What is the Rule of 72?

The Rule of 72 is a shortcut for estimating how long an investment takes to double: divide 72 by the annual rate of return, and the result is the approximate number of years. At an 8% return, 72 / 8 gives about 9 years to double your money.

You can do it in your head. There’s no need for a compound interest formula or a spreadsheet to get a usable answer, which makes the rule handy for quick back-of-the-envelope planning.

The Rule of 72 Formula

Years to double = 72 / annual rate of return

Use the whole number for the rate, not the decimal. For an 8% return you divide by 8, not 0.08. You can also run it in reverse: if you want your money to double in a set number of years, divide 72 by that number to find the return you’d need. Doubling in 6 years, for example, requires 72 / 6 = 12% per year.

Rule of 72 Examples

At an 8% return, the rule gives 72 / 8 = 9 years, so $10,000 becomes roughly $20,000 after 9 years, then about $40,000 after 18 years, and $80,000 after 27 years. Each doubling stacks on the last, which is what makes compound growth feel slow at first and dramatic later.

Rate of Return and Years to Double

Small differences in return compound into large differences in doubling time. A portfolio earning 10% doubles in about 7.2 years, compared with 12 years at 6%, which over a multi-decade horizon can mean an extra doubling or two.

Why 72 Works

The exact time to double comes from logarithms. With annual compounding, it’s the natural log of 2 (about 0.693) divided by the natural log of 1 plus the return, so at 8% the exact answer is 0.693 / ln(1.08), or about 9.01 years. For small rates, ln(1 + r) is close to r itself, which simplifies the formula to roughly 69.3 divided by the rate expressed as a percentage. That simpler version is exact only for continuous compounding. With annual compounding it comes up short by about a third of a year at any rate, which is a small share of a long doubling time and a larger share of a short one.

72 gets used instead because it’s a friendlier number to divide in your head. It splits cleanly by 2, 3, 4, 6, 8, 9, and 12, which covers most of the return rates people actually care about. Being a little higher than 69.3 also offsets that gap for annually compounded returns: at 8%, 72 / 8 gives 9 years against an exact 9.01. The estimate runs slightly long at low rates (36 years at 2% against an exact 35.0) and slightly short at high ones (3.6 years at 20% against an exact 3.8).

Limitations to Keep in Mind

The Rule of 72 assumes a single, steady rate of return, which real markets don’t deliver. Actual returns arrive as a jagged sequence of up and down years, so the doubling time you experience can vary even when the long-run average matches your assumption.

• Volatility. The estimate uses one smooth rate. A portfolio that averages 8% through a rough sequence of returns may double on a different timeline than the formula implies.
• Taxes and fees. Doubling your pre-tax balance isn’t the same as doubling your spendable money. Investment fees and taxes on gains both drag on the rate that actually compounds for you.
• Inflation. A nominal doubling doesn’t mean your purchasing power doubled. To estimate how long it takes to double in real terms, run the rule on your real rate of return (your nominal return minus inflation) rather than the nominal interest rate. At a 7% nominal return with 3% inflation, use 4%, so real doubling takes about 18 years, not the roughly 10 years the nominal rate suggests.

For anything beyond a mental estimate, you can project your net worth in ProjectionLab using a historical sequence of returns in place of one fixed rate.

Related Rules of Thumb

• Rule of 70 and Rule of 69.3. Both estimate doubling time more precisely at lower rates. The Rule of 69.3 is exact for continuous compounding, where interest is credited constantly rather than in discrete periods.
• Rule of 114. Divide 114 by the rate to estimate how long it takes to triple your money.
• Rule of 144. Divide 144 by the rate to estimate how long it takes to quadruple (two doublings).

Frequently Asked Questions

How does the Rule of 72 work? Divide 72 by your annual rate of return, and the answer is the approximate number of years for your investment to double. At 9% a year, 72 / 9 = 8 years. It works because it approximates the logarithmic math behind compound growth, using a number (72) that’s easy to divide in your head.

What is the Rule of 72 formula? Years to double = 72 / annual rate of return, using the whole number for the rate (divide by 8 for an 8% return, not 0.08). Run it in reverse to find the return you’d need for a target doubling period: divide 72 by the number of years.

How accurate is the Rule of 72? Close enough for mental math. It lands within a fraction of a year of the true doubling time for returns in the 6% to 10% range, and only loses a little precision at very low or very high rates.

What is the Rule of 72 vs the Rule of 70? Both estimate doubling time, but the Rule of 70 is more accurate at lower rates and the Rule of 72 is easier to compute because 72 divides cleanly by more numbers. With annual compounding, 70 / 2 = 35 years matches the exact figure at a 2% return, while at 8% the Rule of 72’s 9 years is closer than the Rule of 70’s 8.75 to the exact 9.01.