The Rule of 72: The Time for Money to Double
At a 8% annual return, after how many years does your principal double? You can answer in 9 seconds without a calculator. 72 / 8 = 9 years.
What Is the Rule of 72?
The Rule of 72 is a way to quickly estimate how long it takes for your principal to double in a compounding investment.
Formula: doubling period (years) is approximately 72 / annual return (%)
Examples: 6% per year: 72/6 = 12 years to double 9% per year: 72/9 = 8 years to double 12% per year: 72/12 = 6 years to double 2% per year (a deposit): 72/2 = 36 years to double
This rule is an approximation of the exact formula ln(2)/ln(1+r), and it is very practical, with an error under 1% in the 6-12% return range.
Seeing the Return Gap Through the Rule of 72
You can intuitively see, via the Rule of 72, how big a gap a 1% difference in return creates over the long run.
6% per year: doubles in 12 years -> 8x after 36 years 9% per year: doubles in 8 years -> 8x after 24 years (reaching it 12 years earlier)
That is a 12-year difference in the time to reach the same result. This rule immediately shows why cutting fees by 1% matters over the long run.
Used in reverse: at 3% inflation, the value of money shrinks to half after 72/3 = 24 years.
The Precondition for Compounding: Reinvestment and Time
For the Rule of 72 to work, two conditions are required.
First, you must reinvest your gains rather than spend them. Taking dividends in cash to spend, or withdrawing part of your gains, weakens the compounding effect.
Second, sufficient time is needed. The compounding effect is far more powerful in the later years than the early ones. The amount that grows between year 20 and year 30 is larger than between year 0 and year 20. This is why "starting early" can matter more than "investing a lot."
常见问题
Q. Does the Rule of 72 apply to stocks too?
Yes, it applies to any investment where compound growth occurs. You can use it for stocks, bonds, deposits, and even debt (calculating how long until a debt doubles). Note that since a stock's return is not fixed each year, the Rule of 72 is an estimate assuming a long-term average return.
Q. Are there cases where a number other than 72 is used?
When returns are low (1-3%), 69 or 70 is more accurate. When returns are high (15% or more), 78 is more accurate. 72 is a convenient and accurate approximation for the everyday range of investment returns (4-12%).
📋 结果基于历史数据计算,过去的收益不代表未来的收益。
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