The rule of 72: how long it takes money to double.

The formula

Years to double = 72 / annual rate (in percent)

Examples: at 4% it is 72 / 4 = 18 years. At 8% it is 72 / 8 = 9 years. At 12% it is 6 years. You can flip it round to find the rate you need: to double in 10 years you need about 72 / 10 = 7.2% a year.

The rule assumes interest compounds, meaning each period's growth earns growth too, and that the rate stays steady. If you want the background on compounding itself, read compound interest explained.

Where the 72 comes from

With yearly compounding, money doubles when (1 + r)^t = 2, so the exact time is t = ln(2) / ln(1 + r). For small rates, ln(1 + r) is close to r, and ln(2) is about 0.693. That would give 69.3 / rate, which is the most accurate version for continuous compounding.

People use 72 instead because it is close enough and divides evenly by many numbers: 2, 3, 4, 6, 8, 9 and 12. That makes mental maths easy. Some use 70 or 69.3 for low rates, and 73 or 74 for higher ones, but 72 is the usual compromise for rates around 8%.

Rule of 72 vs the exact answer

This table compares the shortcut with the exact doubling time under yearly compounding. The exact figure is ln(2) / ln(1 + r).

The shortcut is within about a tenth of a year between 6% and 10%, overestimates slightly below that and underestimates above it. For planning, those gaps are small compared with the uncertainty in any real return.

Check it yourself

Do not just trust the shortcut for a decision. Put your numbers into the Compound interest calculator: enter a starting balance, a rate and a time, and read the balance at the end. If you start with 1,000 at 8%, the balance after 9 years is 1,999.00, which is almost exactly double. Try different rates and see where the rule drifts.

The calculator also lets you add monthly contributions, which the rule of 72 cannot handle. The rule only answers one question: how long does a single lump sum take to double?

Useful ways to apply it

• Inflation. At 3% inflation, prices double in roughly 72 / 3 = 24 years (exact: 23.45). That means cash earning nothing loses about half its buying power over that span. See how inflation affects savings.
• Fees. A 1% yearly fee takes a 7% return down to 6%. Doubling time moves from about 10.3 years to 12. Over decades, that gap compounds.
• Debt. A credit card at 24% APR that you do not pay down roughly doubles in about 3 years (exact is 2.92 years with monthly compounding and no payments). See compound interest on debt and the Credit card payoff calculator.
• Comparing options. A 5% account doubles in about 14.4 years, a 7% one in about 10.3. That difference helps frame why rate and time both matter.

Limits of the rule

• Returns are not steady. Investments rise and fall, and a stated average does not mean a smooth path. The rule uses a constant rate.
• Contributions and withdrawals. The rule covers only a lump sum with nothing added or removed.
• Taxes and fees. Use the rate you actually keep, after both.
• Extreme rates. At very low or very high rates the error grows, as the table shows.
• Simple interest. If interest is not compounded, the rule does not apply. At 5% simple interest, money takes 20 years to double, not 14.4.

Treat the answer as a rough guide, and use it to sanity-check a figure from a calculator. For goals with a deadline, the Savings goal calculator turns a target into a monthly amount.

Frequently asked questions

What is the rule of 72?

It is a shortcut: divide 72 by the annual interest or growth rate to estimate the years needed for money to double. At 9% that is about 8 years.

How accurate is the rule of 72?

It is closest for rates of about 6% to 10%, where it is within roughly a tenth of a year. At 2% it is off by a year, and at 24% by about a fifth of a year.

Can I use the rule of 72 for inflation or debt?

Yes, any steadily compounding rate works. At 3% inflation prices roughly double in 24 years, and unpaid debt at 24% APR roughly doubles in about 3 years.

What about the rule of 70 or 69?

Those are variants. 69.3 is more exact for continuous compounding and 70 suits lower rates. 72 is popular because it divides evenly by many common rates.