How to Calculate the Time for Your Principal to Double

The core is really simple. If you do '72 ÷ annual return (%),' you get the approximate number of years it takes for your principal to double.

For example, at a 8% annual return, 72 ÷ 8 = 9 years. That is, in about 9 years about $740 becomes about $1,480.

At 6% per year it takes 72 ÷ 6 = 12 years, and at 4% per year, 72 ÷ 4 = 18 years. You can see that the higher the return, the sharply shorter the time to double, right?

This is called the 'Rule of 72.' It's an approximation method used for money that grows through compounding (interest earning interest again).

In fact, the mathematically most accurate number is about 69.3. This comes from the natural logarithm ln(2) ≈ 0.693—that is, from the target of 'doubling.'

The rigorous formula is a bit complicated. Doubling time = ln(2) ÷ ln(1 + return). It's hard to solve without a calculator.

So people use 72, which is easy for mental math, instead. 72 divides evenly by 2, 3, 4, 6, 8, 9, and 12, making it very easy to calculate in your head.

How about accuracy? In the 6–10% annual range, the error is well under 2%, so it fits nicely. Especially at 8%, the approximation is 9 years and the actual value is about 9.01 years, an almost perfect match.

The Rule of 72 isn't all-powerful. When returns are very high or very low, the error grows.

For example, at 20% per year, 72 ÷ 20 = 3.6 years, but the exact calculation is about 3.8 years. It comes out a bit short.

Conversely, for low values around 2%, like inflation rates, the 'Rule of 70' (70 ÷ return) fits better. When interest is added daily/continuously, the 'Rule of 69.3' is most accurate.

Still, when approximating investment returns (roughly 5–10%) in everyday life, 72 alone is enough. You don't need to memorize all three.

What the Rule of 72 tells you is a story of 'when the average return continues steadily.' Reality is not that smooth.

For example, the U.S. S&P 500 index has recorded roughly a nominal return of around 10% per year since 1926 when dividends are included (sources range from 10–10.5%). 72 ÷ 10 = about 7 years, meaning it doubles roughly every 7 years.

But this is only an 'average.' In some years it rises greatly, and in others it falls -30% or -40%. There have been periods where it took several years to recover the loss. You must always remember the maximum drawdown and drawdown duration hidden behind the average.

Also, when fees, taxes, and exchange rates eat into the actual return, the time to double lengthens by that much. Conversely, applying this rule to inflation is scary too. If prices rise 3% per year, 72 ÷ 3 = 24 years means the value of money halves in that time.