The rule of 72 is the quickest way to feel what a growth rate means. Divide 72 by the yearly rate, and you get roughly how many years it takes something to double. At 6%, about 12 years. At 8%, about 9.
Rule of 72 vs the exact answer
| Yearly rate | Rule of 72 | Exact (annual compounding) |
|---|---|---|
| 2% | 36.0 years | 35.0 years |
| 3% | 24.0 | 23.4 |
| 4% | 18.0 | 17.7 |
| 5% | 14.4 | 14.2 |
| 6% | 12.0 | 11.9 |
| 7% | 10.3 | 10.2 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
The exact answer is ln(2) ÷ ln(1 + rate). The rule works because ln(2) ≈ 0.693, and 72 is a handy number near 69.3 that divides evenly by 2, 3, 4, 6, 8, 9 and 12. It slightly overestimates at low rates and slightly underestimates at high ones.
Doubling, then doubling again
The real lesson is what happens after the first doubling. $10,000 at 7% a year doubles in about 10 years, doubles again by 20 and again by 30: roughly $80,000 on the rule's estimate. The exact figure at 7% compounded annually is $76,123 after 30 years. Either way, most of that growth arrives in the last decade.
See the year-by-year curve for your own numbersOpen calculator ›Using it in reverse
You can also turn the rule around to find the rate you would need. Want money to double in 10 years? You need about 72 ÷ 10 = 7.2% a year. In 18 years, about 4%. It is a quick way to judge whether a goal is realistic before running the full numbers.
Why compounding frequency barely matters here
The table above uses yearly compounding. Monthly compounding makes money grow a little faster: at 6% a year compounded monthly the exact doubling time is 11.6 years instead of 11.9. For a mental shortcut that difference is too small to matter, which is part of why the rule has lasted so long.
Other things that double
- Prices: at 3% inflation, prices double in about 24 years, so $100 today buys what $50 will in 2050.
- Debt: a credit card balance at 24% a year, left alone, doubles in about 3 years.
- Fees: a 1% yearly fee takes a slice of every doubling. Over decades that adds up.
A shortcut, not a promise
The rule assumes a steady rate. Real investment returns change every year and can be negative, so treat the result as a way to understand growth, not a forecast. This is not financial advice.
To go the other way, from a goal to a monthly amount, use the savings goal calculator.
Questions people ask
What is the rule of 72?
A shortcut for compound growth: years to double ≈ 72 ÷ yearly rate. At 6% a year, money doubles in about 12 years.
How accurate is the rule of 72?
Very close for rates between about 4% and 12%: within a few months of the exact answer. It drifts at very low or very high rates.
Does the rule of 72 work for inflation?
Yes, in reverse: 72 ÷ inflation rate estimates how many years it takes prices to double, or the value of cash to halve. At 3% inflation that is about 24 years.
