What Is the Rule of 72? How to Use It

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The rule of 72 is a shortcut for estimating how long an amount growing at a fixed compound rate takes to double: divide 72 by the annual percentage rate. At 8% a year, money doubles in about 72 ÷ 8 = 9 years. Run it in reverse and it gives the approximate annual rate needed to double money in a given number of years. The result is an estimate, but within the range of rates most savers and investors work with, it lands close to the exact answer.

The rule of 72 formula

The rule has two forms, depending on which number you already know:

Years to double = 72 ÷ annual rate of return

Annual rate needed = 72 ÷ years to double

Use the percentage as a whole number. A 6% return goes in as 6, giving 12 years. Entering 0.06 would return 1,200, which is clearly wrong. Fractional answers are fine: 72 ÷ 7.5 = 9.6 years, about nine years and seven months.

The formula assumes a single, steady rate over the whole period, compounded once per period. The answer is in the same time unit as the rate. A rate of 1% per month, compounded monthly, doubles in about 72 months, or six years.

Worked examples

Hypothetical example, assuming a constant 8% annual return compounded yearly, with no withdrawals, fees or taxes:

A $10,000 investment doubles about every 9 years. That makes roughly $20,000 after 9 years, $40,000 after 18, $80,000 after 27 and $160,000 after 36. The exact figure at year 36 is about $159,700, so four rounds of the rule are within a fraction of a percent.

Reverse questions work the same way:

• Double in 10 years: 72 ÷ 10 = 7.2% a year. Exact: about 7.18%.
• Double in 6 years: 72 ÷ 6 = 12%. Exact: about 12.25%.
• Double in 5 years: 72 ÷ 5 = 14.4%. Exact: about 14.87%.

The pairing behind the so-called 7/10 shortcut follows directly from the rule. Money at 10% doubles in about 7.2 years, and money at 7% doubles in about 10.3 years.

Why the number is 72

The exact doubling time for annual compounding is:

Years = ln(2) ÷ ln(1 + r)

Here r is the rate as a decimal. The natural log of 2 is about 0.693. For small rates, ln(1 + r) is close to r, so the exact answer is close to 69.3 ÷ the rate in percent. As rates rise, that approximation drifts, and a slightly larger numerator compensates. Around 8%, the numerator that gives the exact answer is very close to 72.

The other reason is convenience. 72 divides evenly by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36, so most common rates give a clean result you can work out in your head.

How accurate is the rule of 72?

Comparing the rule with the exact annual-compounding result:

• 2%: rule 36 years, exact 35.0
• 4%: rule 18 years, exact 17.7
• 6%: rule 12 years, exact 11.9
• 8%: rule 9 years, exact 9.0
• 10%: rule 7.2 years, exact 7.3
• 12%: rule 6 years, exact 6.1
• 18%: rule 4 years, exact 4.2
• 24%: rule 3 years, exact 3.2
• 36%: rule 2 years, exact 2.25

At low rates the rule slightly overstates the time to double. At high rates it understates it, and the gap widens as the rate climbs.

Adjusting the rule: 73, 70 and 69.3

A common refinement adds 1 to the numerator for every 3 percentage points the rate sits above 8%, and subtracts 1 for every 3 points below. At 11%, three points above 8%, the rule of 73 gives 73 ÷ 11 = 6.64 years, which matches the exact figure of about 6.64. The plain rule of 72 gives 6.55.

Compounding frequency matters too. With daily or continuous compounding, the exact doubling time is 69.3 ÷ the rate, so 69.3 (or the rounder 69 or 70) is the better numerator. Hypothetical example: a deposit earning 3.2% compounded monthly doubles in about 21.7 years. The rule of 69.3 gives 21.7, while the rule of 72 gives 22.5.

The rule of 70 is also standard in economics, where growth rates for GDP or population are often low, in the 1% to 3% range.

Rule of 72 vs. related rules

Rule of 114 (tripling). Dividing 114 by the rate estimates the time to triple. At 8%, 114 ÷ 8 = 14.25 years; the exact figure is about 14.3.

Rule of 144 (quadrupling). Dividing 144 by the rate estimates the time to quadruple. Since quadrupling is two doublings, the result is twice the rule-of-72 answer: 18 years at 8%.

Simple interest. The rule does not apply when interest is paid only on the original principal. Under simple interest, doubling takes 100 ÷ the rate, so 12.5 years at 8% instead of about 9. The gap is the effect of earning interest on interest, explained in more detail under compound interest.

How to use the rule of 72

Comparing returns. The rule turns a percentage into a time frame that is easier to picture. At 4%, money doubles in about 18 years; at 8%, in about 9. Over a 36-year horizon, that is two doublings (4x) against four (16x), which shows how a few points of return compound over long periods.

Counting doublings toward a goal. To see how many doublings a target needs, divide the goal by the starting amount and count powers of two. Going from $300 to $1 million is a multiple of about 3,333, or nearly 12 doublings (2¹² is 4,096). At 8%, that would take around 105 years at a constant rate.

Inflation. The rule estimates how long it takes for purchasing power to halve. At 3% inflation, a dollar buys about half as much in roughly 24 years. At 6%, it takes about 12. For past rates to plug in, see U.S. inflation rate by year.

Fees. Fees lower the net rate that compounds. Hypothetical example: a portfolio earning 8% before costs doubles in about 9 years. A 1% annual fee cuts the net return to 7%, stretching doubling to about 10.3 years. Over several decades, that delay compounds into a large difference in ending value.

Debt. Unpaid compounding debt doubles on the same schedule. Hypothetical example: a balance charging 20% a year with no payments made would double in about 72 ÷ 20 = 3.6 years. Card interest is often compounded more frequently than once a year, which would make it double slightly sooner.

Economic and population growth. An economy growing 4% a year doubles in about 18 years. A population growing 1% a year doubles in about 72 years.

Limitations of the rule of 72

• It assumes a constant rate. Investment returns vary year to year, so the result is a rough guide to a possible outcome, not a forecast.
• Volatility lowers the compound rate. The rule needs the compound annual growth rate, not a simple average of yearly returns. Hypothetical example: +50% one year and −50% the next averages 0%, but $100 ends at $75. Using an arithmetic average overstates growth.
• Taxes, fees and contributions are not included. Unless you use an after-cost rate, the estimate is for gross growth. Regular deposits or withdrawals also change the timeline.
• Accuracy fades at extreme rates. At very high or very low rates, or with frequent compounding, the adjusted numerators or the exact log formula are more reliable.
• It only measures doubling. It says nothing about risk or the chance of earning the assumed rate.

For precise planning, a spreadsheet or calculator using the exact formula is more reliable. The rule’s value is speed: it lets you check whether a return claim or a savings plan is in the right range before working out exact numbers.

Who came up with the rule of 72?

The rule appears in Luca Pacioli’s Summa de Arithmetica, a mathematics text published in 1494. Pacioli stated the rule without deriving it, which suggests it was already known before his book. It remains a staple of financial literacy teaching, and the U.S. Securities and Exchange Commission has included it in its educational materials.

The Bottom Line

Savers, investors and borrowers can use the rule of 72 to turn a percentage into a time frame they can picture, whether for returns, fees, inflation or unpaid debt. It works best for compound growth at rates of roughly 6% to 10% and assumes a steady rate with no taxes or fees. For precise planning, a spreadsheet or calculator using the exact formula is more reliable.