- Purchasing power and future cost are inverses of the same price level — always be clear which one you are asking for.
- A constant-rate projection compounds, so small differences in the assumed rate diverge sharply over long horizons.
- At 2.5%, money loses half its purchasing power in about 28 years — the relevant timescale for any retirement plan.
- The rate here is your assumption, not a published index. Re-run it at a higher and a lower rate rather than trusting one number.
How inflation changes what money is worth
Inflation is a rise in the general price level, which is the same thing as a fall in what a unit of currency buys. Those are two descriptions of one event, and which one you use depends on which side of a transaction you are standing on.
If you are holding money — a savings balance, a fixed pension, a sum you plan to spend in fifteen years — the question is what it will buy. That is the amount divided by the price level. If you are planning to buy something — a house, a car, a year of tuition — the question is what it will cost. That is today’s price multiplied by the price level.
This calculator does both, from the same input, because confusing them is the most common inflation mistake. "$50,000 will be worth $30,514" and "$50,000 of goods will cost $81,931" are both true at 2.5% over twenty years, and they are not the same sentence.
The math
The price level after n years at rate i is (1 + i)ⁿ. Purchasing power is the amount divided by that; future cost is the amount multiplied by it. The two are exact inverses, which is why running one through the other returns the amount you started with — an identity the test suite checks rather than assumes.
The halving figure is the number of years until purchasing power falls by half: log(2) ÷ log(1 + i). At 2.5% that is 28 years, which is a useful sanity check on any plan measured in decades.
**No published price index is used anywhere on this page.** The rate is your assumption. A calculator that carried a historical consumer price series would be making a claim about the past that has to be re-verified every time the series is revised or extended, and a stale one is wrong in a way nothing on the page reveals. A historical lookup and a cost-of-living comparison are separately-sourced tools, not features to approximate here.
Worked example
$50,000 at 2.5% inflation over 20 years. The price level rises to 1.64 times today’s — so the $50,000 buys what $30,514 buys today, having lost $19,486 of purchasing power without a single dollar leaving the account.
Read the other way, the same inputs say that a basket of goods costing $50,000 today will cost $81,931 in twenty years. And the halving figure: at 2.5%, money loses half its purchasing power every 28 years. A retirement plan that runs thirty years past its start date is therefore planning across roughly a halving, which is the reason a nominal target set today is not the target it appears to be.
Key terms
- Inflation rate
- The annual rate at which the general price level rises. Here it is an input you choose, held constant across the horizon.
- Purchasing power
- What a nominal amount actually buys. It falls as prices rise, even when the number in the account has not changed.
- Nominal and real
- Nominal is the number on the statement; real is that number adjusted for the price level. A return that beats inflation is a real gain; one that does not is a nominal one only.
- Price level
- The cumulative multiple prices have risen by over the horizon — 1.64× after twenty years at 2.5%. It is the single number both directions of the calculation turn on.