The Rule of 72: How to Estimate How Long Your Money Takes to Double, With Worked Examples

One division problem you can do in your head tells you how fast savings grow, how fast inflation eats cash and how fast unpaid debt snowballs.

What is the Rule of 72?

The Rule of 72 is a mental-math shortcut for compound growth. Divide 72 by an annual growth rate, written as a whole number, and the answer is roughly how many years it takes money to double at that rate. At 6% a year, 72 divided by 6 is 12, so money doubles in about 12 years.

That is the whole rule. It works because of compound interest, which the Consumer Financial Protection Bureau describes as earning interest "on the money you've saved and on the interest you earn along the way." Its own example shows the effect: $1,000 at 5% compounded once a year becomes $1,050 after one year and $1,102.50 after two, because the second year's interest is paid on $1,050, not $1,000. You can read the basics in our guide to how compound interest works.

The rule matters because growth that compounds is hard to picture. Most people can tell you what 6% of $10,000 is, but few can say off the top of their head what $10,000 becomes after 36 years at 6%. The Rule of 72 turns that into a simple chain: 36 years is three 12-year doubling periods, so $10,000 becomes about $20,000, then $40,000, then $80,000. The exact answer, $81,473, is close enough that the shortcut tells you the right story.

How do you use it? Three quick worked examples

The rule runs in two directions. You can start with a rate and find the years, or start with a goal in years and find the rate you would need.

Example 1, rate to years. Say a savings account pays 4.5% a year. Divide 72 by 4.5 and you get 16. Money left alone at that rate would take about 16 years to double. The exact figure is about 15.7 years, so the estimate is within a few months.

Example 2, years to rate. Say you want a sum of money to double in 10 years. Divide 72 by 10 and you get 7.2, so you would need about 7.2% a year. The exact rate is about 7.18%. Reversing the rule like this is a fast way to test whether a goal is realistic. Doubling in six years needs about 12% a year (72 divided by 6), which is a much higher rate than you might expect.

Example 3, counting doublings. At 8% a year, money doubles about every 9 years (72 divided by 8). Over 36 years that is four doublings: $10,000 becomes about $20,000, $40,000, $80,000 and then $160,000. The exact result at 8% compounded yearly is $159,682. Notice how much the extra two percentage points matter. At 6% the same $10,000 reached about $81,000 in 36 years. At 8% it roughly doubles that, because it fits in one more doubling.

These are illustrations with steady, made-up rates. Real investments do not grow at a fixed rate every year, and returns are never promised. The rule describes the math of compounding, not what any account or fund will actually earn.

How accurate is the Rule of 72?

The shortcut is an estimate. The exact doubling time comes from logarithms, which is why calculators exist. We ran the exact math for yearly compounding so you can see where the rule is close and where it drifts.

• At 2%: the rule says 36 years; the exact answer is 35.0.
• At 4%: the rule says 18 years; the exact answer is 17.7.
• At 6%: the rule says 12 years; the exact answer is 11.9.
• At 8%: the rule says 9 years; the exact answer is 9.0.
• At 10%: the rule says 7.2 years; the exact answer is 7.3.
• At 12%: the rule says 6 years; the exact answer is 6.1.
• At 20%: the rule says 3.6 years; the exact answer is 3.8.

The pattern is easy to remember. Between roughly 6% and 10%, the rule is almost spot on. At low rates it slightly overstates the time, and at high rates it slightly understates it. At 1%, the rule says 72 years while the exact answer is about 69.7. At 30%, the rule says 2.4 years while the exact answer is about 2.6. For everyday decisions those gaps rarely change the conclusion.

Some people use 69 or 70 instead of 72 for low rates or for interest that compounds daily or continuously. The number 72 stays popular because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which makes the mental math easy. If you need a precise figure, the SEC's Investor.gov site has a free compound interest calculator that lets you set the rate, the years and how often interest compounds.

The rule also assumes the rate holds steady and that nothing is added or withdrawn. Regular deposits make a balance grow faster than the rule suggests, while withdrawals, taxes and fees slow it down.

Using the rule on inflation, fees and debt

The same division works for anything that grows at a percentage rate, including things that work against you. This is where the Rule of 72 earns its place as a planning tool.

Inflation. If prices rise 3% a year, they double in about 24 years (72 divided by 3). Put another way, cash that earns nothing loses about half its buying power over that stretch. The exact math says $1 buys about 49 cents' worth of today's goods after 24 years of 3% inflation. You can check the actual inflation rate in the Bureau of Labor Statistics' Consumer Price Index reports, since it changes over time. This is why some savers compare an account's interest rate with inflation, not just with zero. If your savings rate is below inflation, your money is shrinking in real terms even as the balance rises.

Fees. Imagine two otherwise identical investments, one growing 8% a year and the other 7% because of a 1-percentage-point yearly fee. At 8%, $10,000 doubles about every 9 years. At 7%, it doubles about every 10.3 years. Over 36 years, that difference adds up: the exact results are about $159,700 versus $114,200, a gap of roughly $45,000 on a single $10,000 deposit. A fee that sounds small takes away part of a doubling over a long time horizon, which is why it can pay to compare expense ratios when choosing funds.

Debt. A credit card balance charging 24% APR would roughly double in about 3 years if no payments were made (72 divided by 24). Card interest usually compounds more often than yearly, which makes it a little faster. At 2% a month, the exact figure is about 2.9 years. Nobody plans to ignore a card for three years, but the math shows why minimum payments can leave a balance shrinking very slowly.

Low-rate savings. On the other end, money earning 0.5% a year takes about 144 years to double by the rule (about 139 years exactly). Comparing that with an account paying several percentage points more shows how much the rate on idle cash can matter. Our guide to building a CD ladder walks through one way some savers lock in rates for set periods.

A 5-step way to use the Rule of 72 on your own numbers

You do not need a spreadsheet to put the rule to work. A pencil and a few minutes is enough.

1. Write down the rate. Use the annual rate on the account, loan or assumption you want to test, such as 4% for a savings account or 22% for a card.
2. Divide 72 by the rate. That gives the approximate years to double. Write it next to the rate.
3. Count the doublings in your time frame. Divide the number of years you care about by the doubling time. Fifteen years at a 5-year doubling time is three doublings.
4. Multiply your starting amount by 2 for each doubling. Three doublings means 2 x 2 x 2, or 8 times the starting amount.
5. Check the answer with a calculator for big decisions. The rule is for quick comparisons. Before you act on a number, run it through an exact calculator and remember that taxes, fees, deposits and changing rates all affect real results.

A second shortcut, sometimes called the Rule of 115, estimates how long money takes to triple. At 8%, 115 divided by 8 is about 14.4 years, and the exact answer is about 14.3. It is less well known but works the same way.

Common mistakes with the rule

The most common mistake is plugging in a rate as a decimal. The rule needs 6, not 0.06. Dividing 72 by 0.06 gives 1,200, which is clearly wrong.

The second is treating an assumed rate as a promise. Stock and bond returns vary from year to year, and past averages do not guarantee future ones. The rule can show what a steady 7% would do, but it cannot tell you whether you will get 7%.

The third is forgetting about the other side of the ledger. A balance can double on paper while inflation also doubles prices, leaving buying power where it started. Comparing your rate with inflation, and thinking about fees and taxes, gives a more honest picture. If you are planning for retirement, our explainer on the 4% rule covers a different shortcut used for withdrawals.