The Rule of 72: compound interest in your head
Divide 72 by your return and you get the years it takes to double your money. A ten-second trick worth keeping.
Divide 72 by your annual return and you get the number of years it takes to double your money. That is the whole trick. Earn 8% a year and your balance doubles in about nine years, because 72 divided by 8 is 9. You can run it in your head at a party, no spreadsheet, no app. It is an estimate, not an exact answer, but it lands close enough to be useful and it makes compounding something you can feel instead of something you have to look up.
The one line of math
Take the annual growth rate as a plain number, not a decimal. For 6%, you use 6, not 0.06. Then:
Years to double = 72 / rate.
At 6%, that is 72 divided by 6, which equals 12 years. Put $10,000 in something growing 6% a year and in roughly 12 years you have about $20,000, with nothing added. Wait another 12 years and you are near $40,000, because the doubling repeats. That repeat is the part people underrate. Each double works on a bigger base, so the dollars added in the second double dwarf the first.
The numbers at common rates
Here is the rule run across the returns you actually run into, from a sleepy savings account up to the kind of long-run stock return people plan around.
| Annual return | 72 / rate | Years to double |
|---|---|---|
| 3% | 72 / 3 | 24 years |
| 6% | 72 / 6 | 12 years |
| 8% | 72 / 8 | 9 years |
| 10% | 72 / 10 | 7.2 years |
| 12% | 72 / 12 | 6 years |
Read down that table and the gap between rates stops being abstract. Money at 3% takes 24 years to double. The same money at 12% doubles four times in those 24 years: $10,000 becomes $20,000, then $40,000, then $80,000, then $160,000. Two percentage points of return, three points, these look small on a fund page. Over a working life they decide whether you double twice or five times. When you want the exact figure instead of the estimate, run it in our compound interest calculator, and for how returns get generated in the first place, the investing guide walks through it.
Note
The Rule of 72 assumes the money is left alone to compound and the rate holds steady. Real returns bounce around year to year. A stock fund might average 8% over decades while dropping 20% in a bad year. The rule tells you the trend, not the ride. Use it to compare options and set expectations, then check the precise dollar path with a calculator before you commit to a plan.
Why 72, and not some other number
Doubling is really a question about exponents. If your money grows by a rate r each year, the years to double is the solution to a logarithm: the natural log of 2, divided by the natural log of (1 + r). The natural log of 2 is about 0.693, or 69.3%. So the truly exact constant for continuous growth is closer to 69.3 than 72.
72 wins anyway because it divides cleanly. It splits evenly by 2, 3, 4, 6, 8, 9, and 12, which covers most of the interest rates you ever care about. 69 divides by almost nothing you would use. For the annual compounding that savings accounts and funds actually do, 72 also tracks the real curve a touch better than 69 in the middle of the range. You get a number that is both accurate and easy to do without a pen. That trade is the whole reason the rule survives.
How accurate is it
Close, and closest right where you need it. Compare the rule to the exact doubling time and the error stays small across the normal band of returns.
| Annual return | Rule of 72 | Exact doubling time |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 6% | 12 years | 11.9 years |
| 10% | 7.2 years | 7.3 years |
| 20% | 3.6 years | 3.8 years |
Between 5% and 12% the rule is within a few weeks of the exact answer, which is the band most investing and saving lives inside. Push to very high rates and it drifts. At 20% the rule says 3.6 years and the true figure is about 3.8, so it runs a little optimistic. At very low rates it is also slightly off the other way. For the returns a regular investor or saver deals with, the miss is small enough to ignore.
It runs in reverse on debt
The same math that grows your savings grows what you owe, and credit cards charge rates that make the doubling fast. A card at 24% APR puts 72 divided by 24, which is 3, so an unpaid balance roughly doubles in about three years if you ignore it. Carry $5,000 and treat it like a problem for later, and you are looking at near $10,000 in three years from interest alone, before a single new purchase.
That is why a balance you would never choose to take on as a loan quietly becomes one. The rule reframes a credit card from a payment you make into a clock that is running. The exact mechanics, the daily compounding and the way the rate is applied, are in how credit card interest is really calculated. The headline from the Rule of 72 is blunt: at card rates, doing nothing doubles the debt about as fast as a good investment doubles your savings. The interest does not care which side it is working on.
Where to actually use it
- Sizing a goal. You have $20,000 and want $80,000. At 8% that is two doubles, so roughly 18 years. Now you know if the timeline fits.
- Comparing accounts. A 0.5% savings account doubles your cash in 144 years. A 4% account does it in 18. The rule makes the gap obvious in one division.
- Judging a debt. Any rate above roughly 10% doubles the balance inside seven years. That is your line for what to pay off fast.
- Spotting a scam. Someone promising to double your money in a year is claiming a 72% return. Real, repeatable, and almost always false.
The rule does not replace a calculator. It replaces not thinking about compounding at all. Carry it in your head and you start checking returns, fees, and rates against a simple yardstick instead of taking numbers at face value. A 1% fee, for instance, looks tiny until you see it eat a chunk of every double, which is the case made in what a 1% fee really costs you over 30 years.
FAQ
Why is it 72 and not the exact number?
The mathematically exact constant for continuous growth is about 69.3, which comes from the natural log of 2. 72 is used instead because it divides evenly by so many common rates: 2, 3, 4, 6, 8, 9, and 12 all go in cleanly. That makes the mental math fast. For ordinary annual compounding, 72 also happens to track the real doubling curve slightly better than 69 across the middle of the rate range, so you lose almost no accuracy and gain a number you can divide in your head.
How accurate is the Rule of 72?
Very accurate between about 5% and 12%, where it lands within a few weeks of the exact doubling time. At 6% the rule says 12 years and the true figure is 11.9. Outside that band it drifts: at 20% the rule says 3.6 years while the real answer is closer to 3.8, so it gets a touch optimistic at high rates and slightly off at very low ones. For the returns most savers and investors deal with, the error is small enough that the estimate is fine for planning.
Does it work for debt too?
Yes, and that is exactly when it stings. Interest compounds the same way whether it is growing your savings or your balance owed. A credit card at 24% APR doubles what you owe in about three years if you make no payments, because 72 divided by 24 is 3. The rule is a fast way to see how dangerous a high rate is. Any debt above roughly 10% doubles inside seven years, which is a clear signal to pay it down before you invest anywhere else.
What return should I plug in for investing?
For a broad stock index fund, many people plan around a long-run average near 7% to 10% before inflation, which puts doubling somewhere between about 7 and 10 years. That is an average across decades, not a promise for any single year, since the market can drop hard and recover. Use a conservative rate when you plan, then check the precise dollar figures in a compound interest calculator. The Rule of 72 sets the expectation; the calculator confirms it.
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