Five Percentage Mistakes That Quietly Cost You Money
Stacked discounts, reversed price rises, and percent versus percentage points — the everyday percentage errors that make things look cheaper than they are.
Percentages feel like simple arithmetic, which is exactly why they are so easy to get wrong. The errors below are not obscure — they show up in shop windows, news headlines and payslips, and each one reliably makes something look better than it is.
1. Assuming stacked discounts add up
A shop advertises 20% off, then a coupon takes a further 20% off at the till. Most people read that as 40% off. It is 36%.
The reason is that the second discount applies to an already-reduced price. On a $100 item, the first 20% takes it to $80. The second 20% comes off the $80, removing $16 rather than $20. You pay $64.
| Stacked offer | Sounds like | Actually is |
|---|---|---|
| 20% + 20% | 40% off | 36% off |
| 30% + 20% | 50% off | 44% off |
| 50% + 20% | 70% off | 60% off |
| 50% + 50% | 100% off | 75% off |
The formula is 1 − (1 − d₁)(1 − d₂). Two 50% discounts can never reach free, because each one only ever removes half of what remains.
2. Thinking a rise and a fall of the same percentage cancel out
They do not, and the asymmetry is larger than most people expect.
A stock falls 50%, then rises 50%. It is not back where it started — it is 25% down. To recover from a 50% fall you need a 100% gain.
| Fall | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 33% | 50% |
| 50% | 100% |
| 80% | 400% |
The same trap works in reverse with prices. If a supplier raises a price 20% and later offers 20% off, you are still paying 4% more than the original.
3. Subtracting a percentage instead of dividing it out
This one turns up whenever tax is involved. A price is $120 including 20% VAT. What was the price before tax?
Subtracting 20% of $120 gives $96. That is wrong. The $120 represents 120% of the original, so you divide: 120 ÷ 1.2 = $100.
The rule: to remove a percentage that was added, divide by (1 + rate). To remove a discount that was applied, divide by (1 − rate). Subtraction only works when you know the percentage of the original figure, which by definition you do not.
4. Confusing percent with percentage points
An interest rate moves from 4% to 5%. Has it gone up by 1% or by 25%?
Both, depending on what you mean — which is why the two need different words. It has risen by one percentage point, and by 25 percent in relative terms.
This distinction is routinely blurred in reporting, and the ambiguity almost always flatters whoever is presenting the number. "Unemployment rose 0.5%" sounds trivial if it means half a percentage point on a 5% rate; that is actually a 10% increase in the number of people out of work.
5. Tipping on the wrong total
Etiquette says a tip is calculated on the pre-tax subtotal, because sales tax is money the restaurant never receives. Tipping on the post-tax total quietly adds a tip on the tax itself.
On a $60 meal with 8% sales tax, a 20% tip is $12.00 pre-tax and $12.96 post-tax. The gap is small, but it is a gap that only ever runs one way. Most people tip on the total for simplicity, which is a perfectly reasonable choice — just make it a choice rather than an accident.
The mental shortcuts worth learning
Three tricks cover most everyday percentage work.
- Find 10% first. Move the decimal one place left, then build: 20% is double it, 5% is half it, 15% is 10% plus half of 10%.
- Reverse the numbers. X% of Y always equals Y% of X. Working out 4% of 75 is fiddly; 75% of 4 is obviously 3.
- Divide to undo. Any percentage that was applied by multiplying is removed by dividing, never by subtracting.
If you would rather not do it in your head, the percentage calculator shows the working for all three question types, and the discount calculator handles stacked offers and sales tax together.