ValueWhere the 72 comes from
Doubling at a steady annual rate r means solving (1 + r)^t = 2, which gives t = ln(2) / ln(1 + r). For small rates, ln(1 + r) is close to r, so t is about 0.6931 / r, or 69.31 when r is expressed in percent. That is the exact constant for continuous compounding.
But savings accounts, bonds, and investment returns compound discretely, usually annually, which makes doubling take slightly longer than the continuous case. The constant gets nudged up from 69.31 to 72, a number chosen because it divides evenly by 1, 2, 3, 4, 6, 8, 9, and 12. That is the whole trick: 72 is the nearest highly-divisible number to the true constant, so the mental math stays easy.
How accurate is it?
The rule is at its best for rates between 6% and 10%, where it is nearly exact. Compare the rule against the exact formula:
- At 4%: rule says 18.0 years, exact is 17.7.
- At 8%: rule says 9.0 years, exact is 9.01.
- At 12%: rule says 6.0 years, exact is 6.12.
- At 20%: rule says 3.6 years, exact is 3.80.
The drift grows as you move away from the sweet spot, in both directions. The same idea extends to other multiples: dividing 114 by the rate estimates tripling time, and 144 estimates quadrupling time, with the same kind of accuracy.
Using it to gut-check forecasts
The rule of 72 turns abstract growth percentages into concrete multiples, which makes aggressive forecasts easier to spot. A company forecast to grow 25% a year for a decade doubles roughly every 3 years (72 / 25), so it would have to grow about 9x over the decade. Stated as "9x in 10 years," many forecasts reveal themselves as wishful thinking.
Use this workflow: compute a company's historical growth with the CAGR calculator, translate your forecast into a multiple with the rule of 72, and ask whether the multiple is believable given the company's size and history. Then test the forecast inside the DCF calculator and see what it implies for the share price.
Limitations
- It assumes a constant rate. Real returns bounce around, and volatile returns compound worse than steady returns at the same average. The rule only holds for smooth, constant growth.
- It is an approximation everywhere. Fine for ballpark estimates, not for contracts, loan documents, or formal models, where you should use the exact formula.
- It does not handle contributions or withdrawals. Adding money along the way changes the math; use the compound interest calculator for that.
- It says nothing about risk. A 12% return that doubles your money in 6 years is only good if the risk of getting there was acceptable. Doubling time is half the story.
Frequently asked questions
What is the rule of 72?
A mental-math shortcut for compound growth: divide 72 by an annual rate of return to estimate how many years it takes money to double. At 8% a year, money doubles in about 9 years; at 6%, about 12 years.
Why 72 and not 70?
The exact constant for continuous compounding is about 69.3, and 72 is a nearby number with many divisors (1, 2, 3, 4, 6, 8, 9, 12), which makes mental division easy for common rates. It also compensates slightly for discrete annual compounding, which 69.3 does not. 69 and 70 are used too, but 72 divides more evenly.
How accurate is the rule of 72?
Very close for rates around 6 to 10 percent: at 8% it gives 9.0 years versus 9.01 exactly. Outside that band the drift grows: at 4% it says 18.0 years versus 17.7 exact, and at 20% it says 3.6 versus 3.8. Good for ballpark estimates, not precision.
What about the rule of 69 or 70?
69.3 is exact for continuous compounding, so 69 works best when interest compounds very frequently. 70 is sometimes used as a rounder alternative to 72 but has fewer divisors. For ordinary annual compounding, 72 is the best general-purpose choice.
When should I not use the rule of 72?
When you need an exact answer, when rates are very high or very low, when returns are volatile rather than steady, or when the calculation feeds a formal model. Use a calculator or the exact formula, ln(2) / ln(1 + r), in those cases.
How does the rule of 72 relate to CAGR?
The rule of 72 runs the same math in reverse: CAGR asks what steady rate took a value from A to B, while the rule of 72 asks how long a steady rate takes to double. Both assume smooth, constant compounding, and both are sanity checks, not predictions.