The rule of 72: how fast your money doubles

What is the rule of 72?

The rule of 72 is a shortcut for how long money takes to double at a steady rate of growth: divide 72 by the yearly rate. At 6% a year, money doubles in about 72 ÷ 6 = 12 years. At 9%, about 8 years.

It works because of compound interest, which means you earn interest on your past interest as well as on the money you put in. Compounding makes growth speed up over time, and that makes the exact math awkward to do in your head. The rule of 72 trades a little accuracy for an answer you can get in two seconds, at a dinner table or while reading a fund brochure.

It answers questions like: how long until my savings double? How fast is inflation shrinking my money? How quickly does a credit card balance get out of hand? And what rate would I need to double my money by a certain date?

How do you use the rule of 72?

Two ways, depending on what you know. Write the rate as a whole number: 8 for 8%, not 0.08.

To find the years it takes to double

To find the rate you need

Here is the rate you need to double your money in a given time, by the rule and exactly:

It works for anything that grows by a steady percentage, not just savings. Rent that rises 4% a year doubles in about 72 ÷ 4 = 18 years (17.7 exactly). A cost rising 5% a year doubles in about 14.4 years (14.2 exactly). A salary rising 3% a year doubles in about 24.

Rule of 72 calculator

Type a yearly rate. You get the rule of 72 answer next to the exact one, and the table shows both for common rates, along with what $10,000 grows to in 30 years at each.

Why does the rule of 72 work?

Short answer: the exact doubling time is 0.693 ÷ the rate (as a decimal), and 72 is a rounded-up version of 69.3 that corrects for interest being added once a year instead of continuously.

Money growing at rate r for t years becomes (1 + r)^t times as much. To double, that has to equal 2. Solving for t gives the exact formula:

ln 2 is 0.6931. For small rates, ln(1 + r) is close to r itself, so t is close to 0.6931 ÷ r. Multiply top and bottom by 100 and you get 69.3 ÷ R, with R as a whole number. That is the exact rule when interest compounds continuously, every instant.

With interest added once a year, ln(1 + r) is a little smaller than r, so the true doubling time is a little longer. Nudging the top number up from 69.3 makes up for it. The best number to use rises with the rate: about 70 at 2%, 72 at about 7.8%, and 76 at 20%. People settled on 72 because it suits the rates most savers see, and because 72 divides evenly by 1, 2, 3, 4, 6, 8, 9 and 12, which makes the mental math easy.

How accurate is the rule of 72?

Very close between about 4% and 12%, where it is off by under 2%. Below that it slightly overstates the wait; above it, it understates it. Here is every version of the rule against the exact answer for money compounded once a year:

• The rule of 70 is the better pick at low rates, such as inflation or a savings account: at 2% it is exact to the month.
• The rule of 69.3 is exact for continuous compounding, and close for daily compounding. Use it when interest is added very often.
• The rule of 72 is best for yearly compounding at everyday investing rates, which is why it is the one people remember.

How to use the rule of 72 for inflation

Divide 72 by the inflation rate to see how long prices take to double, which is also how long it takes your cash to lose half its buying power. At 3% inflation, that is about 72 ÷ 3 = 24 years (23.45 years exactly).

Inflation also slows the doubling of what your money can buy. At a 7% return with 3% inflation, your balance doubles about every 10 years, but its buying power grows at about 3.9% a year and doubles about every 18 years. Plans made in today’s dollars should use that slower rate.

How fast does debt double?

The rule works the same way on what you owe. A credit card balance at 24% a year doubles in about 72 ÷ 24 = 3 years if nothing is paid. Card interest is added often, not once a year, which makes it slightly faster still.

Other card rates, compounded monthly: at 18%, a balance doubles in about 3.9 years; at 29.99%, in about 2.3 years.

How many times will your money double?

Divide the years you have by the doubling time. At 7% a year, money doubles roughly every ten years (10.24 exactly), so 40 years is about four doublings. Exactly, it is 40 ÷ 10.24 = 3.9 doublings.

Each doubling adds more dollars than all the earlier ones put together. In the example, the first doubling adds $10,000 and the fourth adds $80,000. That is why the years at the end of a career do the most, and why time spent invested is worth so much. Here is the same $10,000 over 40 years at different rates:

One extra doubling doubles the final result, so a single point of rate (from 6% to 7%) adds about half a doubling and about $47,000 here. That is also why a 1% yearly fee matters so much over a working life. We use 7% before inflation as a cautious planning figure for a stock portfolio, not a promise; real returns jump around a lot from year to year, and the future can be worse than the past.

Doubling time in Excel and Google Sheets

You don’t need the shortcut in a spreadsheet; the exact answer is one formula. These work the same in Excel and Google Sheets:

• Years to double at 8%: =NPER(8%, 0, -1, 2) returns 9.006. NPER finds the number of periods for $1 (entered as −1, money going in) to grow to $2 with no extra payments.
• The same thing with logarithms: =LN(2)/LN(1+8%) also returns 9.006.
• Rate needed to double in 6 years: =RRI(6, 1, 2) returns 0.1225, or 12.25% a year. RRI takes the number of periods, the starting value and the ending value.

For monthly compounding, use the monthly rate and divide the answer by 12: =NPER(8%/12, 0, -1, 2)/12 returns 8.69 years.

The rule of 114 and the rule of 144

The same trick works for other multiples. To triple your money, divide 114 (some use 115) by the rate. To quadruple it, divide 144, which is just two doublings: 72 × 2.

All of these are the same idea as the rule of 72: compound growth is faster than it looks, in both directions. For anything with regular deposits or a goal date, a full calculator is better than any shortcut.

Common mistakes with the rule of 72

• Using a decimal. 72 ÷ 0.08 is 900, not 9. Use the rate as a whole number.
• Using a simple average return. For investments that go up and down, use the compounded (annualized) rate, which is lower.
• Forgetting fees, taxes and inflation. Take them off the rate first, or the doubling time is too optimistic.
• Applying it to regular deposits. The rule is for one lump sum. A balance you keep adding to grows faster.
• Trusting it at very high rates. Above about 20%, the rule of 72 understates the wait by 5% or more with yearly compounding.