The Rule of 72: An Approximation, with Exact Comparisons
Compare the Rule of 72 with logarithmic doubling times and see where rates, cash flows and compounding change the answer.
The short answer
The Rule of 72 estimates doubling time by dividing 72 by a positive annual percentage rate. It is an approximation for constant compound growth, not a guarantee or a model of contributions and variable market returns.
The shortcut is years ≈ 72 / annual percentage rate. At 7%, it gives 10.29 years. The rate must be expressed as a percentage, so use 7 rather than 0.07 in this shortcut. It does not say an investment will actually earn that rate.
For a constant effective annual rate y with no contributions or withdrawals, the logarithmic doubling time is t = ln(2) / ln(1+y). This is the modeled crossing time, using fractional-year interpolation. If interest is credited only at annual dates, the balance first reaches or exceeds double at the next relevant crediting date.
Using effective annual rates and no cash flows, the comparisons are 2%: Rule of 72 36.00 years, logarithmic result 35.00 years; 4%: Rule of 72 18.00 years, logarithmic result 17.67 years; 7%: Rule of 72 10.29 years, logarithmic result 10.24 years; 10%: Rule of 72 7.20 years, logarithmic result 7.27 years; 20%: Rule of 72 3.60 years, logarithmic result 3.80 years. The approximation error varies with the rate. It is not exact at every rate, and no fixed accuracy range should be treated as universal.
No cash flows; effective annual rates; fractional-year model
| Rule of 72 | Logarithmic model | |
|---|---|---|
| 2% | 36.00 years | 35.00 years |
| 4% | 18.00 years | 17.67 years |
| 7% | 10.29 years | 10.24 years |
| 10% | 7.20 years | 7.27 years |
| 20% | 3.60 years | 3.80 years |
Both assume constant growth; actual investment performance is uncertain.
Rate basis matters. If 7% is a nominal rate compounded monthly, use t = ln(2) / (12 × ln(1+0.07/12)). Do not put an APY into a nominal-rate formula and compound it again. More frequent compounding at the same nominal rate changes the effective annual yield.
At zero return, growth alone never doubles the balance. A fixed negative return does not create a positive doubling time. With variable market returns, an arithmetic average is insufficient: the sequence of multiplicative returns matters, and deposits or withdrawals require a cash-flow model.
The same shortcut can illustrate how a constant inflation assumption might erode purchasing power, but it is not a forecast of future prices. For exact purchasing-power scenarios use the chosen inflation rate and horizon once; do not mix real and nominal rates.
Use the shortcut for mental estimates and a full calculation for decisions. In CalcMyCompound, use zero contributions to compare growth of the starting principal, select the actual nominal rate basis and compounding frequency, and inspect the year-by-year balances. Adding contributions can make the account double sooner without implying the investment itself doubled.
Correction, October 29, 2026: examples, assumptions, FAQs and visuals were reviewed together. Unsupported current statistics and promises were removed. The stated calculations use independent high-precision references.
Frequently Asked Questions
Is 72 divided by the rate exact?
No. For constant effective annual growth with no cash flows, ln(2)/ln(1+y) gives the modeled doubling time.
How long at a 7% effective annual rate?
The logarithmic model gives 10.24 years; the Rule of 72 gives 10.29. Annual-only interest crediting and fractional-year interpolation are different conventions.
Can I apply it to a monthly savings plan?
It does not model regular deposits. Use a cash-flow calculation and distinguish contributions from investment growth.