The Percentage, and Then the Real Number
A raise is easy to calculate and easy to misread:
``
increase % = (new salary − old salary) ÷ old salary × 100
`
A $4,000 rise on $80,000 is 5%. Whether that is a raise at all depends on inflation.
Real Terms Is the Only Terms
| Nominal raise | Inflation | Real change |
|---|---|---|
| 5% | 2% | +2.9% |
| 3% | 3% | 0% |
| 2% | 4% | −1.9% |
| 0% | 3% | −2.9% |
The exact calculation is (1 + raise) ÷ (1 + inflation) − 1, not raise minus inflation,
though the difference is small at ordinary rates.A 3% raise in a 3% inflation year is not a raise. It is being paid the same. Any negotiation
that starts from "we gave you 3%" should be answered in real terms.
Compounding Cuts Both Ways
Small annual differences compound into large gaps over a career:
| Annual raise | $80,000 after 10 years |
|---|---|
| 2% | $97,519 |
| 3% | $107,513 |
| 4% | $118,412 |
| 5% | $130,312 |
One percentage point a year is $10,000 of annual salary after a decade — and every future
raise is calculated on the larger base, so the gap widens indefinitely.Promotions and External Moves
Internal raises typically run 2–5%. Promotions add 8–15%. External moves have historically
produced the largest jumps, because a new employer prices you at market and an existing one
prices you against last year.
That is not an argument for leaving. It is an argument for knowing the market rate for your
role and raising it in a review, where the counterfactual is explicit.
Total Compensation, Not Salary
A 5% salary increase with a reduced bonus target can be a pay cut. Compare the whole package:
base, bonus target and actual payout history, equity grant and vesting, pension
contribution, and the value of any benefit that changed.
The Four Percentage Questions
Almost every percentage problem is one of these, and mixing them up is the most common
arithmetic error there is:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × (X ÷ 100) | 15% of 80 = 12 |
| X is what % of Y? | (X ÷ Y) × 100 | 12 is 15% of 80 |
| X is Y% of what? | X ÷ (Y ÷ 100) | 12 is 15% of 80 |
| % change from X to Y | ((Y − X) ÷ X) × 100 | 80 → 92 is +15% |
Percentage Points Are Not Percent
A rate moving from 4% to 5% is one percentage point, and a 25% increase. Both
statements are true and they are not interchangeable — headlines routinely use the smaller
one when reporting a rise and the larger one when reporting a fall.
Increases and Decreases Do Not Cancel
| Start | Change | Result |
|---|---|---|
| 100 | +50%, then −50% | 75 |
| 100 | −50%, then +50% | 75 |
| 100 | −20%, then +25% | 100 |
The reason is that the second percentage applies to a different base. To reverse a −20% you
need +25%, not +20%. This is why a stock that falls 50% must double to break even, and why
"we cut costs 30% then grew 30%" leaves you 9% down.Reversing a Percentage
To find the price before a 20% discount, divide by 0.8 — do not add 20%:
`
before = after ÷ (1 − discount)
$80 ÷ 0.8 = $100 ✓
$80 × 1.2 = $96 ✗
``
The same asymmetry applies to tax, tips, markups and platform fees.