The Rule of 72: Quick Math for Doubling Money

The Rule of 72 is a simple mental-math shortcut for estimating how long an investment takes to double at a given annual return. You don’t need a calculator or a spreadsheet — just one quick division:

Years to double ≈ 72 / annual return %

The formula

Enter the annual return as a whole percentage, not a decimal. At an 8% annual return, divide 72 by 8 — not by 0.08:

72 ÷ 8 = 9 years

Dividing by 0.08 is the most common mistake, and it gives a nonsensical 900. Keep the return as the plain number you’d say out loud (“eight percent” → 8).

Examples in seconds

• At 8%: 72 ÷ 8 = 9 years to double
• At 6%: 72 ÷ 6 = 12 years
• At 3%: 72 ÷ 3 = 24 years
• At 12%: 72 ÷ 12 = 6 years

No calculator, no spreadsheet — just division you can do in your head.

How it works with real money

Suppose you invest $10,000 and earn an average annual return of 8%. Applying the rule:

72 ÷ 8 = 9 years

So the Rule of 72 estimates that the investment would take about 9 years to double from $10,000 to roughly $20,000. This is an illustration based on a constant annual growth rate — a real investment’s path will vary from year to year.

How the exact calculation works

The Rule of 72 approximates a precise compound-growth relationship. The exact doubling time is:

Exact doubling time = ln(2) / ln(1 + r)

Here r is the annual return expressed as a decimal, and the formula gives the exact number of years for a constant rate to double a balance. At 8% (r = 0.08):

ln(2) / ln(1.08) ≈ 9.01 years

Compare the two approaches at 8%:

• Rule of 72: 72 ÷ 8 = 9 years
• Exact: ≈ 9.01 years

At 8%, the shortcut is extremely close to the exact result: 9 years versus about 9.01 years.

Why is it called the Rule of 72?

The exact relationship is t = ln(2) / ln(1 + r). For moderate rates, ln(1 + r) is close to r, giving approximately 0.693 / r when r is expressed as a decimal. If the rate is written as a percentage number, this becomes roughly 69.3 / return percentage. So the “true” constant is nearer to 69.3 than 72.

The rule uses 72 anyway because it’s far friendlier for mental arithmetic — 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12, which happen to be common return rates. It trades a little precision for a lot of convenience.

How accurate is it?

The Rule of 72 is a shortcut, not an exact calculation. It works well for many moderate annual rates, but the difference from the exact logarithmic calculation varies with the rate. When precision matters, use the exact formula or a Rule of 72 Calculator.

Annual return	Rule of 72	Exact doubling time
3%	24.00 years	≈ 23.45 years
6%	12.00 years	≈ 11.90 years
8%	9.00 years	≈ 9.01 years
10%	7.20 years	≈ 7.27 years
12%	6.00 years	≈ 6.12 years

The rule is most accurate near the middle of this range and drifts slightly at the extremes.

It works in both directions

The rule also shows how inflation erodes value. At a constant 3% inflation rate, the general price level roughly doubles in about 24 years, meaning the purchasing power of a fixed amount of money falls by about half over that stretch. That’s an illustration assuming a constant rate — individual prices don’t all rise at exactly the same pace. For more, see How Inflation Eats Into Your Real Returns.

You can also flip the formula. To find the return needed to double in a target number of years, divide 72 by the years instead:

Required annual return ≈ 72 / years

To double in 12 years, that’s 72 ÷ 12 ≈ 6%.

When the Rule of 72 can mislead

The estimate rests on simplifying assumptions, so keep its limits in mind:

• It assumes a constant annual growth rate.
• It’s an approximation, not an exact calculation.
• Real investment returns fluctuate from year to year.
• It doesn’t account for taxes or investment fees.
• Regular contributions and withdrawals change the actual path of an account.
• A historical or assumed average return doesn’t guarantee an investment will double on the estimated schedule.

In short: the Rule of 72 estimates doubling time under a simplified constant-rate assumption. It does not predict when a real portfolio will actually double.

What if I keep adding money?

The Rule of 72 is built to estimate how long a single balance takes to double at a constant rate. Once you add regular contributions or take withdrawals, the time for the account balance to double depends on several moving parts:

• your starting balance
• how much you contribute
• how often you contribute
• any withdrawals
• the investment return

For that kind of projection, model the full picture with the Compound Interest Calculator or the Investment Return Calculator.

Rule of 72 vs. Rule of 70

You’ll sometimes see the Rule of 70 or even 69.3 used instead:

• The Rule of 72 is popular because it’s the easiest to calculate mentally.
• The Rule of 70 is another common approximation, often used for growth and inflation rates.
• 69.3 is closest to the mathematical constant behind the approximation (from ln(2) × 100).

All three estimate the same thing; 72 simply wins on convenience thanks to its many divisors.

Key takeaways

• The Rule of 72 estimates how long money takes to double.
• Divide 72 by the annual return percentage (entered as a whole number).
• At 8%, the estimate is about 9 years.
• It can also approximate how inflation reduces purchasing power.
• It’s a shortcut, not an exact calculation.
• Actual investment returns vary over time.
• Use the exact formula, ln(2) ÷ ln(1 + r), when precision matters.

Methodology

Rule of 72 examples use the standard approximation 72 ÷ annual return. Exact comparisons use ln(2) ÷ ln(1 + r), where r is the annual return expressed as a decimal. Examples assume a constant annual rate and are illustrative rather than forecasts. For more on the limits of these estimates, see our Disclaimer.