because:
- ❌ Sequential discounts look bigger than they are (50% + 20% ≠ 70%)
- ❌ "Up to X%" is meaningless (average discount is way lower)
- ❌ Markup percentages don't reverse with equal discount percentages
- ❌ Percentage changes aren't symmetrical (50% down ≠ 50% up to recover)
- ❌ "Additional" language obscures real total discount
Defense strategy:
- Ignore percentage claims. Calculate final dollar price.
- Use a calculator for sequential discounts (your phone has one)
- Compare final prices, not discount percentages
- Remember: "Up to" = "probably not"
- For stock/investments: percentage losses require larger gains to recover
My friend at the Black Friday sale? She calculated the real price ($40), compared it to other stores, and found the same jacket for $35 at a competitor with a straight 65% off (no stacking nonsense).
Math literacy saves money.
💬 Related Shopping Math Tools
Calculate real costs and savings:
- Percentage Calculator - Calculate accurate discounts
- Discount Calculator - Compare sale prices
- Sales Tax Calculator - Calculate final price with tax
- Markup Calculator - Understand retailer pricing
About the Author: This article was created by the Calcs.top editorial team. All percentage calculations use standard mathematical formulas. Retail tactics described are common industry practices as of 2025. Statistics on "up to" savings from CouponFollow 2019 consumer behavior study. This is educational content about mathematical literacy.