What Is the Rule of 72 and How Does It Work?

You have $10,000 in a savings account earning 4% APY. Your friend has $10,000 in an index fund averaging 8% per year. When will each of you have $20,000? You can pull out a financial calculator and solve for the doubling time. Or you can do it in your head in about three seconds.

The Rule of 72 is a mental math shortcut that estimates how long it takes any compounding quantity to double. Divide 72 by the annual growth rate and you get the approximate number of years. At 4%, your money doubles in 18 years. At 8%, it doubles in 9 years. That is the entire rule, and it has been helping people make financial decisions for over 500 years.

What the Rule of 72 Is and Why It Matters

The Rule of 72 applies to anything that grows at a compound rate: investments, savings, inflation, population, GDP, debt. The formula is:

Years to double = 72 / annual growth rate (as a percentage)

Examples:

• 6% investment return: 72 / 6 = 12 years to double
• 3% inflation: 72 / 3 = 24 years for prices to double
• 18% credit card APR: 72 / 18 = 4 years for debt to double
• 2% population growth: 72 / 2 = 36 years for population to double

The rule works because compound growth is exponential. Your money earns returns, and those returns earn returns. The exact doubling time comes from the natural logarithm of 2, which is about 0.693. For continuous compounding, the exact formula is:

Exact doubling time = ln(2) / r = 69.3 / r

The number 72 is used instead of 69.3 because it is more divisible (by 2, 3, 4, 6, 8, 9, and 12) and it is more accurate for annual compounding at common interest rates.

Use our Rule of 72 Calculator to calculate doubling times for any rate.

The Origin: Luca Pacioli, 1494

The earliest known written reference to the Rule of 72 appears in Summa de arithmetica, geometria, proportioni et proportionalita, published in Venice in 1494 by Fra Luca Pacioli. Pacioli is better known as the father of double-entry bookkeeping. On folio 181, he wrote:

"When you want to know at what interest any amount will double in a given number of years, keep 72 as a rule. Divide 72 by the interest, and the result is the number of years in which the capital will double."

Pacioli did not derive the rule. He recorded the business mathematics that was already in use among Italian merchants. The rule predates logarithms, which were not invented until 1614 by John Napier. The fact that merchants had figured out an approximation for compound doubling a century before logarithms existed shows how demanding Renaissance banking was.

How Accurate Is the Rule of 72?

The Rule of 72 is most accurate for rates between 6% and 10%. Outside that range, the error grows. Here is how it compares to the exact calculation:

Rate	Rule of 72 estimate	Actual years	Difference
2%	36.0	35.0	+1.0
4%	18.0	17.7	+0.3
6%	12.0	11.9	+0.1
8%	9.0	9.0	0.0
10%	7.2	7.3	-0.1
12%	6.0	6.1	-0.1
20%	3.6	3.8	-0.2
50%	1.4	1.7	-0.3

For rates below 6%, the rule slightly overestimates the doubling time. For rates above 10%, it slightly underestimates. A common adjustment: add or subtract 1 from 72 for every 3 percentage points the rate moves away from 8%. At 5%, use 71. At 14%, use 74.

The Rule of 69.3 and Rule of 70 Alternatives

For continuous compounding (which applies to many financial instruments that compound daily), the Rule of 69.3 is more accurate because it is based on ln(2) = 0.693. The Rule of 70 is a compromise that is easy to use and slightly more accurate than 72 at low rates.

Rate	Actual	Rule of 72	Rule of 70	Rule of 69.3
2%	35.0	36.0	35.0	34.7
4%	17.7	18.0	17.5	17.3
6%	11.9	12.0	11.7	11.6
8%	9.0	9.0	8.8	8.7
10%	7.3	7.2	7.0	6.9

For most personal finance decisions, the Rule of 72 is accurate enough. The difference between 12.0 and 11.9 years is not going to change your retirement plan.

2026 Applications with Real Rates

Let us apply the rule to actual 2026 financial rates.

Savings account (FDIC national average, August 2026): 0.38% APY 72 / 0.38 = 189 years to double. At the national average savings rate, $10,000 becomes $20,000 in roughly 189 years. This is why keeping all your savings in a low-yield account is a wealth killer.

12-month CD (FDIC national average, August 2026): 1.71% APY 72 / 1.71 = 42 years to double. Better than the savings account, but still slower than inflation.

High-yield savings (top accounts, August 2026): 4% APY 72 / 4 = 18 years to double. A high-yield account at 4% doubles your money in 18 years. This is the minimum most people should accept for their emergency fund.

U.S. stock market (Vanguard 10-year forecast, 2026): 5 to 6% nominal 72 / 6 = 12 years to double. A diversified U.S. equity portfolio doubles roughly every 12 years based on current forward-looking estimates. The historical average of about 10% would give 7.2 years, but Vanguard's 2026 forecast is more conservative due to high valuations.

