Rule of 72, 114, and 144: Estimating Doubling, Tripling, and Quadrupling Time
October 21, 2026
The Rule of 72 is a quick mental shortcut for estimating how long it takes for money to double at a given annual return: divide 72 by the percentage rate. At 6%, 72 ÷ 6 = 12 years. Two lesser-known cousins work the same way for larger multiples: the Rule of 114 estimates tripling time, and the Rule of 144 estimates quadrupling time. At 6%, tripling takes about 114 ÷ 6 = 19 years, and quadrupling about 144 ÷ 6 = 24 years.
These come from the exact formulas: years = ln(multiple) ÷ ln(1 + r). For doubling at 6%, ln 2 ÷ ln 1.06 = 11.9 years; for tripling, ln 3 ÷ ln 1.06 = 18.9 years; for quadrupling, ln 4 ÷ ln 1.06 = 23.8 years.
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For small rates, ln(1 + r) is close to r, so years ≈ ln(multiple) ÷ r. Since ln 2 = 0.693, doubling takes about 69.3 ÷ rate (in percent). The rule uses 72 instead of 69.3 because 72 is divisible by many common rates (2, 3, 4, 6, 8, 9, 12) and because it corrects for the fact that ln(1 + r) is a bit smaller than r at typical rates. Similarly, ln 3 = 1.099, giving 110 as the base, and 114 works better in the 5% to 10% range. ln 4 = 1.386, giving 138.6, and 144 is the convenient value near typical rates.
Because quadrupling is two doublings, the Rule of 144 is twice the Rule of 72.
| Annual rate | Doubling: rule 72 (exact) | Tripling: rule 114 (exact) | Quadrupling: rule 144 (exact) |
|---|---|---|---|
| 2% | 36 (35.0) | 57 (55.5) | 72 (70.0) |
| 4% | 18 (17.7) | 28.5 (28.0) | 36 (35.3) |
| 6% | 12 (11.9) | 19 (18.9) | 24 (23.8) |
| 8% | 9 (9.0) | 14.3 (14.3) | 18 (18.0) |
| 10% | 7.2 (7.3) | 11.4 (11.5) | 14.4 (14.5) |
| 12% | 6 (6.1) | 9.5 (9.7) | 12 (12.2) |
Using the Rules for Planning
If you earn 7% a year, your money doubles roughly every 10 years: $10,000 becomes $20,000 in 10 years, $40,000 in 20, and $80,000 in 30. Compare with 4%, where each doubling takes 18 years, so 30 years yields less than a 3.2-fold increase instead of 7.6-fold. The comparison shows how much the return rate matters over long periods. For inflation, the rule shows how fast prices double: at 3% inflation, prices double in 24 years, so today's $100 will buy what $50 does then.
The rule also helps with debt. A credit card at 24% doubles the debt in 3 years if no payments are made.
Accuracy and Limits
The Rule of 72 is most accurate for rates from 6% to 10% and gets less accurate at very low or very high rates. At 20%, it estimates 3.6 years and the exact answer is 3.8; at 1%, it gives 72 years and the exact answer is 69.7. For continuous compounding, 69.3 is exact. All these rules assume a constant rate with reinvestment and no additional contributions, taxes, or fees. If rates vary from year to year, use the compound annual growth rate for the period.
To find the rate needed to double in a given time, reverse the rule: rate = 72 ÷ years. To double in 8 years, you need 9%.
Other Applications
The rules work for any exponential growth: population (a country growing 2% a year doubles in 36 years), web traffic, and the spread of infections in early stages. For decay processes, such as depreciation or radioactive half-life, the same math gives half-lives: at 5% annual decline, a value halves in roughly 14 years. Remember that these are estimates for mental math and not substitutes for a calculator when decisions are important.
Frequently Asked Questions
How does the Rule of 72 work?
Divide 72 by the annual growth rate in percent to estimate years to double.
What is the Rule of 114?
A shortcut for tripling time: divide 114 by the percentage rate.
What is the Rule of 144?
A shortcut for quadrupling time: divide 144 by the rate.
How accurate is the Rule of 72?
It is within a few percent for rates between roughly 4% and 12%.
Can I use it for inflation?
Yes. At 3% inflation, prices double in about 24 years.