How the Rule of 72 works
The rule runs in two directions. To find a doubling time, divide 72 by the yearly rate written as a whole number: money growing 8% a year doubles in about 72 ÷ 8 = 9 years. To find a required rate, divide 72 by the years you have: to double in 10 years you need about 7.2% a year.
Because doublings stack, the rule also sketches long horizons. At 8%, $10,000 becomes roughly $20,000 in 9 years, $40,000 in 18, $80,000 in 27 and $160,000 in 36; the exact figures, $19,990, $39,960, $79,881 and $159,682, are within a fraction of a percent. Savings growing 6% a year from age 35 get about 2½ doublings by 65, or roughly 5.7 times the starting balance.
The rule works because of compound interest: growth is a constant percentage of a growing balance, so each doubling takes the same number of years however large the balance already is. The exact doubling time is ln 2 ÷ ln(1 + r); the rule swaps that logarithm for one division you can do in your head.
How accurate is the Rule of 72?
The rule is an approximation, and its error depends on the rate. It is almost exact near 8%, a little generous at low rates and a little short at high ones, as the table below shows. At 2% it says 36 years when the true answer is 35; at 24% it says 3 years when the truth is about 3.2. Across the 4%–12% range where most long-run planning assumptions sit, it is off by a third of a year or less.
Two adjustments tighten the fit. The Rule of 70, or 69.3, suits low rates such as inflation and any rate compounded continuously. At high rates, some people add 1 to 72 for every three points of rate above 8%, so 24% would use 77, giving 3.2 years. When the answer has to be precise, use the exact formula or a calculator such as the SEC’s Investor.gov compound interest calculator.
Using the rule for inflation, fees and debt
The same arithmetic works for anything that grows against you. Divide 72 by an inflation rate to estimate how long prices take to double, which is when a fixed dollar amount has lost half its purchasing power. At 3% that is about 24 years (23.4 exactly), shorter than many retirements. A pension or annuity payment with no cost-of-living increase would buy about half as much after 24 years of 3% inflation, one reason longevity risk is also an inflation risk.
When growth should be judged in buying power, apply the rule to the real rate of return: 7% nominal growth with 3% inflation is about 3.9% real, which doubles purchasing power in roughly 18 to 19 years, not 10.
Fees and debt follow the same logic. A portfolio earning 7% before a 1% yearly fee, such as an expense ratio plus advisory costs, grows at about 6%, stretching its doubling time from about 10.3 years to 12. An unpaid balance at 18% interest doubles in roughly four years, a vivid case for paying high-rate debt first.
Limits of the Rule of 72
The rule answers one narrow question: how long a single sum takes to double at one steady compound rate. Real plans break that assumption in several ways, and the rule says nothing about risk: two investments with the same expected rate can have very different odds of reaching it. It also loses accuracy at very high rates. Treat the answer as a sanity check on a rate, not a forecast of what an account will do.
- It needs a compound rate. For a volatile investment, use the compound annual growth rate, not the average of yearly returns, which runs higher and makes doubling look faster.
- It ignores contributions and withdrawals. Each new deposit starts its own doubling clock, and withdrawals slow the whole balance.
- It ignores the order of returns, which matters once you are withdrawing; see sequence-of-returns risk.
- Keep the rate consistent: before or after fees and taxes, nominal or real, price-only or total return with dividends.
- Enter the rate as a percent number, 6 rather than 0.06.
Illustrative numbers
Checking a 2026 EE savings bond with the Rule of 72
- 72
- The rule’s constant, most accurate for annual compounding at rates near 8%
- Annual rate
- The steady compound growth rate as a whole number, such as 6 for 6%
Exact doubling time = ln 2 ÷ ln(1 + r), with r as a decimal. Rearranged, the rate needed to double in n years ≈ 72 ÷ n.
Fixed rate, EE bonds issued May–October 20262.40%, compounded semiannually
Rule of 72 doubling time at 2.40%72 ÷ 2.4 = 30 years
Exact doubling time at 2.40%About 29.1 years
Treasury’s guaranteeValue doubles at 20 years
Rate implied by doubling in 20 years72 ÷ 20 = 3.6% (exactly about 3.53%)
Value at 20 years from the 2.40% rate aloneAbout 1.61 times the purchase price
At its stated rate alone, a $1,000 bond would be worth about $1,611 after 20 years, so Treasury adds the difference to reach $2,000. Held exactly 20 years, the bond earns about 3.5% a year; cashed earlier, after the required first 12 months, it earns only the 2.40% rate, less three months of interest before year five. The rule got both answers within a year or a tenth of a point, which is plenty for comparing it with a CD or I bond.
At a glance
Rule of 72 estimate vs. exact doubling time, with interest compounded once a year
| Annual rate | Rule of 72 (years) | Exact (years) | Rule’s error (years) |
|---|---|---|---|
| 2% | 36.00 | 35.00 | +1.00 |
| 3% | 24.00 | 23.45 | +0.55 |
| 4% | 18.00 | 17.67 | +0.33 |
| 6% | 12.00 | 11.90 | +0.10 |
| 8% | 9.00 | 9.01 | −0.01 |
| 10% | 7.20 | 7.27 | −0.07 |
| 12% | 6.00 | 6.12 | −0.12 |
| 18% | 4.00 | 4.19 | −0.19 |
| 24% | 3.00 | 3.22 | −0.22 |
Put it in your plan
Rule of 72 in MoneyWhatIf
The Rule of 72 assumes one steady rate on one lump sum. A MoneyWhatIf projection instead compounds each account every year at the growth and dividend rates set for it, net of its yearly fee, around the contributions and withdrawals the plan makes. Turn on Today’s money to read balances in purchasing power, the view in which a doubling means twice the buying power. Market Simulator swaps the steady rate for an index’s actual annual returns in selected accounts, showing how similar long-run growth can arrive in a very different order.
Common questions
Rule of 72 FAQs
Why is it 72 and not 70 or 69?
The exact constant is 100 × ln 2, about 69.3, but only for continuous compounding. With interest compounded once a year, the constant that gives the right answer rises with the rate: about 70 at 2%, 71 at 6% and 72 at 8%. The number 72 also divides evenly by 2, 3, 4, 6, 8, 9 and 12, which keeps the mental math easy, so it won out as the everyday version.
How long does it take money to double at 7%?
The Rule of 72 gives 72 ÷ 7 ≈ 10.3 years, and the exact answer with annual compounding is 10.24 years. That assumes 7% is a steady compound rate after fees and that nothing is added or withdrawn. With regular contributions the balance doubles sooner because new money keeps arriving, even though each dollar still takes about 10 years to double on its own.
Does the Rule of 72 work with monthly or daily compounding?
Yes, if you feed it the annual percentage yield, which already reflects compounding, instead of the stated rate. At 6% compounded monthly, the APY is about 6.17%, and 72 ÷ 6.17 gives about 11.7 years against an exact 11.6. Using the 6% rate alone gives 12 years, a little slow. With continuous compounding, 69.3 divided by the rate is exact.
Does the Rule of 72 work for stocks?
Only as a rough guide. Stock returns swing from year to year, so plug in a compound annual growth rate rather than an average return, which overstates growth when returns vary. Even then, the doubling time describes an assumption, not a promise: markets can fall short of any rate for a decade, and the order of returns matters once you are withdrawing.
What are the Rule of 114 and the Rule of 144?
They extend the same idea. Dividing 114 by a rate estimates the years to triple money, and dividing 144 estimates the years to quadruple it, since quadrupling is two doublings (2 × 72). At 8%, money triples in about 14 years and quadruples in about 18. Like the Rule of 72, both assume a steady compound rate.