Inflation (June 2026 CPI): 3.5% 72 / 3.5 = 20.6 years for prices to double. At 3.5% inflation, what costs $100 today costs $200 in about 21 years. Your investments need to beat 3.5% just to maintain purchasing power.

Use our Compound Interest Calculator and Investment Calculator to see exact projections.

Example 1: Comparing Two Investment Strategies

Jenna is 30 and has $25,000 to invest. She is choosing between a high-yield savings account at 4% and a diversified stock portfolio that she expects will average 7% per year.

High-yield savings: 72 / 4 = 18 years to double Stock portfolio: 72 / 7 = 10.3 years to double

By age 48 (18 years), her savings account doubles to $50,000. By age 40 (10.3 years), her stock portfolio doubles to $50,000.

By age 60 (30 years):

• Savings account: doubled 1.67 times, worth about $81,000
• Stock portfolio: doubled 2.91 times, worth about $190,000

The difference is $109,000. The Rule of 72 makes this comparison instant without a spreadsheet.

Example 2: The Inflation Damage

Carlos has $50,000 sitting in a checking account earning 0.1% interest. Inflation is 3.5% per year.

Real growth rate: 0.1% minus 3.5% = -3.4% per year Rule of 72 on the real rate: 72 / 3.4 = 21.2 years for purchasing power to halve

In about 21 years, his $50,000 will still show as $50,000 in the account, but it will only buy what $25,000 buys today. Inflation is silently taxing his savings. Moving the money to a 4% high-yield account changes the real rate to 0.5% (4% minus 3.5%), which means purchasing power grows slowly instead of shrinking.

Use our Inflation Calculator to see how inflation erodes your money over time.

Common Mistakes to Avoid

1. Applying the rule to simple interest. The Rule of 72 only works for compound growth, where returns are reinvested. If you withdraw your interest each year, the rule does not apply.

2. Using nominal returns without adjusting for inflation. A 10% nominal return at 3.5% inflation is a 6.5% real return. The Rule of 72 on the nominal rate tells you when your account balance doubles. The rule on the real rate tells you when your purchasing power doubles. These are very different questions.

3. Expecting precision at extreme rates. The rule is a mental math shortcut, not a precise formula. At 1% or 50%, the error exceeds 5%. Use the exact formula (ln(2) / ln(1+r)) for precise calculations.

4. Forgetting that the rule assumes constant growth. Real investment returns are volatile. A portfolio that averages 8% does not grow at exactly 8% every year. Sequence risk means the actual doubling time may be longer or shorter than the rule predicts.

External Research and Resources

• Investopedia: What Is the Rule of 72? provides a clear explanation of the formula, its accuracy, and worked examples.
• Stanford University: The Rule of 72 explains the mathematical derivation and the error bounds at different interest rates.
• Vanguard Capital Markets Model Forecasts provides the 2026 forward-looking equity return estimates (4.2% to 6.2% over 10 years) used in the examples above.

People Also Ask

What is the Rule of 72 formula?

The Rule of 72 formula is: Years to double = 72 / annual growth rate (as a percentage). For example, at an 8% annual return, 72 / 8 = 9 years for your money to double.

How accurate is the Rule of 72?

The Rule of 72 is most accurate for growth rates between 6% and 10%. At 8%, it is nearly exact. For rates below 6% it slightly overestimates doubling time, and for rates above 10% it slightly underestimates. The error at most common rates is under 1 year.

What is the difference between the Rule of 72 and the Rule of 69.3?

The Rule of 69.3 is based on the natural logarithm of 2 and is exact for continuous compounding. The Rule of 72 uses 72 instead of 69.3 because it is more divisible and more accurate for annual compounding at typical interest rates. For most purposes, the Rule of 72 is sufficient.

Who invented the Rule of 72?

The earliest known written reference is in Luca Pacioli's Summa de Arithmetica, published in Venice in 1494. Pacioli recorded the rule as business mathematics already in use among Italian merchants. He did not derive it mathematically.

Does the Rule of 72 work for inflation?

Yes. Divide 72 by the inflation rate to estimate how long it takes prices to double. At 3.5% inflation, 72 / 3.5 = 20.6 years. This also tells you how long it takes for the purchasing power of your money to halve if it is not invested.

Related Calculators

• Rule of 72 Calculator - Calculate doubling time for any rate
• Compound Interest Calculator - Calculate compound growth
• Investment Calculator - Project investment growth
• Inflation Calculator - See how inflation erodes purchasing power
• Savings Calculator - Calculate savings growth
• Savings Goal Calculator - Plan to reach a savings target
• ROI Calculator - Calculate return on investment
• CAGR Calculator - Calculate compound annual growth rate
• Future Value Calculator - Calculate future value of an investment
• Credit Card Payoff Calculator - Plan credit card debt payoff