Rule of 72 Formula
Use the Rule of 72 to estimate how long it takes to double your money.
Years to Double = 72 / Interest Rate.
A quick mental math shortcut for investors.
The Formula
The Rule of 72 is a simple shortcut to estimate how many years it takes for an investment to double in value. Just divide 72 by the annual interest rate. No calculator needed.
Variables
| Symbol | Meaning |
|---|---|
| 72 | A constant that makes the approximation work (derived from ln(2) ≈ 0.693) |
| Interest Rate | The annual rate of return (as a whole number, so 6% = 6) |
| Years to Double | Approximate number of years for the investment to double |
Example 1
You invest in a fund earning 8% per year. How long until your money doubles?
Years to Double = 72 / 8
Years to Double = 9 years — At 8% annual return, your investment doubles in about 9 years.
Example 2
Your savings account earns 3% interest. How long to double your savings?
Years to Double = 72 / 3
Years to Double = 24 years — At 3%, it takes much longer to double compared to higher rates.
When to Use It
Use the Rule of 72 when:
- You want a quick mental estimate without a calculator
- Comparing different interest rates to see their long-term impact
- Explaining the power of compound interest in simple terms
- Making back-of-the-envelope financial projections
Note: The Rule of 72 is most accurate for interest rates between 2% and 12%. For very high or very low rates, use the exact compound interest formula instead.
Key Notes
- Rule: years to double ≈ 72 / annual return %: At 8% annual return, money doubles in approximately 72/8 = 9 years. This is a mental math shortcut derived from the exact formula: n = ln(2) / ln(1+r) ≈ 0.693 / r ≈ 69.3/r for small r.
- Why 72 instead of 69.3: 72 is divisible by more integers (2, 3, 4, 6, 8, 9, 12) making mental arithmetic easier. At typical investment rates (6–10%), 72 gives slightly better accuracy than 69.3 due to how compound interest curves behave in that range.
- Reverse use — implied growth rate: If an investment doubled in 6 years, the approximate annual return is 72/6 = 12%. This works for any compounding quantity: population, debt, GDP, anything growing at a constant rate.
- Rule of 72 for inflation: At 4% inflation, purchasing power halves in 72/4 = 18 years. At 2% inflation (central bank target), halving takes about 36 years. This makes the long-term cost of inflation very tangible.
- Accuracy limits: The rule is most accurate between 2% and 20% annual rates. At 100% annual return, the rule predicts 0.72 years; the exact answer is 1 year. For very high rates, use the actual formula n = ln(2)/ln(1+r).