Black Friday email: "50% OFF + EXTRA 20% OFF!" You see "70% off!" and hit checkout. Then you look at the final price and think Wait, that can't be right. It's not. Stores are banking on you not understanding sequential percentages. Here's the math they hope you never learn.
❌ THE MYTH
50% off + 20% off = 70% off total
✅ THE REALITY
50% off + 20% off = 60% off total (you lost 10%)
The Sequential Discount Trap
Here's what actually happens with "50% off, then an additional 20% off":
Step 1: Apply first discount (50% off)
$100 × 0.50 = $50 discount
Price after first discount: $100 - $50 = $50
Step 2: Apply second discount (20% off remaining price)
$50 × 0.20 = $10 discount
Final price: $50 - $10 = $40
Total savings: $60 out of $100 = 60% off (NOT 70%)
The second discount applies to the reduced price, not the original price. You "lost" that extra 10% because 20% of $50 is only $10, not $20.
The Correct Formula:
Where d1 and d2 are decimals (50% = 0.50, 20% = 0.20)
Example:
Effective = 0.50 + 0.20 - (0.50 × 0.20)
= 0.70 - 0.10
= 0.60 (60%)
💡 Quick Mental Math Trick
To find the final price multiplier:
50% off + 20% off:
= (1 - 0.50) × (1 - 0.20)
= 0.50 × 0.80
= 0.40 (you pay 40% of original = 60% off)
Real Store Scenarios (How They Trick You)
Scenario 1: The Membership "Bonus"
Store ad: "30% off for members, PLUS an extra 15% off this weekend!"
| Original Price | What You Think | What You Actually Get | Difference |
|---|---|---|---|
| $200 jacket | 45% off = $110 | 40.5% off = $119 | -$9 |
(1 - 0.30) × (1 - 0.15) = 0.70 × 0.85 = 0.595
You pay 59.5% of original = 40.5% total discount
$200 × 0.595 = $119.00 (not the $110 you expected)
Scenario 2: The Coupon Stack
Item: $80, on sale for 25% off. You have a 10% coupon.
Your brain: "35% off! I'm paying $52!"
Reality: 32.5% off, you're paying $54.
Step 2: 10% coupon → $60 × 0.90 = $54
vs.
If it were truly 35% off: $80 × 0.65 = $52
You "lost" $2 to sequential percentage math.
The Order Matters (Sometimes)
Here's a weird truth: with sequential percentages, the order doesn't matter for the final price.
Option A (40% first):
$100 → $60 → $54
Option B (10% first):
$100 → $90 → $54
Same final price! (Multiplication is commutative)
BUT... this only applies to pure discounts. Once you introduce:
- Flat-amount coupons ($10 off)
- Caps ("up to $50 discount")
- Minimum purchase requirements
...then order absolutely matters.
🧮 Calculate Real Discount Percentages
Stack multiple discounts and see your actual savings. No surprises at checkout.
Try Percentage Calculator →The Markup-Then-Discount Scam
Classic retailer move:
- Sell item for $100 (actual value: $80)
- Raise "original price" to $150
- Put it "on sale" for 33% off
- Final price: $100
You think: "Wow, $50 savings!"
Reality: You paid full (inflated) price.
But the item was never worth $150. It's a fake reference price.
⚠️ The "Compare At" Lie
Look for weasel words on price tags:
- "Compare at $199" (we made up this number)
- "Suggested retail $299" (nobody actually pays this)
- "Regular price $149" (was never sold at this price)
Unless you know the item's actual market price, the "savings" are fiction.
The Tax / Tip Confusion
Percentages get especially weird when adding (tax/tip) vs subtracting (discounts).
Example: Dinner Bill with Tip and Discount
Bill: $100, you have a 20% off coupon. Tax is 8%, tip is 20%.
