Scope and assumptions
Inflation % from CPI change; purchasing power falls by the same rate. Illustrative (CPI is a US BLS measure).
Inflation is decay applied to money. A 3% year doesn't subtract three dollars from your wallet — it shrinks what each of those dollars can reach, and because the shrink repeats annually, a decade of modest inflation removes a quarter of your purchasing power.
The rate itself comes from one subtraction on a price index. The consequences come from compounding.
Reading the rate off the index
Inflation % = (CPI_new − CPI_old) ÷ CPI_old × 100
The CPI tracks what a standard basket of goods costs relative to a base year. Its level is not inflation; its change is.
| CPI old | CPI new | Inflation |
|---|---|---|
| 250.0 | 257.5 | 3.0% |
| 250.0 | 265.0 | 6.0% |
| 200.0 | 206.0 | 3.0% |
What happens to your money
At 3%, the same basket costing $100 today costs $103 next year. Looked at from the other end, $100 a year from now buys only what $97.09 buys today — 100 ÷ 1.03.
The bank balance is unchanged. The reach is what moved.
Nominal versus real
This is the distinction that decides whether a raise is a raise:
- A 5% pay rise with 3% inflation is a 2% real increase.
- A 2% pay rise with 3% inflation is a 1% real cut, delivered as a bigger number on the payslip.
The same logic governs investments. A 3% return during 3% inflation is not growth; it's standing still in real terms.
Ten years of "only" 3%
Compounding is where intuition fails. $100 at 3% inflation for a decade retains:
100 ÷ 1.03¹⁰ ≈ $74.41
A 25.6% loss of purchasing power, not the 30% a naive "3 × 10" suggests — and far more than the $30 that "3% a year" feels like. The erosion is quiet, which is exactly why it goes unnoticed.
Inflation Math That Understates the Erosion
Dividing by the new CPI instead of the old; reading the index level as if it were the inflation rate; assuming linear addition over multiple years; mixing nominal and real figures in the same comparison; treating one item's price rise as economy-wide inflation; and comparing CPI levels between countries, where the baskets and base years differ.
Related growth & decay guides
For the rest of the growth-and-decay cluster, start at the hub: Population Growth Percentage. Adjacent: Percentage Change Over Time and Percentage Return on Investment.
FAQ
What's the difference between CPI and the inflation rate? CPI is an index level — the price of a standard basket relative to a base year. The inflation rate is the percentage change in that index between two dates.
How do I compare inflation across countries? Compare each country's own CPI change, not the index levels. The baskets and base years differ, so index numbers aren't comparable across borders.
How do I tell whether my wage is keeping up? Compare the percentage rise in your pay with the percentage rise in CPI over the same period. If pay rose 4% and prices 5%, your real wage fell about 1%.
Why do economists watch "core" inflation separately? Core strips out food and energy, which swing widely with weather and geopolitics. The core rate is a steadier read on underlying price pressure.
Sources: U.S. BLS, CPI; Investopedia, Inflation.
Disclaimer: Illustrative. CPI methodology is set by statistical agencies; figures are examples. Informational only.
Sources and references
- U.S. BLS — Consumer Price Indexhttps://www.bls.gov/cpi/
- Investopedia — Inflationhttps://www.investopedia.com/terms/i/inflation.asp
Maintenance and corrections
The named author or publishing brand is responsible for this article. Worked examples are illustrative, not user testimonials, professional advice or approval by the institutions cited. Maintenance responsibility and review methods · Report an error