How long will it take your money to double? With the Rule of 72, you can answer that question in your head, in seconds, with one simple division. Divide 72 by your annual interest rate, and the result is roughly the number of years it takes an investment to double. No spreadsheet, no logarithms, no calculator required.
This shortcut has survived for centuries because it is both simple and surprisingly accurate. It works for savings accounts, investment returns, inflation, and even debt. This guide explains the formula, works through a fully checked example, compares it with the Rule of 70 and the Rule of 69.3, and shows where the shortcut stops being trustworthy.
The Rule of 72 is a mental math shortcut for estimating the doubling time of anything growing at a steady compound rate. The formula has two directions:
The rule only works for compound growth, where earnings are reinvested and start earning on their own. It does not work for simple interest, where interest is paid out and never compounds. It also assumes the rate stays constant for the whole period, which real investments almost never do. Treat every answer as an estimate, not a promise.
Here is what the rule gives at common rates:
| Annual rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 3% | 24.0 years | 23.45 years |
| 6% | 12.0 years | 11.90 years |
| 8% | 9.0 years | 9.01 years |
| 10% | 7.2 years | 7.27 years |
| 12% | 6.0 years | 6.12 years |
Notice how close the shortcut lands in the 6% to 10% range. That band covers most savings rates, bond yields, and long run investment assumptions people actually use.
Suppose you invest $5,000 at a steady 8% per year, compounded annually, and add nothing more.
Step 1: apply the rule. 72 / 8 = 9, so the rule predicts your money doubles in about 9 years. Step 2: check it against the exact compound formula. The exact doubling time is ln(2) / ln(1.08), which equals 9.01 years, so the shortcut is off by only about 4 days. Step 3: check the money itself. After 9 years, $5,000 at 8% grows to $5,000 x 1.08 to the power of 9 = $9,995.02, just short of a clean double because the exact doubling point falls a few days past year 9.
Leave it alone for a second doubling and the effect compounds. After 18 years, the same $5,000 grows to $19,980.10, close to four times the starting amount. Two doublings turn $5,000 into roughly $20,000, and that is the real lesson of the rule: time matters at least as much as the rate you earn.
The mathematically exact constant behind all three rules is the natural logarithm of 2, about 0.693. That is why 69.3 is the theoretically correct numerator, and why 69.3 works best for continuous compounding, where growth never pauses.
So why does everyone use 72? Because 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12, which makes mental division easy, and because it slightly corrects for annual compounding at typical rates. The Rule of 70 sits in between: it fits low rates under about 5% better, and economists often prefer it for population and GDP growth. A practical guide:
At very high rates, all three rules drift. At 18%, the Rule of 72 predicts 4.0 years while the exact answer is 4.19 years. One old adjustment helps here: add 1 to 72 for every 3 percentage points above 8%. At 14%, use 74 instead of 72, giving 74 / 14 = 5.3 years, close to the exact 5.29 years. An early reference to the rule appears in Luca Pacioli's Summa de arithmetica, published in 1494, which already gave the 6% example: 72 / 6 = 12 years.
The rule is just as useful for things working against you, because the same division measures halving time. Replace the return with the rate of decay, and the answer tells you how long something takes to lose half its value.
A handy companion is the Rule of 115, the tripling version of the same idea. Divide 115 by the rate to estimate tripling time: at 8%, your money triples in about 115 / 8 = 14.4 years.
The Rule of 72 is a screening tool, not a financial plan. It assumes one constant rate, but real returns bounce around from year to year, and a volatile path to the same average return ends in a different place than a smooth one. It ignores taxes, fees, and inflation unless you deliberately use an after tax or after inflation rate. It counts no new contributions, so it understates the growth of someone adding money every month. And at extreme rates, above roughly 20% or below 2%, the error grows large enough that you should use the exact formula instead.
Compounding frequency matters too. The rule assumes annual compounding. With monthly or daily compounding, money doubles slightly faster than the rule predicts, so use the effective annual rate first if you want the closest estimate. None of this makes the rule useless. It makes it honest: a quick, transparent estimate for comparing options, and a reason to run the exact numbers before committing real money. These are estimates for education, not professional financial advice.
Run your own numbers in seconds with our free calculators. The Rule of 72 Calculator gives you both the shortcut estimate and the exact doubling time side by side. The Compound Interest Calculator shows the year by year balance for any starting amount, rate, and time period. And the Inflation Calculator shows what today's money will be worth after years of rising prices, which is the halving side of the rule in action.
Divide 72 by your annual interest rate to estimate how many years it takes an investment to double. At 8%, that is 72 / 8 = 9 years. It is an approximation for compound growth, not an exact formula.
Divide 72 by the number of years you have. To double in 10 years, you need about 72 / 10 = 7.2% per year. To double in 6 years, you need about 72 / 6 = 12% per year.
Very accurate between 6% and 10%, where it is usually within a few months of the exact answer. At 8%, it predicts 9.0 years against an exact 9.01 years. Outside that band the error grows, so use the exact formula for very low or very high rates.
Yes. Divide 72 by the inflation rate to find how long prices take to double, or equivalently how long cash takes to lose half its purchasing power. At 3% inflation, both take about 24 years.
Yes, as long as the rate and the answer use the same period. At 0.5% per month, doubling takes about 72 / 0.5 = 144 months, which is 12 years.
Both estimate doubling time, but 70 is slightly more accurate at low rates, while 72 is more accurate at typical investment rates of 6% to 10% and much easier to divide in your head.