Estimate how many years it takes money to double with the Rule of 72, or the yearly return needed to double in a set time, compared with exact compounding.
Rule of 72 Formula
The Rule of 72 estimates how long it takes a value to double at a fixed annual compound growth rate. Divide 72 by the annual rate expressed as a percentage:
You can rearrange the shortcut to estimate the annual return required to double within a chosen number of years:
The calculator also shows the exact annual-compounding result:
Variables:
- T72 is the estimated doubling time in years
- r is the annual compound growth or interest rate as a percentage
- T is the desired doubling time in years
- ln is the natural logarithm
Choose annual rate or doubling time. The main result is the Rule of 72 estimate; Calculation details compare the Rules of 69.3 and 70 with the annual-compounding formula. An optional starting value only illustrates P and 2P and does not affect the time or rate. Money uses USD; prices and other values retain the entered units.
Both calculations assume steady positive growth with no deposits, withdrawals, taxes, fees or changing rate. The comparison is exact for the fixed annual-compound model, not a forecast of investment performance. Fractional years interpolate that model; actual interest-credit dates may differ. Choosing price growth models inflation itself and does not inflation-adjust an investment return.
Rule of 72 Doubling-Time Table
This table compares the Rule of 72 estimate with the exact doubling time for annual compounding.
| Annual rate | Rule of 72 | Exact time | Shortcut difference |
|---|---|---|---|
| 2% | 36.0 years | 35.0 years | 1.0 year longer |
| 4% | 18.0 years | 17.7 years | 0.3 year longer |
| 6% | 12.0 years | 11.9 years | 0.1 year longer |
| 8% | 9.0 years | 9.0 years | Nearly exact |
| 10% | 7.2 years | 7.3 years | 0.1 year shorter |
| 12% | 6.0 years | 6.1 years | 0.1 year shorter |
| 15% | 4.8 years | 5.0 years | 0.2 year shorter |
Example Problems
Example 1: Estimate doubling time from a return.
An account grows at 8% per year. Divide 72 by 8:
T = 72 / 8 = 9 years. The exact annual-compounding result is about 9.01 years, so the shortcut is exceptionally close at this rate.
Example 2: Estimate the return needed to double.
You want a balance to double in 12 years. Divide 72 by 12:
r = 72 / 12 = 6% per year. Solving the exact compound formula requires about 5.95% annually.
Frequently Asked Questions
Why does the Rule of 72 work?
Doubling time is based on logarithms. For moderate interest rates, the exact expression can be approximated by a simple constant divided by the percentage rate. The number 72 is convenient because it has many divisors and gives a close estimate across common long-term rates.
When is the Rule of 72 most accurate?
It is especially accurate around 6% to 10% annual growth and remains useful across a wider range as a quick estimate. At very low or very high rates, use the exact result shown by the calculator.
Can I use the Rule of 72 for inflation or debt?
Yes. It can estimate how long prices may take to double at a steady inflation rate or how quickly a debt balance could double when unpaid interest compounds. Real-world rates can change, so treat the answer as a scenario rather than a guarantee.
