The Rule of 72: A Shortcut That Works, and Where It Breaks
Divide 72 by an interest rate and you get roughly how many years it takes money to double. Here is how accurate that is, why it works, and how to use it on debt too.
The Rule of 72 is the most useful piece of financial arithmetic you can do in your head. Divide 72 by an annual growth rate, and the answer is approximately how many years it takes for something to double.
At 6%, money doubles in about 12 years. At 9%, about 8. At 3%, about 24.
How accurate it is
Here is the Rule of 72 compared with the exact doubling time for annual compounding:
| Annual rate | Rule of 72 | Exact years to double |
|---|---|---|
| 2% | 36.0 | 35.0 |
| 4% | 18.0 | 17.7 |
| 6% | 12.0 | 11.9 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
| 18% | 4.0 | 4.2 |
| 24% | 3.0 | 3.2 |
Show the numbers behind this chart
| Annual rate | Rule of 72 | Exact (annual compounding) |
|---|---|---|
| 2% | 36.0 yrs | 35.0 yrs |
| 4% | 18.0 yrs | 17.7 yrs |
| 6% | 12.0 yrs | 11.9 yrs |
| 8% | 9.0 yrs | 9.0 yrs |
| 10% | 7.2 yrs | 7.3 yrs |
| 12% | 6.0 yrs | 6.1 yrs |
| 18% | 4.0 yrs | 4.2 yrs |
| 24% | 3.0 yrs | 3.2 yrs |
Between roughly 6% and 10%, the rule is almost exact. At low rates it slightly overstates the time; at high rates it slightly understates it. For quick thinking, the error rarely matters.
Why it works
The exact doubling time is ln(2) ÷ ln(1 + r). For small rates, ln(1 + r) is close to r, and ln(2) is about 0.693. That would suggest a "Rule of 69." People use 72 instead because it gives better results at typical rates when compounding is annual, and because 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12.
If interest compounds continuously, the Rule of 69.3 is the precise version. For most everyday use, 72 is close enough.
Using it in reverse
Want to know what rate would double money in a given time? Divide 72 by the number of years. Doubling in 10 years implies roughly 7.2% a year.
Using it on fees and inflation
The rule works on anything that compounds, including things that work against you:
- Inflation at 3% cuts the purchasing power of cash roughly in half in about 24 years.
- Inflation at 6% does it in about 12.
- A 1% annual fee on its own would consume half of a static balance's value in roughly 72 years, which sounds harmless until you remember it is also slowing every year of growth. Our guide on what a 1% fee really costs works through that.
Using it on debt
At 24% APR, an unpaid credit card balance roughly doubles in about 3 years if nothing is paid and interest keeps accruing. That is a much more vivid way to think about high-rate debt than the APR alone.
Where it breaks
- Very high rates. Above about 20%, the rule understates doubling time noticeably.
- Variable returns. Investments do not earn a steady rate. A portfolio averaging 8% may double in 9 years, or 7, or 12, depending on the order of good and bad years. The rule describes math, not markets.
- Contributions and withdrawals. It applies to a single lump sum. Regular deposits or withdrawals change the timeline.
The takeaway
Divide 72 by the rate. It is a fast, surprisingly accurate way to feel the weight of compounding, whether it is working for you or against you.
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