Inflation Adjuster

Nominal cost vs. real purchasing power — two lines, one story.

Worked example — Inflation Adjuster

Future nominal equivalent	1280.1
Real purchasing power	781.2
Purchasing power lost	21.88%

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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The rule of 72 and why central banks fear 8% 🖖

Divide 72 by the inflation rate to approximate how many years it takes for purchasing power to halve. At 2% that is about 36 years. At 8% it is about 9, so a working career watches money halve twice. Central banks target ~2% for exactly that reason: high enough to stay clear of deflation, low enough that wage growth can outpace it. The nominal value line rising above your fixed amount is the price tag moving, not money earned.

Why the same money buys less 🖖

Inflation is compound interest run in reverse: each year the same coins buy a little less, and the shortfalls stack up like interest. The nominal line climbs because it multiplies by (1+π)ⁿ; the real line falls because it divides by the same factor — one story told from two directions. Keep €1000 as cash at 3% inflation for 20 years and it still reads €1000, yet buys only what €554 buys today.

When prices doubled every 15 hours 🖖

This tool caps inflation at 50% a year, but reality has blown far past that. In Hungary in 1946 prices doubled roughly every 15 hours — the worst hyperinflation ever recorded — and the highest-denomination banknote ever issued reached 10²⁰ pengő. At those speeds the halving time of purchasing power is measured in hours, not years, and the printing presses literally cannot keep pace.

Problem solved in full

Ten years of 2.5% inflation on £1000 5 steps
£1000, ten years, 2.5% inflation. Most people answer that it loses 25% of its value. Work out the real figure and find where the missing 3 percentage points went.
1. Inflation compounds, so ten years at 2.5% is not ten lots of 2.5%. The multiplier is 1.025 raised to the tenth.
  
  $(1 + i)^{n} = 1.02 5^{10} = 1.280085$
2. That multiplier answers the forward question: what a basket costing £1000 today will cost then.
  
  $nominal = 1000 \times 1.280085 = 1280.1$
3. The backward question is the one about your savings, and it is the reciprocal — what £1000 held in a drawer will then buy.
  
  $real = \frac{1000}{1.280085} = 781.2$
4. So the loss is 21.88%, not 25%. The naive answer is too pessimistic, which is the opposite of what compounding usually does, and the reason is that we are dividing by the compounded factor rather than multiplying by it.
  
  $lost = 1 - \frac{781.2}{1000} = 21.88% (not 10 \times 2.5% = 25%)$
5. Solving for when the real value halves gives an exact answer that does not depend on the amount at all. The panel reports a different figure beside it, because it uses the rule of 72 — the shortcut that trades accuracy for arithmetic you can do in your head.
  
  $t_{1/2} = \frac{ln 2}{ln 1.025} = 28.1 yr vs \frac{72}{2.5} = 28.8 yr$
Answer

The tool prints 1280.1 nominal, 781.2 real, and 21.88% of purchasing power lost. The asymmetry is what to keep: prices rose by 28.0% and purchasing power fell by 21.9%, and these are the same event. A 28% rise and a 22% fall look like different numbers because a fraction of a bigger thing is being compared with a fraction of a smaller one — the same reason a 50% loss needs a 100% gain to undo. At 2.5%, money halves in 28.1 years exactly — and the panel says 28.8, because 72/2.5 is the rule of 72 and it runs about 2.5% high at this rate. Both are on the screen and neither is wrong; the rule is a mental shortcut, tuned to be accurate near 8%, and it drifts either side of that. Set inflation to 7% and the two agree far better — 10.25 exact against 10.29 — while the same £1000 keeps only 508.35 after ten years.

$t_{1/2} = \frac{ln 2}{ln ( 1 + i )} = 28.1 exact; \frac{72}{i %} = 28.8 is 2.5% high$

Learning path

Money over time

References (1)

Insight block 3 — the Hungarian hyperinflation, and the 15-hour doubling time: W. A. Bomberger and G. E. Makinen, "The Hungarian Hyperinflation and Stabilization of 1945–1946." Journal of Political Economy 91(5), 801–824, 1983.

By the 42Math team · Updated 2026-06-23

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

moderate inflation - Moderate inflation over a decade erodes purchasing power materially.
high inflation - High inflation rapidly changes nominal and real value comparisons.
long-run - Long-run compounding inflation strongly impacts real purchasing power.