Glossary · Investing and personal finance
Rule of 72
The rule of 72 is a shortcut for compound growth: divide 72 by the yearly rate to find roughly how many years it takes money to double.
Also called: rule of 70, rule of 69, doubling time
At 9.4% a year since 1871, dividends reinvested. The rule of 72 says 7.7 years.
At the 4.05% paid by 3-month Treasury bills in Oct 2026, before inflation.
At the latest US rate of 3.7% a year.
In plain words
You put $5,000 in an account that earns 8% a year. When will it be $10,000? Instead of reaching for a calculator, divide 72 by 8: about 9 years. That shortcut is the rule of 72, and it is surprisingly accurate: the exact answer is 9.01 years.
It works for anything that grows by a steady percentage: savings, prices, an economy, even debt. At 6% a year money doubles in about 12 years (72 ÷ 6), at 12% in about 6. Turn it around to find the rate you need: to double in 10 years, you need about 7.2% a year.
It works against you too. With inflation of 3% a year, prices double in about 24 years, so cash kept in a drawer buys only half as much.
Example
The rule of 72 against the exact answer
- At 2% a year: 72 ÷ 2 = 36 years to double. Exact: 35.0 years.
- At 6%: 72 ÷ 6 = 12 years. Exact: 11.9.
- At 10%: 72 ÷ 10 = 7.2 years. Exact: 7.3.
- At 24%, a typical credit-card rate: 72 ÷ 24 = 3 years. Exact: 3.2.
Between about 4% and 15% a year the shortcut is off by less than half a year; far outside that range it drifts, but it still gives the right idea.
One level deeper
Why 72? The exact doubling time is ln 2 ÷ ln(1 + rate), and ln 2 ≈ 0.693. For small rates that is close to 69.3 ÷ the rate in percent. 72 is used instead because it fits the common rates of 6% to 10% better, and because it divides evenly by 2, 3, 4, 6, 8, 9 and 12. For very low rates, or for growth that compounds continuously, people use 69 or 70.
Doublings stack up: two doublings make ×4, three make ×8, ten make ×1,024. Since 1871, US stocks with dividends reinvested returned 9.4% a year, which the rule turns into a doubling every 7.7 years. After inflation the rate was 7.1%: a doubling of purchasing power about every 10.1 years.
Real markets do not double on schedule. Since 1871 the purchasing power of money in US stocks doubled 15 times, but one doubling took only about 3 years (1925–1928) and another 21 years (1965–1987).
Every doubling of US stocks after inflation, since 1871
Each bar is one doubling of what $1 put into US stocks in 1871 could buy, with dividends reinvested, and the number is the years it took. At 7.1% a year the rule of 72 predicts about 10.1 years each. The average was 10.2 years, but single doublings took anywhere from 3 years to 21 years.
The numbers behind the chart
| Value | |
|---|---|
| 1871–1879 | 8.0 |
| 1879–1885 | 6.7 |
| 1885–1897 | 11.8 |
| 1897–1905 | 7.6 |
| 1905–1925 | 20.6 |
| 1925–1928 | 2.6 |
| 1928–1945 | 17.4 |
| 1945–1954 | 8.7 |
| 1954–1958 | 4.5 |
| 1958–1965 | 6.9 |
| 1965–1987 | 21.3 |
| 1987–1995 | 8.6 |
| 1995–1998 | 2.8 |
| 1998–2017 | 18.9 |
| 2017–2024 | 7.1 |
Why it matters
It turns a percentage into a time you can feel. “7% a year” sounds small; “doubles about every ten years” does not.
It shows what small differences do over decades: a 2% yearly fee halves the end result over about 36 years, compared with no fee.
It works for debt: an unpaid credit-card balance at 24% a year doubles in about 3 years.
A common mistake
Myth: Money at 7% a year takes about 14 years to double, because 7% × 14 ≈ 100%.
In fact: That is simple-interest thinking. With compounding, 7% a year doubles money in about 10 years (72 ÷ 7 ≈ 10.3), because each year’s growth earns growth too.
Questions people ask
Rule of 72 or rule of 70: which is right?
Both are rules of thumb. 70 (or 69.3) is closer for low rates and for continuous growth, like GDP or inflation; 72 is closer for rates of about 6% to 10% and easier to divide. At 8%, 72 gives 9 years and 70 gives 8.75; the exact answer is 9.01.
How long does it take money to double at 10%?
About 7.2 years by the rule of 72 (72 ÷ 10); exactly, 7.27 years. $1,000 becomes $2,000 after a little over 7 years, $4,000 after about 14.5 and $8,000 after about 22.
How long does it take for prices to double?
Divide 72 by the inflation rate. At 2% a year, 36 years. At the latest US rate of 3.7%, about 19 years.
Read more on BigCapital
About the numbers
- The numbers on this page are recalculated from the data every night; the sources are listed at the end of the page.
- Consumer price index, all items (CPI-U): U.S. Bureau of Labor Statistics, Consumer Price Index, series CPIAUCSL; retrieved from FRED, Federal Reserve Bank of St. Louis.
- 3-month Treasury bill, secondary market rate: Board of Governors of the Federal Reserve System, H.15 Selected Interest Rates, series TB3MS; retrieved from FRED, Federal Reserve Bank of St. Louis.
- S&P Composite price and total return since 1871, and US consumer prices: Robert J. Shiller, Online Data (shillerdata.com); total return with dividends reinvested monthly, calculated by BigCapital.
- This page explains a term. It is not investment advice.