The rule of 72 is a simple mathematical principle that allows you to estimate how long it will take for an investment to double in value at a given annual rate of return. It is commonly used in financial planning and investing as a quick way to gauge the impact of compound interest over time.
The rule of 72 works by taking the number 72 and dividing it by the expected annual rate of return. The result is the approximate number of years it will take for the initial investment to double. For example, if you expect an investment to earn a 6% annual rate of return, dividing 72 by 6 results in 12 years. Therefore, at a 6% rate of return, you can expect your money to double roughly every 12 years.
The rule of 72 provides a shortcut to understand compound interest calculations without having to actually work through the math. While it’s not perfectly precise, it gives a good ballpark estimate to illustrate the power of compounding over long time horizons. This can help investors plan and make better-informed decisions when comparing investment options.
How the Rule of 72 is Calculated
The calculation behind the rule of 72 is simple:
The Formula
Number of Years to Double = 72 / Annual Rate of Return
For example:
| Annual Rate of Return | Calculation | Years to Double |
| 6% | 72 / 6 | 12 years |
| 8% | 72 / 8 | 9 years |
| 10% | 72 / 10 | 7.2 years |
As you can see from the examples above, a higher rate of return results in a faster doubling time. At 6% it takes 12 years for money to double, while at 10% it only takes around 7 years.
The rule of 72 approximation works across all rates of return, but it gets less precise at very high and very low rates. Still, for returns between 3% and 15% it provides a good estimate of compounding impact.
Why the Rule of 72 Works
The math behind the rule of 72 gives insight into why it provides a reasonable estimate for compound interest calculations.
Compounding interest means that interest earned gets added to the principal amount, so that interest in future periods is calculated on an ever-growing balance. For example, say you invest $1,000 at a 6% annual rate. In the first year you would earn $60 interest, making your balance $1,060. In the second year you earn 6% interest on $1,060, which is $63.60. And so on.
The effects of compounding grow exponentially over time. After enough periods, the balance will approximately double from compounding alone.
The rule of 72 works because:
Exponential Growth
At a perfectly consistent growth rate, compound interest follows an exponential curve, doubling at regular intervals. The rule of 72 calculates these approximate intervals.
The Rule of 69
Compounding interest increases a balance by 100% over periods where the interest earned equals the original principal. At a 6% rate, it takes about 12 periods (69/6=11.5). The rule of 72 simplifies this to intervals of 72/interest rate.
Natural Logarithm
The natural log of 2 (0.693) multiplied by the rate of return approximates doubling time. The number 72 is simply a rounded integer simplification.
So while not perfectly precise, the rule of 72 gives a good estimate for doubling time that is easy to calculate mentally.
Using the Rule of 72 for Investing
Here are some ways the rule of 72 can be applied for personal finance and investing:
Compare Investment Returns
Quickly evaluate and compare historical or projected rates of return. For example, compare savings accounts, CDs, stocks, bonds, or real estate investments.
Estimate Time to Double
Get an easy ballpark for when an investment might double in value at a given return. Useful for retirement planning or projecting investment growth.
Savings Goals
Estimate how long it will take to save up to a specific goal amount at a regular savings rate.
Impact of Fees/Inflation
See the long term impact of reduced returns from fees and inflation in cutting the doubling time. Emphasizes importance of minimizing costs.
Illustrate Compounding
Use simple examples to demonstrate the exponential growth from compound interest over time.
Pros and Cons of the Rule of 72
Here are some key pros and cons to keep in mind when using the rule of 72:
Pros
- Provides quick, easy estimates without calculations
- Works for any interest rate in a reasonable range
- Allows easy comparisons across investment options
- Illustrates exponential compounding effect
Cons
- Not perfectly mathematically precise
- Gets less accurate at very high or low rates
- Doesn’t account for variable returns each year
- Only calculates doubling time, not actual future balance
The rule of 72 is best used as a quick approximation alongside more robust compound interest calculations for financial modeling and planning.
Alternatives to the Rule of 72
The rule of 72 provides a simple shortcut for compound interest doubling time. But there are other methods that can give more accuracy or detail:
Compound Interest Calculator
Use an online calculator that can project actual future balances at specific rates of return. Allows modeling of irregular contributions, withdrawals, or return fluctuations.
Spreadsheet Projections
Build a detailed projection model in a spreadsheet to calculate future balances year-by-year, with flexibility to customize assumptions.
Logarithmic Approach
As mentioned earlier, using the natural log of 2 multiplied by rate approximates doubling time more precisely.
Account for Yearly Compounding
For more accuracy, the calculation can factor in that interest compounds yearly, not continuously.
Conclusion
The rule of 72 provides a quick and simple shortcut to estimate how long it will take an investment to double in value. While not perfectly precise, it allows easy approximations and illustrates the impressive power of compound interest. Investors can use the rule of 72 for high-level comparisons, projections, and financial planning estimates. It’s a great education tool to see compounding in action. Combined with more precise methods, the rule of 72 gives useful intuition for investment doubling times.