How inflation compounds over time
Inflation compounds exactly like interest. Each year’s price rise is calculated on prices that have already risen, not on the original starting price, so the increases stack on top of each other rather than adding up in a straight line. That single mechanic explains why a modest, steady inflation rate — the kind central banks openly target — can still double the cost of living over a working life. Anyone who already understands compound interest already understands inflation: it is the same formula, pointed at prices instead of savings.
The same loop
A savings balance growing at 5% a year and a price level rising at 2% a year are obeying the identical formula: multiply by (1 + rate), then do it again next year on the new, larger number. A bank account doesn’t earn its second year of interest only on the money you deposited — it earns interest on the deposit plus the first year’s interest. Prices work the same way. If a basket of goods costs more after year one, year two’s rise is calculated on that higher figure, not on what things cost when you started paying attention. There’s no separate “inflation math.” It’s the compounding loop wearing a different label.
The long-run table
That loop is why small rates matter over long periods. Something costing €100 today, compounding at 2% a year, costs €121.90 after 10 years, €148.59 after 20 years, and €199.99 after 35 years.
| Years | Cost of today’s €100, at 2% inflation |
|---|---|
| 10 | €121.90 |
| 20 | €148.59 |
| 35 | €199.99 |
Notice the shape: roughly €22 added in the first decade, but the price level still climbs steadily rather than slowing down, because each later year is compounding on an already-larger base. Over 35 years, a 2% rate has effectively doubled the price.
Both forces at once
Real life rarely gives you inflation on its own — savings and prices compound simultaneously, and what matters to a saver is the gap between them. A balance growing at 5% nominal while prices rise at 2% doesn’t leave the saver 3% better off in real terms; it leaves them 2.94% better off, because both processes are compounding and the exact gap has to be worked out by dividing, not subtracting. At 10% nominal against 8% inflation, the real return is 1.85% — noticeably less than the 2% a quick subtraction would suggest. Run the numbers the other way, with 2% nominal growth against 5% inflation, and the real return is negative: -2.86%. The saver is losing purchasing power even though their account balance is rising every year. This is why “nominal minus inflation” is only ever a rough shortcut, and why the size of the error grows as the rates involved get larger.
The same logic applies to money received in the future rather than saved today. €10,000 to be received in 30 years, discounted at 2% inflation, buys only €5,520.71 of today’s purchasing power. €26,533 received in 20 years is worth about €17,856 today under the same 2% assumption. A number written on a future payslip, pension statement or contract is not the same number in spending power — it has to be translated back through the same compounding formula, run in reverse.
The rule-of-72 shortcut works here too
The rule of 72 — divide 72 by the rate to estimate a doubling time — applies to prices exactly as it applies to savings. At 2% inflation, 72 divided by 2 gives roughly 35 years, which lines up with the table above: a 2% rate turns today’s €100 into close to €200 by year 35. It’s an estimate, not an exact figure, but it’s a fast way to sense-check the damage a “low” inflation rate does given enough time. The same shortcut works for any compounding rate, in either direction — savings growth or price growth — because it comes from the same underlying formula, not from anything specific to money or prices.