What Is the Rule of 72? Doubling Time in Plain English

The Rule of 72 is a shortcut for how long a balance takes to double at a constant annual rate. Divide 72 by the rate in percent. At 8% a year, 72 ÷ 8 is 9 years.

Key takeaways

• Years to double ≈ 72 ÷ annual return in percent.
• The exact compound-interest time is the natural log of 2 ÷ the natural log of (1 + the rate).
• At 8%, the shortcut is 9 years and the exact time is about 9.01 years.
• The shortcut is closest near 8%. It drifts as the rate moves away from that neighborhood.

The formula

Years to double ≈ 72 ÷ annual return in percent

Exact years = natural log of 2 ÷ natural log of (1 + annual rate)

The rate stays constant, and the balance compounds once a year. No contributions are added along the way.

A worked example

Take an 8% annual return and a $10,000 start.

• Rule of 72: 72 ÷ 8 = 9 years.
• Exact doubling time ≈ 9.01 years.
• The $10,000 becomes about $20,000 after 9.01 years, $40,000 after 18.01 years, and $80,000 after 27.02 years.

Each step applies the exact doubling time again. The Rule of 72 calculator prints the shortcut and the exact years side by side.

What the Rule of 72 tells you

It turns a rate into a span of years you can check in your head. Use the exact line when the rate is far from 8%, or when you want the milestones on a starting amount.

What the Rule of 72 leaves out

Contributions, withdrawals, taxes, and a rate that changes are all outside the shortcut. It also describes a smooth path. A balance that doubles over nine bumpy years still doubled. The rule does not show the bumps.

If you want the balance after a contribution schedule, use compound growth. A company page such as Apple shows today's price. It does not show how long that price takes to double.

For general education only. Nothing here is investment advice.