How this instrument works
Inflation names whatever rate some basket of prices climbs at, and this sheet aims that single rate in two opposite directions. Multiply by (1 + i)ⁿ and you get what any price tag becomes after n years — Equivalent cost later. Divide by that same factor and you get what cash held for n years still commands, measured in today's prices — What today's money will buy then. One growth factor, two questions, and most muddle about inflation comes from conflating them.
Those answers are reciprocals, not mirror images, and that asymmetry trips almost everyone. Push Annual inflation, % to 100 and a $1,000 price becomes $2,000 — up 100 percent, exactly as expected. Yet $1,000 in cash does not fall to nothing; it falls to $500, down 50 percent. Fraction of purchasing power surrendered in a year is i ⁄ (1 + i), never i itself. At an ordinary 3 percent, prices gain 3 percent while cash loses 2.913 percent — small enough to shrug at across one year, quite large enough to matter across thirty.
Limits are worth naming. One uniform rate is applied here, while real baskets move at wildly different speeds: tuition and medical bills have outrun published averages for decades as televisions fell outright. Any published index tracks some representative basket, not yours, so renters in hot cities and owners holding fixed mortgage payments live quite different numbers behind one identical headline figure. Nothing about wages, taxes, interest earned, or shoppers switching to cheaper goods enters this arithmetic. It answers price questions, never income ones.
- Put whatever figure you care about in Amount today, $ — price tags, salaries, or cash sitting untouched in a drawer.
- Set Annual inflation, % to whichever rate you want to test. Type 3 for three percent; a negative entry models deflation.
- Enter how far ahead to look in Years. Decimals work, so eighteen months is 1.5.
- Read Equivalent cost later when your question is what something will cost you by then.
- Read What today's money will buy then when your question is what idle cash is quietly losing. Both come from one factor, used in opposite directions.
Worked example — one year at 100 percent
Set Amount today, $ to 1000, Annual inflation, % to 100, and Years to 1. Growth factor is 1 + 1.00 = 2 across a single year. Equivalent cost later reads $2,000: whatever cost a thousand in January carries a two-thousand price tag by December. What today's money will buy then reads $500, because 1000 ⁄ 2 = 500 — your untouched thousand now commands half of what it once did.
Both answers are checkable in your head, which is why this case is worth running before trusting a thirty-year figure you cannot verify. It is also no hypothetical: Argentina's annual rate ran past 200 percent during 2024, and Weimar Germany in 1923 reached a pace where prices doubled inside days. Note what this pair refuses to let you say loosely. Cost rose 100 percent, buying power fell 50 percent, and those two sentences describe one identical event.
Swap in something ordinary and that shape holds. At Annual inflation, % of 3 across 10 Years, $1,000 of groceries bills $1,343.92 — up 34.4 percent, not the 30 percent that adding ten threes suggests — while $1,000 left in a drawer buys $744.09 worth, a 25.6 percent loss. Exponents refuse to add. That gap is what separates decades estimated in your head from decades actually computed.
Questions
Why doesn't 100 percent inflation take my money to zero?
Because purchasing power is divided, never subtracted. Prices doubling means each dollar commands half of what it did, so $1,000 becomes $500 — a 50 percent loss, not a total one. In general a year at rate i costs you i ⁄ (1 + i) of your buying power: 2.91 percent at a 3 percent rate, 16.67 percent at 20 percent, 50 percent at 100 percent. Cash approaches worthlessness only as an asymptote, which is exactly how hyperinflations behave — brutal, yet never quite finished.
Why is 3 percent over ten years not 30 percent?
Each year's rise applies to prices already lifted by every year before it, so factors multiply instead of adding. Ten years at 3 percent gives 1.03¹⁰ = 1.3439, a 34.4 percent climb, and that gap widens fast: thirty years reaches 142.7 percent rather than 90. Same reason a doubling shortcut exists — divide 70 by the rate. At the Federal Reserve's stated 2 percent long-run goal, prices double in roughly 35 years; at 3 percent, in about 23.
Which output fits a salary or a pension?
Equivalent cost later, if your question is what a target income must become. A $60,000 lifestyle needs $80,635 after ten years at 3 percent merely to stand still. Use What today's money will buy then for the reverse question — what a fixed, unindexed pension of $60,000 will feel like in ten years, which is $44,646 in current terms. A raise landing under this figure is a pay cut phrased politely, and running both directions makes that visible in dollars.
Why does my own cost of living climb faster than the published rate?
Published indexes average a representative basket, and nobody spends like an average. Categories diverge sharply: housing, medical care and higher education have run well above headline figures for decades, while consumer electronics and clothing ran below or fell outright. A household tilted toward rent and childcare lives a personal rate above the printed one; an owner with a fixed mortgage payment and an old car lives less. Enter your own estimate in Annual inflation, % rather than an official number if that is what you want modelled.
Can I enter a negative rate for deflation?
Yes, and it behaves correctly: −2 percent across 5 Years turns $1,000 of prices into $903.92 while making an untouched $1,000 buy $1,106.29 worth. Anything at or below −100 percent is rejected, since prices cannot fall by more than all of themselves and that would drive a zero or negative growth factor. Sustained deflation stays rare in modern records outside Japan's long stretch after 1990 and the early 1930s.
What does this arithmetic leave out?
Tax, interest, and your own behaviour. Cash sitting in an account earning interest is fighting inflation with a return this sheet knows nothing about, so compute that side separately and compare. Tax lands on nominal gains rather than real ones, so a return merely matching inflation still leaves you behind once tax is paid. Shoppers also substitute — beef swapped for chicken when beef jumps — so real spending rises somewhat less than a frozen basket implies. Quality shifts cut alike: a car costing double a 1995 model is not that same car.
References
- Federal Reserve — monetary policy and its 2 percent inflation goal
- IRS — annual inflation adjustments to brackets and deductions
- CFPB — consumer financial education resources
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.