250 to 260 is a 4% rate, because the base is 250
Inflation is the percentage change in the index, not the change in its points: (260 − 250) / 250 is 4%. Index levels are arbitrary — they are set to 100 in whatever base year the statistics office chose — so only changes carry meaning, and only changes expressed relative to the starting level.
This is why the same 10-point move means different things at different levels. From 100 to 110 is 10% inflation; from 250 to 260 is 4%; from 400 to 410 is 2.5%. Reporting index point changes as though they were rates is a common error in secondary coverage and always overstates inflation at higher index levels.
Three years at 4% is 12.49%, not 12%
Each year\u2019s inflation applies to prices that already include the previous year\u2019s. Three years at 4% multiply out to 1.04 cubed, a cumulative 12.49%. Over a decade the gap widens sharply: 4% a year for ten years is 48% cumulative, not 40%.
The rule of 70 gives a quick sense of the scale — dividing 70 by the inflation rate approximates the years for prices to double. At 4% that is about 18 years; at 7%, ten. Any long-horizon plan built by adding annual inflation rates rather than compounding them will understate the eventual price level substantially.
All three are correct, and they can point in different directions
Headline inflation covers the full basket. Core inflation strips out food and energy, whose prices are volatile and often driven by supply shocks rather than monetary conditions — central banks watch core because it is a better signal of persistent pressure. Neither is the rate any individual household faces.
Personal inflation depends on what you buy. A household spending a large share on rent and energy experiences something quite different from one whose spending is weighted toward electronics, where prices routinely fall. A single national rate is a weighted average across every household, and the dispersion around it is wide enough that most people are some distance from it.
A period rate, from an index with known biases
The rate computed here covers whatever interval separates the two readings — monthly, annual or anything else — and it is not annualised. Comparing a monthly rate against an annual one without converting is a straightforward error, and monthly figures are noisy enough that single readings rarely mean much.
Price indices themselves carry known measurement issues: substitution bias when consumers switch away from dearer goods, and quality adjustment, where a product improves while its price holds. Statistics agencies correct for both, imperfectly, and the residual is generally believed to overstate measured inflation modestly.
Sources & References
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