Two ways to say the same thing
Every inflation question is one of two questions, and they are the same arithmetic read in opposite directions. What will my money buy? divides by the price factor. What will this cost? multiplies by it. At 3% for twenty years the price factor is 1.0320 = 1.806111, so $100,000 buys what $55,367.58 buys today, and something costing $100,000 today will cost $180,611.12 then.
Notice that the two percentages are not the same. Prices rise 80.6% over the span, but purchasing power falls by only 44.6%, because the two are measured against different bases. This asymmetry is the most common source of confusion in inflation arithmetic: a 100% rise in prices halves your money, it does not eliminate it. Always convert to a factor and divide or multiply, rather than adding and subtracting percentages.
Which direction you need depends on what you are planning. Retirement income, a fixed pension, a bond coupon and cash savings are all fixed nominal amounts, so you want the real value. A future purchase — college, a roof, a car in ten years — is a future price, so you want the nominal amount. Getting a savings target right means using the second and then feeding it into the savings goal calculator.
Compounding, and the CPI method
Inflation compounds exactly as interest does. Three percent for two years is not 6% but 1.03 × 1.03 − 1 = 6.09%, and over twenty years the gap between the naive 60% and the true 80.61% is large enough to wreck a plan. The calculator always compounds.
When you know the actual index values, use them: the CPI fields override the rate and derive it, with i = (CPIend ÷ CPIstart)1/n − 1. This is how official dollar comparisons are made. The Bureau of Labor Statistics publishes the CPI-U series monthly, with an index set to 100 for the 1982–84 average, and any two dated values give you both the cumulative change and the annualised rate. Using the index rather than a remembered rate matters because inflation is not smooth — a span containing 2021 and 2022 has a very different shape from its average.
Two properties worth knowing. The result is exactly proportional to the amount, so doubling the amount doubles every dollar figure and leaves the percentages alone. And the time to halve purchasing power is ln 2 ÷ ln(1 + i), which at 3% is 23.45 years. The familiar rule of 70 approximates that as 70 ÷ 3 = 23.3 years; the approximation is good to within a few percent for rates under about 10%, and drifts high above that.
Worked example: $100,000 over twenty years at 3%
You have $100,000 in cash and want to know what it will be worth when you retire in twenty years, assuming 3% average inflation.
- Price factor. 1.0320 = 1.806111. Prices are 80.61% higher.
- Real value. 100,000 ÷ 1.806111 = $55,367.58. The money still says $100,000, but it buys what $55,367.58 buys today.
- Purchasing power lost. 100,000 − 55,367.58 = $44,632.42, or 44.63% of what it can buy now.
- The other direction. Something that costs $100,000 today will cost 100,000 × 1.806111 = $180,611.12 then. Note that 44.63% and 80.61% describe the same event.
- Halving time. ln 2 ÷ ln 1.03 = 0.693147 ÷ 0.0295588 = 23.45 years, so a little over one halving fits inside the span — which is why the real value is slightly below half.
Now use it. If your target is to have $100,000 of today's purchasing power in twenty years, the amount you actually need is $180,611.12. If that money sits in an account paying 4% while inflation runs at 3%, the real growth rate is 1.04 ÷ 1.03 − 1 = 0.971% a year, not 1% — the exact Fisher relationship, which the real interest rate calculator handles directly.
Choosing a rate you can defend
The result is only as good as the rate, and the rate is the part you are guessing. Three approaches are defensible. Use the historical average of the CPI-U over a long window, which you can compute from two published index values with the fields on this page. Use the Federal Reserve's stated objective, which since 2012 has been 2% annual inflation as measured by the price index for personal consumption expenditures — a different index from the CPI, and typically a slightly lower one. Or use a market-implied rate: the gap between a nominal Treasury yield and the yield on a Treasury Inflation-Protected Security of the same maturity is the breakeven inflation rate the market is pricing.
What you should not do is use one year's headline number for a twenty-year projection. Inflation is far more volatile year to year than it is over decades, and a projection built on the most recent print will be wrong in whichever direction that print was unusual.
Also match the index to the spending. The CPI-U measures an urban consumer's basket; your basket is not that basket. Healthcare and higher education have risen faster than the overall index for decades, while electronics have fallen outright. If you are pricing a specific future purchase — college in particular — use a category-specific projection rather than the headline rate, and check it with the college cost projection calculator.
What $100,000 keeps, by rate and span
| Years | 2% | 2.5% | 3% | 4% | 6% |
|---|---|---|---|---|---|
| 5 | $90,573 | $88,385 | $86,261 | $82,193 | $74,726 |
| 10 | $82,035 | $78,120 | $74,409 | $67,556 | $55,839 |
| 15 | $74,301 | $69,047 | $64,186 | $55,526 | $41,727 |
| 20 | $67,297 | $61,027 | $55,368 | $45,639 | $31,180 |
| 30 | $55,207 | $47,674 | $41,199 | $30,832 | $17,411 |
| 40 | $45,289 | $37,243 | $30,656 | $20,829 | $9,722 |
The 30-year row is the one that matters for retirement planning: moving the assumption from 2% to 3% costs $14,008 of the answer, and from 3% to 4% a further $10,367.
Mistakes that make an inflation estimate wrong
- Adding the rate instead of compounding it. Twenty years at 3% is 80.61% of cumulative inflation, not 60%. The error grows with the span and is always in the direction of understating the damage.
- Confusing the two percentages. Prices rising 80.61% is the same event as purchasing power falling 44.63%. They are reciprocal, not equal, and mixing them produces answers that are wrong by tens of percent.
- Mixing nominal and real in one plan. Either project everything in today's dollars and use a real return, or project everything in future dollars and use a nominal return. Doing one for income and the other for expenses double-counts inflation or ignores it.
- Using the headline rate for a specific purchase. The CPI-U is an average across a fixed urban basket. Tuition, medical care and insurance have their own histories, and none of them tracks the headline number closely.
- Forgetting tax. Interest and gains are taxed on the nominal amount, so a 4% yield taxed at 22% leaves 3.12% against 3% inflation — a real return of about 0.1%, not 1%.
- Treating a single year's print as a trend. Annual inflation is volatile; the average over a decade is not. Use a long-run figure for a long-run projection.
What protects against it
Nothing in a fixed nominal amount does. Cash, a fixed annuity, a nominal bond held to maturity and a pension without a cost-of-living adjustment all deliver the number they promised and lose whatever inflation takes. That is the specific risk this calculator quantifies, and it is the main argument against holding a very long-horizon goal in cash — see the savings account interest calculator for what a deposit yield actually nets after tax.
Three things adjust. Treasury Inflation-Protected Securities and Series I savings bonds carry principal or rates that move with the CPI, so they deliver a real return by construction. Social Security applies an annual cost-of-living adjustment tied to a CPI series, which is why it behaves differently in a retirement plan from a fixed pension. And debt is the mirror image: a fixed-rate mortgage is a nominal obligation, so inflation erodes what you owe in real terms just as it erodes what you hold. A $2,000 payment twenty years into a 3% inflation environment costs 2,000 ÷ 1.806111 = $1,107.35 in today's money, which is a genuine argument for not rushing to prepay a low-rate fixed loan — run the alternative through the loan payoff time calculator before deciding.