How it works
The Rule of 72 is mental arithmetic that investors have used for centuries: divide 72 by the annual return rate and you have the years it takes money to double. At 8%, that is 72 divided by 8 — nine years. At 6%, twelve years; at 12%, six. It works because the logarithm of two is close enough to 0.72 that the approximation lands within a whisker of the true answer for the rates anyone actually earns. This calculator shows both figures side by side — the rule's estimate and the exact doubling time from the compound-interest formula — so you can see how little the shortcut gives up. It also extends the logic: two doublings quadruple the money, so $10,000 at 8% becomes $20,000 in nine years and $40,000 in eighteen. That is the real lesson the rule teaches. Doubling time converts an abstract percentage into a concrete clock, and the clock is unforgiving about the difference between 4% and 8% — eighteen years against nine. Over a working life of three or four doublings, that gap is the difference between a comfortable sum and a small fortune.
Formula
Doubling years ~ 72 / rate | exact = ln(2) / ln(1 + rate/100)
Tips
- Divide 72 by the rate — at 8%, money doubles in about nine years.
- Two doublings quadruple the money; three multiply it eightfold.
- The rule is most accurate between 6% and 10% — the rates people actually earn.
- The gap between 4% and 8% is nine years per doubling — it compounds into fortunes.
- Use it for debts too: an 18% card doubles what you owe in about four years.
Frequently asked questions
- What is the Rule of 72?
- A mental shortcut: divide 72 by the annual return rate to get the years it takes money to double. At 8% that is nine years, at 6% twelve, at 12% six. It works because the logarithm of two is close to 0.72.
- How accurate is the Rule of 72?
- Remarkably accurate for the rates people actually earn. Between 6% and 10% it lands within a fraction of a year of the exact compound-interest answer. It drifts a little at very high or very low rates, which is why the calculator shows the exact figure alongside.
- How do I use the Rule of 72?
- Divide 72 by your return rate for doubling time, then chain doublings: two doublings quadruple the money, three multiply it eightfold. At 8%, $10,000 becomes $20,000 in nine years and $40,000 in eighteen — a clock that makes growth concrete.
- Does the Rule of 72 work for debt?
- Yes, and soberingly. An 18% credit card doubles what you owe in about four years if left alone; a 24% rate in about three. The same mathematics that builds wealth compounds debt, which is why high-interest balances demand urgency.
- Why 72 and not 70 or 100?
- Seventy-two is the sweet spot between accuracy and convenience. It approximates the logarithm of two well across common rates, and it divides cleanly by 2, 3, 4, 6, 8, 9 and 12 — the rates people quote. Some use 70 for very low rates, but 72 is the standard.