The Rule of 72: Mental Math for Compound Interest
Calculate precise investment doubling times using our Rule of 72 Calculator, or read on to master the most famous mental math shortcut in finance.
Calculating compound interest usually requires a complex algebraic formula with exponents (FV = PV × (1 + r)^n). This makes it virtually impossible to estimate investment growth in your head during a meeting or a casual conversation.
Fortunately, in 1494, the Italian mathematician Luca Pacioli documented a brilliant mathematical shortcut that allows anyone to estimate the power of compound interest in seconds. It is called the Rule of 72.
What is the Rule of 72?
The Rule of 72 is a simplified formula that tells you exactly how many years it will take for an investment to double in value, based on a fixed annual rate of return.
The Formula: 72 / Interest Rate = Years to Double
(Note: You use the whole number for the interest rate, not the decimal. For 8%, use 8, not 0.08).
Example 1: The Stock Market
You invest $10,000 in an S&P 500 index fund. You assume it will return an average of 8% per year. How long until you have $20,000?
72 / 8 = 9
Your money will double every 9 years.
Example 2: The High-Yield Savings Account
You put $10,000 in a safe bank account that pays 4% interest.
72 / 4 = 18
Your money will double every 18 years.
This simple math clearly demonstrates the massive opportunity cost of keeping long-term money in cash. The stock market investment doubled twice (growing to $40,000) in the exact same time it took the bank account to double once (growing to $20,000).
Using the Rule of 72 in Reverse
You can also algebraically flip the formula to figure out what interest rate you need to achieve a specific financial goal.
The Reverse Formula: 72 / Years = Required Interest Rate
Example: You have $50,000 today. You want to retire in 6 years, and you need that money to double to $100,000 by then. What rate of return do you need to find?
72 / 6 = 12
You must find an investment that yields a massive 12% annual return to hit your goal. (Since this is incredibly risky, the math tells you that your goal of 6 years is likely unrealistic without adding more of your own cash).
The Math Behind the Magic
Why the number 72?
If you use complex calculus and natural logarithms (ln) to solve for the exact doubling time of an investment, the mathematically pure constant is actually 69.3.
However, 69.3 is a terrible number for mental math because it doesn't divide cleanly into anything. The number 72 is chosen because it is highly divisible. It divides perfectly by 2, 3, 4, 6, 8, 9, 12, and 24.
Using 72 provides a remarkably accurate estimate (usually within a few months of the true logarithmic answer) while making the division easy enough for a child to do in their head.
The Rule of 72 and Inflation
The Rule of 72 works for any compounding metric, which means you can use it to calculate the devastating effects of inflation on your purchasing power.
If the national inflation rate is averaging 3%:
72 / 3 = 24
The cost of living will double every 24 years. This means if you stuff $100,000 under your mattress today, it will only have the purchasing power of $50,000 in 24 years.
FAQ
Does the Rule of 72 work for very high interest rates? The Rule of 72 is most accurate for interest rates between 4% and 15%. For extremely high rates (like a 30% return), the estimate starts to become inaccurate. For highly precise calculations, you should use the Rule of 69.3 or a financial calculator.
Don't rely on mental math for your actual retirement planning. Generate exact, day-by-day compounding models using the CalcUnit Rule of 72 Calculator.