Common mistake: "20% off + 8% tax + 20% tip = 8% total increase"
Reality: Order matters, and percentages apply to different bases.
| Step | Calculation | Running Total |
|---|---|---|
| Original bill | - | $100.00 |
| 20% discount | $100 × 0.80 | $80.00 |
| 8% tax (on discounted amount) | $80 × 1.08 | $86.40 |
| 20% tip (on original pre-discount? or post?) | ⚠️ This is where it gets messy | |
Tip Calculation Debate:
- Option A (tip on original): $100 × 0.20 = $20 tip → Total = $106.40
- Option B (tip on discounted): $80 × 0.20 = $16 tip → Total = $102.40
- Option C (tip on after-tax): $86.40 × 0.20 = $17.28 tip → Total = $103.68
Etiquette answer: Always tip on the pre-discount amount (Option A). The server didn't give you worse service just because you had a coupon.
The Percentage Increase ≠ Percentage Decrease Trap
This one breaks people's brains:
⚠️ WARNING: Non-Symmetrical Math Ahead
Stock goes up 50%, then down 50%. Where are you?
Up 50%: $100 × 1.50 = $150
Down 50%: $150 × 0.50 = $75
You lost $25 (25% of original) even though percentages "canceled out."
Why? Because the 50% decrease applied to a larger base ($150) than the 50% increase ($100).
To Break Even, You Need a Bigger Increase:
| If You Lose... | You Need to Gain... | To Break Even |
|---|---|---|
| 10% | 11.1% | $100 → $90 → $100 |
| 20% | 25% | $100 → $80 → $100 |
| 25% | 33.3% | $100 → $75 → $100 |
| 50% | 100% | $100 → $50 → $100 |
| 75% | 300% | $100 → $25 → $100 |
| 90% | 900% | $100 → $10 → $100 |
💡 Investment Lesson
This is why "recovering from a market crash" takes exponentially longer than the crash itself. A 50% crash requires a 100% gain to break even.
2008 financial crisis: S&P 500 dropped ~50% in 18 months, took 4+ years to recover to break-even.
The Percentage Point vs Percentage Confusion
News headline: "Interest rates increased from 2% to 4%"
Wrong interpretation: "Rates went up 2%"
Correct interpretation: "Rates went up 2 percentage
points (but that's a 100% increase)"
Percentage change: (4 - 2) ÷ 2 × 100 = 100% increase
Real Example: Mortgage Rate Impact
$400,000 home, 30-year mortgage:
| Interest Rate | Monthly Payment | Total Interest Paid |
|---|---|---|
| 3% | $1,686 | $207,000 |
| 5% | $2,147 | $373,000 |
| Difference (2 percentage points) | +$166,000 | |
A "small" 2 percentage point increase costs you an extra $166,000 over the life of the loan. That's an 80% increase in total interest paid.
Quick Reference: Common Percentage Tricks
✅ Smart Shopper Formulas:
-
Stacked discounts: Multiply the "pay" percentages
Final = Original × (1-d1) × (1-d2) × (1-d3)... -
Find discount percentage from prices:
Discount% = (Original - Sale) ÷ Original × 100 -
Find original price from sale:
Original = Sale ÷ (1 - Discount%) -
Compare "deals":
Calculate final price, not discount %—bigger % doesn't always mean better deal
❌ Don't Fall For:
- "Up to 70% off!" (one clearance item is 70%, rest is 10%)
- Adding sequential discount percentages
- Assuming percentage changes are symmetrical (up 50% ≠ down 50%)
- Confusing percentage points with percentages (especially in finance news)
Final Thoughts
Retailers are not your friends. They have MBAs and marketing teams dedicated to making "50% off + 20% off" sound like 70% off while mathematically being 60% off.
The good news? Now you know the tricks:
- ✅ Sequential discounts multiply, they don't add
- ✅ Always calculate the final price, not just the discount
- ✅ Percentage increases and decreases are not symmetrical
- ✅ "Compare at" prices are often fiction
Next Black Friday, while everyone else is mentally adding "50 + 25 = 75% off!", you'll be the one who whips out the calculator and realizes you're actually only saving 62.5%.
And you'll sleep better knowing you weren't fooled.
💬 Related Math Tools
Master percentage calculations:
- Percentage Calculator - Calculate discounts, increases, and changes
- Discount Calculator - Find final prices after multiple discounts
- Sales Tax Calculator - Calculate total with tax
- Tip Calculator - Calculate tips accurately
About the Author: This article was created by the Calcs.top editorial team, with input from mathematicians and consumer advocates. All calculations follow standard arithmetic principles. Always verify final prices at checkout and read fine print on promotional offers.