Inflation and what your money buys
Your data
If what you have is the accumulated figure for the whole stretch rather than a yearly rate, type it in the rate field and put one year below. The arithmetic is the same either way.
This page is about prices going up. Prices falling is a real thing and the same arithmetic runs backwards for it, but every label here would then read the wrong way round, so the field starts at zero.
Results
What that amount will buy by then, in today's money
—
| How much prices go up over the whole stretch | — |
| How much of the purchasing power is gone | — |
| What the amount would have to become just to stand still | — |
| What a naive sum of the yearly rates would have said | — |
Year by year
| Year | Prices, from the start | What the amount buys | Purchasing power lost |
|---|
The other habit worth dropping is adding the yearly rates up. Ten per cent a year for five years is not fifty per cent, it is sixty one point zero five, because each year climbs on top of the one before. Over twenty years at six per cent the naive sum says one hundred and twenty while the real figure is two hundred and twenty one.
And getting back what was lost costs more than losing it. A pay packet that fell thirty per cent behind needs to rise by nearly forty three per cent to be where it was, not thirty, because the rise is measured against the smaller amount that is left.
If prices went up sixty per cent, did my money lose sixty per cent?
No, it lost thirty eight. The two numbers measure against different things: the price rise is measured against what things used to cost, and the loss of purchasing power against what they cost now.
If prices rise by a given amount, the purchasing power falls by that amount divided by one plus itself. Sixty one per cent on prices is a loss of thirty eight, a doubling of prices is a loss of half, and prices ten times higher is a loss of ninety per cent, never a hundred.
Why can I not just add the yearly rates together?
Because each year climbs on top of the one before. Ten per cent a year for five years is not fifty per cent, it is sixty one point zero five, and the gap widens the longer the stretch runs.
Over twenty years at six per cent a year the naive sum says one hundred and twenty per cent while the real figure is two hundred and twenty one. This page prints the naive sum next to the real one so the distance is visible.
How much does a salary have to rise to keep up?
To keep pace from here, by the same amount prices rise: if they go up ten per cent, the salary needs ten per cent and the two cancel out.
Recovering ground already lost costs more. A salary that has fallen thirty per cent behind needs to rise by nearly forty three per cent to be back where it was, because the rise is measured against the smaller amount that is left.
Where do I get the inflation rate to type in?
From whichever official index applies to you, over the stretch you care about. This page deliberately does not pick one: indices differ by country and by what they measure, and a household's own basket differs from all of them.
If you already have the accumulated figure for the whole period, type it in the rate field and put one year below. The arithmetic is identical.
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