What the Rule of 72 is
The Rule of 72 is a simple trick. It helps you estimate how long it takes for an investment or price level to double at a fixed interest or growth rate. You do one quick division and get a good answer.
Formula in plain terms:
- Years to double = 72 ÷ interest rate (in percent)
So if you earn 8 percent per year, 72 ÷ 8 = 9 years to double.
Why 72? It is a number that gives a close approximation for typical interest rates people use. It is easy to divide in your head because 72 has many divisors.
How to use it
Two common uses:
-
Find years to double
- Divide 72 by the annual rate in percent.
- Example: 6% rate -> 72 ÷ 6 = 12 years.
-
Find what rate you need
- Divide 72 by the number of years you want to double.
- Example: Double in 10 years -> 72 ÷ 10 = 7.2 percent per year.
That is all you need in ordinary situations.
Quick examples
- 8% return: 72 ÷ 8 = 9 years.
- 5% return: 72 ÷ 5 = 14.4 years.
- 3% inflation: 72 ÷ 3 = 24 years for prices to double.
If you put $10,000 at 8 percent, you will have about $20,000 in 9 years, roughly.
How accurate is it
The Rule of 72 is an approximation. It works best for interest rates between about 6 percent and 10 percent. In that range the error is tiny.
For exact math with annual compounding:
- Exact years = ln(2) ÷ ln(1 + r)
- r is the decimal rate. For 7 percent r = 0.07.
Example accuracy check
- 7%: Rule of 72 gives 72 ÷ 7 = 10.286 years. Exact calculation gives about 10.25 years. The error is very small.
If rates are very low or very high the Rule of 72 gets less accurate. For continuous compounding, use 69.3 instead of 72. That comes from 100 times ln 2, which is about 69.3.
People sometimes use 70 because it is easy to divide by 7, 10, and 14 in the head. That cuts errors a little for some rates.
Limitations to remember
- It assumes a constant rate. If your return changes year to year the rule does not apply.
- It assumes compounding, not extra deposits or withdrawals.
- It ignores taxes, fees, and inflation when you calculate real wealth.
- It is an estimate, not an exact number. Use exact formulas when precision matters.
When to use it
- Quick mental checks when planning long term.
- Comparing rough outcomes of different rates.
- Explaining growth to someone without math tools.
- Checking how inflation or interest affects savings over decades.
Alternatives and exact formulas
If you need exact answers use the logarithm formula:
- Years to double = ln(2) ÷ ln(1 + r)
- r is in decimal form, for example 0.05 for 5 percent.
For continuous compounding:
- Years to double = ln(2) ÷ r
If you are solving for r when years are given:
- r = (2^(1/years)) - 1
Cheat sheet
- Years to double = 72 ÷ percent rate
- Percent rate to double in Y years = 72 ÷ Y
- Use 69.3 if compounding is continuous
- Good accuracy around 6 to 10 percent
Summary
The Rule of 72 is not deep math. It is a practical mental shortcut. It gets you a useful estimate fast. Use it to get a sense of time scales for growth or inflation. For exact planning use the logarithm formulas and include taxes and fees.