The rule
Divide 72 by a steady annual percentage rate to estimate doubling time. At 6%, the estimate is 12 years. At 8%, it is 9 years.
Where it works
The shortcut is reasonably close for many ordinary positive rates. It can also illustrate inflation: at 3%, a price level would take roughly 24 years to double if that rate stayed constant.
Its limits
Real returns vary from year to year. Fees, taxes, withdrawals, deposits, and changing rates affect the result. Negative rates and highly volatile assets need different calculations.
Use it as a check
The rule is best for quick mental arithmetic. Use a calculator with several assumptions before relying on a long-term projection.
The rule of 72 table
The estimate next to the exact doubling time (ln 2 ÷ ln(1 + r)). Below about 10%, the shortcut is within a few months of the truth.
| Annual rate | Rule of 72 says | Exact doubling time |
|---|---|---|
| 1% | 72.0 years | 69.7 years |
| 2% | 36.0 years | 35.0 years |
| 3% (typical inflation) | 24.0 years | 23.4 years |
| 4% | 18.0 years | 17.7 years |
| 5% (high-yield savings) | 14.4 years | 14.2 years |
| 6% | 12.0 years | 11.9 years |
| 7% | 10.3 years | 10.2 years |
| 8% | 9.0 years | 9.0 years |
| 10% (historic stock-market average) | 7.2 years | 7.3 years |
| 12% | 6.0 years | 6.1 years |
| 15% | 4.8 years | 5.0 years |
| 20% | 3.6 years | 3.8 years |
| 24% (credit-card APR) | 3.0 years | 3.2 years |
Common questions
- What is the rule of 72 formula?
- Doubling time ≈ 72 ÷ annual percentage rate. At 8%, money doubles in about 9 years. It works in reverse too: to double in 6 years you need roughly 72 ÷ 6 = 12% a year.
- How accurate is the rule of 72?
- Within a few months of the exact answer for rates between roughly 4% and 12% — see the table above. It overestimates slightly at very low rates and underestimates at high ones; for anything above 20%, use 78 instead of 72 for a closer guess.
- Does the rule of 72 work for inflation and debt?
- Yes — any steady percentage. At 3% inflation, prices double in about 24 years (money halves in purchasing power). At a 24% credit-card APR, an unpaid balance doubles in about 3 years. The rule is neutral about whose side it is on.