The rule of 72 and four other rules of thumb, with the error in each
72 divided by the rate is the years to double. It is off by less than a year for any rate between 4% and 12%. The others — the 4% rule, 100 minus age, ten times salary — are less reliable, and the reasons are useful.
Rules of thumb compress a calculation into something that can be done in a parking lot. Each one is an approximation of a real formula under assumptions that are usually left unstated. Stating them is the point of this guide.
The rule of 72
Years to double = 72 ÷ annual rate. At 6%, twelve years; at 9%, eight. The exact figure is ln(2) ÷ ln(1 + r), and the table shows how close the shortcut gets.
| Rate | 72 ÷ rate | Exact | Error |
|---|---|---|---|
| 3% | 24.0 years | 23.4 years | +0.6 |
| 6% | 12.0 | 11.9 | +0.1 |
| 7% | 10.3 | 10.2 | +0.1 |
| 9% | 8.0 | 8.0 | 0.0 |
| 12% | 6.0 | 6.1 | −0.1 |
The rule works for anything that compounds. 72 ÷ 3.4 = 21 years for prices to double at the rate reported for the twelve months to August 2026. A fund fee of 1%, treated as a negative return, takes 72 years to halve a balance on its own — which understates the actual cost, because the fee compounds against a growing balance, not a static one.
The 4% rule, and its cousin the 25× rule
Withdraw 4% of a portfolio in the first year of retirement, raise the dollar amount with inflation each year, and the money lasted 30 years in every historical period tested — that was the finding of a 1994 study of U.S. stock and bond returns since 1926. Turned around, it says a retirement needs a portfolio of 25 times the first year's spending. The assumptions: a U.S. portfolio of roughly half stocks, 30 years, no fees, and a future no worse than the worst 30-year stretch in the record. Change any of them and the number moves — later work using global data and current valuations has put the safe figure below 4%, and work assuming flexible spending has put it above.
100 minus your age in stocks
A 30-year-old holds 70% stocks; a 70-year-old holds 30%. The rule encodes one true thing — that the ability to wait out a fall shrinks with the years left to wait — and ignores everything else: whether there is a pension, how large the portfolio is relative to spending, and the fact that a 70-year-old may have 20 years ahead. Versions using 110 or 120 minus age exist for exactly that reason, which tells you how precise the original is.
Ten times salary by 67
A savings target published by a large fund provider, with waypoints of 1× by 30, 3× by 40, 6× by 50 and 8× by 60. It assumes a savings rate around 15% from 25, a retirement at 67 replacing about 45% of pre-retirement income from savings alongside Social Security, and average returns. It is a useful yardstick and a poor target, because it is denominated in salary rather than spending — a high earner who spends half their income needs far less than 10×, and a low earner who spends all of it may need more.
The rule of 72 is nearly exact because it describes only arithmetic. The others describe people — how long they will live, how they will spend, what returns they will see — and their error is the size of the difference between the assumed person and the real one. Used to check a calculation, they are helpful. Used instead of one, they are the calculation's assumptions wearing a disguise.
Sources
- Determining Withdrawal Rates Using Historical Data (Bengen, 1994)Journal of Financial Planning · checked Sep 24, 2026
- Consumer Price Index Summary — August 2026U.S. Bureau of Labor Statistics · checked Sep 24, 2026