What Is the Rule of 72? Double Your Money Math

The Rule of 72 estimates how long money takes to double: divide 72 by the annual return. At 8% a year, 72 ÷ 8 = 9 years. Below is why it works, how to run it backward, and where it stops being accurate.

What the Rule of 72 Actually Says

The Rule of 72 is a simple approximation for how long it takes an investment to double at a fixed annual rate of return. The formula is:

Years to double ≈ 72 ÷ annual interest rate

You plug in the rate as a whole number—not a decimal—so 6% goes in as 6, not 0.06. The answer comes back in years.

The reason it works comes from the math of compound growth. Doubling means multiplying your money by two, and the natural logarithm of 2 is about 0.693. Multiply that by 100 and you get 69.3, which would technically be the most accurate constant. But 72 is far friendlier to divide by: it splits cleanly into 2, 3, 4, 6, 8, 9, and 12. 72 is also a better fit than 69.3 at typical investment returns, because the rule uses the rate as a simple percentage rather than a continuously compounded one.

Worked Examples at Several Rates

Doubling times at common rates (exact figure with annual compounding in brackets):

At 2%: 72 ÷ 2 = 36 years (35.0)
At 4%: 72 ÷ 4 = 18 years (17.7)
At 6%: 72 ÷ 6 = 12 years (11.9)
At 8%: 72 ÷ 8 = 9 years (9.0)
At 9%: 72 ÷ 9 = 8 years (8.0)
At 12%: 72 ÷ 12 = 6 years (6.1)

Doubling the rate from 6% to 12% halves the doubling time, from 12 years to 6. Over long periods the gap is large: in 36 years, money at 6% doubles three times (8×), while at 9% it doubles four and a half times (about 22×).

Using the Rule in Reverse

The Rule of 72 works just as well backward. Instead of asking "how long to double," you can ask "what rate do I need to double in a set number of years?" Just flip the division:

Required rate ≈ 72 ÷ years to double

Say you want to double a college fund in 10 years. Divide 72 by 10 and you need roughly a 7.2% annual return. Want to double your savings in just 6 years? You'd need 72 ÷ 6 = 12% per year—an aggressive target that signals real risk. Hoping to double in 20 years? A modest 72 ÷ 20 = 3.6% will do it.

This is a quick reality check: if your goal needs a 15% annual return, you are either taking serious risk or expecting too much.

Accuracy and When It Breaks Down

The Rule of 72 is an approximation, and it's most accurate in the middle of the rate spectrum—roughly 6% to 10%. In that band, it's nearly spot-on. At 8%, the rule says 9 years; the precise compound-growth answer is about 9.01 years.

At the extremes, the rule drifts. For very high rates, it underestimates the doubling time: at 24% the rule says 3 years, but the true figure is about 3.22 years, so the rule is slightly optimistic. A common refinement is to add 1 to the 72 for every 3 percentage points above 8%; at 24% that gives 77.3 ÷ 24 ≈ 3.22 years.

For very low rates the rule overestimates instead: at 1% it says 72 years against an exact 69.7, which is why some people use 70 or 69.3 for low rates. Treat 72 as a quick estimate. When precision matters, check it with a compound interest calculator: enter $1, the rate, the estimated years, no monthly contribution and annual compounding, and see whether the result is close to $2.

Using the Rule of 72 for Inflation

The same shortcut works for anything that grows at a steady percentage rate, including prices. Apply the rule to an inflation rate and you learn how fast your purchasing power gets cut in half, because the time for prices to double is the time for a dollar to lose half its value.

At 3% inflation, prices double in about 72 ÷ 3 = 24 years, so a $4 coffee today costs roughly $8 a generation from now. At 6% inflation, prices double in 12 years; at 9%, every 8 years. Savings earning less than the inflation rate lose purchasing power at the same pace.

A Great Shortcut, Not a Substitute

The rule needs no tools, which makes it useful in a conversation or a quick gut-check, and it is good at exposing unrealistic promises.

But it assumes a single, constant rate compounded annually, and the real world rarely cooperates. Actual returns fluctuate year to year, contributions get added over time, fees eat into growth, and taxes take their share. Compounding frequency matters too—monthly or daily compounding doubles money slightly faster than annual. For projecting actual portfolio growth, modeling recurring deposits, or comparing investments, reach for a precise tool. A compound annual growth rate calculator tells you the annual rate an investment actually delivered between a starting and an ending value; for a share position, the stock return calculator does the same from a purchase price and a current price. None of this is a forecast: a rate you plug into the rule is an assumption, not a promise.