Money · 3 min read
The Rule of 72: How Long Until Your Money Doubles?
Divide 72 by the growth rate to see how many years money takes to double. How the rule of 72 works, how accurate it is, and using it on debt and inflation.
By the Cognosc team ·
If money grows 6% a year, how long until it doubles? You could work it out with logarithms, or you could divide 72 by 6 and get 12 years. That’s the rule of 72, and it’s one of the most useful bits of mental maths there is.
Try it
How long until it doubles?
Pick a yearly rate. Each step is one doubling, over fifty years.
At 7% a year, money doubles every 10.2 years. The rule of 72 says 72 ÷ 7 = 10.3, close enough to do in your head. Over 50 years that’s 4 doublings: 16 times what you started with.
The rule
Years to double ≈ 72 ÷ the yearly growth rate (as a percentage)
- At 3% a year: 72 ÷ 3 = about 24 years.
- At 6%: about 12 years.
- At 8%: about 9 years.
- At 12%: about 6 years.
It works in reverse too. If you want money to double in 10 years, you need about 72 ÷ 10 = 7.2% a year.
How accurate is it?
Very, for everyday rates. The exact doubling time at 8% is 9.01 years; the rule says 9. At 6%, the exact answer is 11.9 years; the rule says 12. It drifts at very high or very low rates: at 1% it says 72 years when the truth is 69.7. Some people use 70 or 69 for low rates, but 72 has a practical advantage: it divides neatly by 2, 3, 4, 6, 8, 9 and 12.
Why does it work?
The exact doubling time is the natural logarithm of 2 (about 0.693) divided by the natural logarithm of (1 + the rate). For small rates, that’s close to 69.3 ÷ the rate. The number is nudged up to 72 because it’s slightly more accurate for typical rates of 5 to 10%, and far easier to divide.
You don’t need to remember any of that. The rule just works.
Using it on debt
The rule works just as well against you. A credit card charging 24% a year doubles an unpaid balance in about 72 ÷ 24 = 3 years. That’s a vivid way to see why high-interest debt is so dangerous, and why paying it off early is usually one of the best returns available.
Using it on inflation
At 3% inflation, prices double in about 24 years. So anything you save has to grow faster than that just to hold its value. At 6% inflation, prices double in 12 years. See inflation explained.
Doublings add up fast
The real power of the rule is counting doublings over a long time. At 7% a year, money doubles about every 10 years. Over a working life of 40 years, that’s four doublings:
1 → 2 → 4 → 8 → 16 times what you started with.
At 10% a year it doubles about every 7 years, so 40 years is almost six doublings: around 45 times. Small differences in the rate make enormous differences over decades. There’s more in compound interest explained.
A caution
The rule assumes the rate stays steady. Real investments go up and down, and returns aren’t guaranteed; the rule tells you what a given average rate does, not what you’ll actually get. This is general education, not financial advice.
Test yourself
The free money test opens with a doubling question and covers nine more common money traps.