At 7%, your money doubles in about 10 years. That is why starting early matters more than contributing more: time inside the market is the multiplier.
Why 72 and not 70 or 100
The exact doubling time is t = ln(2) / ln(1 + r). Over the range of returns most people actually plan around, dividing 72 by the rate gets close: at 7%, the exact answer is 10.24 years and the Rule of 72 gives 10.29 — a difference of about a month over a decade.
The divisor 72 works because it is close to 69.3 (the value that would make the rule exact for small rates) and because it divides evenly by common rates: 72 ÷ 6 = 12, 72 ÷ 8 = 9, 72 ÷ 9 = 8. That makes the mental arithmetic easy at exactly the rates people use most.
How to use it
- Enter your rate. Use the annual return you are assuming, not the one you hope for. A savings account might pay 4%; a diversified stock portfolio has historically averaged near 7% nominal over long periods.
- Enter a starting amount. Any figure works. The interesting comparison is the same rate with different starting amounts — a larger base compounds faster.
- Compare the two numbers. The gap between the Rule of 72 estimate and the exact answer tells you how much the shortcut is costing you in accuracy at this particular rate.
Common doubling times at a glance
A quick reference for how long doubling takes at rates people actually use:
- At 3% (a typical savings account), money doubles in about 24 years.
- At 4.5% (a high-yield savings account), roughly 16 years.
- At 7% (a diversified stock portfolio, long-run average), about 10.3 years.
- At 10% (an aggressive stock allocation), about 7.2 years.
- At 24% (a credit card APR), debt doubles in about 3 years — which is why paying down high-interest debt is so urgent.
Where the shortcut stops working
The Rule of 72 is a linear approximation to an exponential process, so it is exact at only one rate and close at the others. At 7% it overstates the doubling time by about two weeks. At 2% it overstates it by nearly a year. At 20% it understates it by about two and a half months. The direction flips because the approximation curve crosses the true curve near 7.8%.
That matters less than it sounds, because the rule is used for a rough sense of scale rather than for a financial decision. Where it does mislead is at very low rates, where a small difference in doubling time is a large difference in percentage terms: the rule says 24 years at 3% where the exact answer is 23.4, which sounds trivial until you notice the rule has overstated the time by more than six months.
The rule also assumes a single deposit left alone, compounding annually. It does not model monthly contributions, taxes, or fees. A fund charging 1% a year against a 7% return is really growing at 6%, and the doubling time stretches from 10.2 years to 11.9 — a difference the shortcut hides completely.
Frequently asked questions
Is the Rule of 72 or the Rule of 69 better?
Rule of 69 is more accurate for low rates, Rule of 72 for higher ones. At the 5% to 10% range most people use, 72 is easier to divide and close enough.
Can I use the Rule of 72 for debt?
It works in reverse: divide 72 by your credit card APR to estimate years to pay off with no new charges. At 24% APR, that is three years. Use the savings goal calculator for a precise answer.