Portfolio
Rule of 72
Reviewed
Rule of 72 formula
Years to double ≈ 72 ÷ annual rate in percent
How to use the Rule of 72
The Rule of 72 estimates doubling time under a constant positive annual return: years to double ≈ 72 / annual percentage rate. Use 6 for a 6% rate, not 0.06. The Investor.gov World Investor Week bulletin describes this compounding shortcut.
At 6%, the estimate is 72 / 6 = 12 years. At 8%, it is 9 years. These are hypothetical constant-rate cases with no contributions, withdrawals, fees or taxes. They are not predictions about the time it will take a stock portfolio to double.
The exact doubling-time formula
With annual compounding at a constant effective rate r, the exact mathematical doubling time is ln(2) / ln(1 + r). Here r is a decimal: use 0.06 for 6%. The logarithm formula solves (1 + r)^t = 2, whereas 72 is a convenient approximation.
For 6%, the exact result is about 11.90 years, compared with 12 under the shortcut. At 2%, the exact result is about 35.00 years versus 36. At 20%, it is about 3.80 years versus 3.60. These comparisons show why the shortcut should not replace an exact calculation when timing matters. Fractional years describe the mathematical growth model; an account that credits interest only at discrete dates may cross the threshold on a later crediting date.
Use the Rule of 72 calculator for an estimate and the compound interest guide to understand rates, contributions and compounding conventions.
When the rule does not answer the question
A zero return never doubles principal by compounding alone. A negative constant return shrinks a positive balance. Neither produces a meaningful positive doubling time under this rule. Deposits may double an account balance sooner, but that combines saving with investment growth.
Variable returns also matter. A positive arithmetic average does not establish a constant compound growth rate. Read the CAGR guide before substituting an average of historical yearly returns into a projection. Fees and taxes reduce the amount available to compound; inflation changes what the resulting balance can buy.
Using it with inflation
If prices rise at a constant 4% per year, the shortcut estimates they double in 18 years. An unchanged cash balance would then buy about half as much. The exact constant-rate model gives approximately 17.67 years. This is a purchasing-power illustration, not an inflation forecast or a reason to assume any particular investment will keep pace.
Example
At a constant 6% annual effective return, the Rule of 72 estimates 12 years to double. The exact logarithmic model gives about 11.90 years, before fees and taxes.
Common mistakes
- Relying on the shortcut at very high or very low rates, where it drifts from the exact result.
- Applying it to returns that are withdrawn rather than reinvested.
Related terms
Rule of 72 — FAQ
What is Rule of 72?
The Rule of 72 is a quick mental shortcut for estimating how many years it takes an investment to double, found by dividing 72 by the annual rate of return.
Can you give an example of Rule of 72?
At a constant 6% annual effective return, the Rule of 72 estimates 12 years to double. The exact logarithmic model gives about 11.90 years, before fees and taxes.
Do I enter 6 or 0.06 for a 6% return?
Use 6 in the shortcut 72 divided by the percentage rate. Use 0.06 in the exact formula ln(2) divided by ln(1 + r).
Does the Rule of 72 work at zero or negative returns?
No. Zero return does not grow principal and a negative constant return reduces it. Neither has a positive doubling time from compounding alone.
Can regular deposits make the rule inaccurate?
Yes. The shortcut describes growth of an existing balance without cash flows. Regular deposits add capital and can bring the account to twice its initial size sooner.
The term is free. The call is membership.
Rule of 72 is the vocabulary. Members get the monthly thesis that uses it: what changed, who could benefit, and what would prove the view wrong. $39/month or $249/year.
Members-only research
$39/mo or $249/yr · cancel future renewals anytime · sources included