What is my raise actually worth?

What a pay rise is worth once inflation is counted, and what the new salary buys in the money you have today. It is before tax, and a raise that crosses a tax band keeps less of itself than this shows, and it compares a full year at the new salary with a full year at the old one, so a rise arriving mid-year is worth less than the figure says.

A 7% raise against 5% inflation is 1.90% in real terms: the new salary is 16,050 a month, and it buys what 15,286 buys today, assuming a full year at the new salary.

A raise of 7% against inflation of 5% is not a gain of 2%. It is 1.90%, and the difference is not rounding — it is that the erosion applies to the whole salary rather than to the increase alone. What survives is one plus the raise, divided by one plus inflation, less one.

The two answers agree closely at low numbers and part company exactly where this region needs them most. At 15% against 25% the subtraction says you are 10 points down; the division says 8. At 5% against 12% the subtraction says 7 down and the division says 6.25. Whenever prices are rising the subtraction overstates the answer in whichever direction it points — it exaggerates a gain and it exaggerates a loss — and the faster they rise the further out it is.

The inflation that counts is the one where the salary is spent, not where it is earned. A salary paid in a pegged currency and sent to a household living somewhere else is being eroded by the second country's prices, and the letter announcing the raise says nothing about that.

Below zero the picture inverts rather than clamping. A raise smaller than inflation is a real cut: the figure on the contract went up and what it buys went down, both at once, and the card says both.

(1 + raise) ÷ (1 + inflation) − 1

Both figures are annual, and the inflation that counts is the one where the salary is actually spent.

What it assumes

• The raise is annual and applies for a full year. A rise granted in the ninth month is worth a quarter of this in the year it arrives, and the whole of it only from the next one.
• Inflation is the rate where the money is spent, over the same year. Where a household's own basket is heavier in food and rent than the published index, the rate that matters to them is higher than the headline one.
• The figure is the monthly salary before tax and before any deduction. A raise that pushes income into a higher band, or past a threshold for a benefit, keeps less of itself than the percentage suggests.
• Nothing else in the package moves. Allowances, a bonus and an end-of-service entitlement are usually calculated on the basic wage, so a raise that lands entirely on an allowance is worth less over time than one on the basic.