The Rule of 72: How Long to Double Your Money

The rule of 72 is a shortcut for working out how long it takes money to double at a fixed rate of growth: divide 72 by the annual percentage rate. At 6% a year, money doubles in about 72 ÷ 6 = 12 years. It works for savings, investments, debts and even inflation, and you can do it in your head.

The rule of 72 formula

Years to double ≈ 72 ÷ annual interest rate (%)

You can also run it backwards to find the rate you need: rate ≈ 72 ÷ years. To double your money in 9 years, you need roughly 72 ÷ 9 = 8% a year.

The rate is entered as a plain number, so 8% is 8, not 0.08.

How accurate is it?

The exact answer for annual compounding is ln(2) ÷ ln(1 + r). Here is how the shortcut compares:

Annual rate	Rule of 72	Exact (yearly compounding)	Rule of 70
2%	36.0 years	35.0 years	35.0 years
4%	18.0 years	17.7 years	17.5 years
6%	12.0 years	11.9 years	11.7 years
8%	9.0 years	9.0 years	8.8 years
10%	7.2 years	7.3 years	7.0 years
12%	6.0 years	6.1 years	5.8 years

Between about 6% and 10%, the range most people use it for, the rule of 72 is within a few months of the exact answer. That is why 72 is the popular choice: it is easy to divide by 2, 3, 4, 6, 8, 9 and 12, and it happens to be most accurate around 8%.

Rule of 72 vs rule of 70 and 69.3

The “true” constant for continuous compounding is 69.3 (100 × ln 2). Some people use 70 for low rates, such as inflation or GDP growth, where it is slightly more accurate, and 72 for typical investment returns. For quick decisions the difference rarely matters; for a precise figure, use the compound interest calculator, which shows the exact doubling time under every result.

How long to double money: four practical uses

1. Long-term investing

At an average 8% return, money doubles about every 9 years. Over 36 years that is four doublings: $10,000 becomes roughly $160,000. The exact figure at 8% compounded yearly is $159,682, very close to the shortcut. It also shows why time matters so much: the last doubling adds as much as the first three put together.

2. Comparing savings accounts

An account paying 2% doubles your money in about 36 years. One paying 4% does it in 18. Small differences in rate become large differences in outcome over decades.

3. Understanding debt

The rule works for money you owe, too. A credit card balance at 24% doubles in about 3 years if nothing is paid off. With monthly compounding the exact figure is just under 3 years (2.9). That is a useful way to show why high-interest debt should usually be paid before investing.

4. Inflation

Divide 72 by the inflation rate to see how long it takes prices to double, or the value of cash to halve. At 3% inflation, prices double in about 24 years (exactly 23.4). Money left in an account paying less than inflation loses buying power even though the balance grows.

Where the rule of 72 goes wrong

• Very high or very low rates. At 20%+ or under 2% the error grows. Use an exact calculation instead.
• Returns that change every year. Investments do not grow at a steady rate. The rule tells you what happens at an average rate, not what will happen in a bad decade.
• Regular contributions. The rule is for a single sum. If you add money every month, your balance grows faster than it suggests. The compound interest calculator handles monthly contributions.
• Fees and tax. Use your return after fees and tax. A 7% return with a 1% annual fee doubles in 12 years, not 10.

Why the rule of 72 works

Money growing at rate r doubles when (1 + r)ⁿ = 2, so n = ln 2 ÷ ln(1 + r). For small r, ln(1 + r) is close to r, which gives n ≈ 0.693 ÷ r. Multiply top and bottom by 100 and you get 69.3 ÷ rate%. Because ln(1 + r) is a little smaller than r at typical rates, nudging the constant up to 72 compensates and makes the shortcut more accurate in the 6–10% range.

Frequently asked questions

What is the rule of 72 in simple terms?

Divide 72 by the yearly interest rate to estimate how many years it takes to double your money. At 9% a year it takes about 8 years.

Is the rule of 72 accurate?

It is within a few months of the exact answer for rates between about 6% and 10%. It becomes less accurate at very high or very low rates.

Does the rule of 72 work for monthly compounding?

Yes, approximately. Monthly compounding doubles money slightly faster, so the true figure is a little shorter than the rule suggests; at 7% it is about 9.9 years rather than 10.3.

Can I use the rule of 72 for inflation?

Yes. Divide 72 by the inflation rate to see how long it takes prices to double. At 3% inflation that is about 24 years.

Sources

• Investor.gov (US SEC): Rule of 72
• MoneyHelper: Interest rates explained