What is the rule of 72?

The rule of 72 is a mental shortcut for doubling time: divide 72 by your annual interest rate and the result is the approximate number of years it takes money to double. At 7 percent, money doubles in about 10.3 years; at 10 percent, about 7.2 years.

How accurate is the rule of 72?

Very accurate for rates between about 5 and 10 percent. At 7 percent it estimates 10.29 years versus the exact 10.24 years. At 5 percent it gives 14.40 versus the exact 14.21, and at 10 percent it gives 7.20 versus the exact 7.27.

What is the rule of 70?

The rule of 70 is a variant that is slightly more accurate for lower interest rates, because 69.3 is the mathematical constant behind the shortcut and 70 is closer to it than 72. In practice the two rules differ by a fraction of a year.

Why is the number 72 used?

72 is divisible by many common rates, including 3, 4, 6, 8, 9, and 12, so the division comes out clean. It also happens to land near the exact answer for the rates most savers and investors care about.

Can the rule of 72 work monthly?

Yes, if you use the rate per period and read the answer in periods. At 1 percent per month, money doubles in about 72 months. The exact answer is 69.66 months, so the shortcut is close but slightly overstates the time at monthly granularity.

Rule of 72: Double Your Money Faster (Calculator + Examples)

The rule of 72 turns doubling time into one division you can do in your head. Here is the shortcut, the math behind it, and exactly how close it lands.

The rule of 72 estimates how long money takes to double: divide 72 by the annual interest rate. At 7 percent, savings double in about 10.3 years (72 / 7 = 10.29). At 10 percent, about 7.2 years. At 5 percent, about 14.4 years. The rule is accurate to within a few months for rates between 5 and 10 percent, and works for any compounding investment.

The one formula

Years to double = 72 / annual interest rate. That is the whole rule. Earning 8 percent? Your money doubles in 72 / 8 = 9 years. Earning 6 percent? 72 / 6 = 12 years. Earning 12 percent? 72 / 12 = 6 years. The inputs you need are exactly one number, and you can run the division without touching a calculator.

The table below shows what the rule predicts for the rates people ask about most, alongside the exact answer from the doubling formula ln(2) / ln(1 + rate). Every value in the exact column was computed directly, so you can see for yourself how little the shortcut gives up.

Rate	Rule of 72	Exact doubling time
3%	24.00 years	23.45 years
5%	14.40 years	14.21 years
6%	12.00 years	11.90 years
7%	10.29 years	10.24 years
8%	9.00 years	9.01 years
10%	7.20 years	7.27 years
12%	6.00 years	6.12 years

Across the whole useful range, the rule misses by no more than about two months. That is why finance professionals still teach it: the answer arrives in seconds and the error is smaller than the uncertainty in the rate itself.

Worked example: $5,000 at 8 percent

Put $5,000 in an account earning 8 percent. The rule says it doubles to $10,000 in 72 / 8 = 9 years. Now project the full 30-year run with the rule alone: 30 years holds 30 / 9 = 3.33 doublings, so $5,000 x 2^3.33 = $50,397. The exact future value is $5,000 x 1.08^30 = $50,313. The rule of 72 nails a 30-year projection within $84, which is close enough to settle any "should I bother?" question.

Doubling more than once: use 144

Two doublings make money quadruple, so the shortcut scales cleanly: divide 144 (2 x 72) by the rate to estimate quadrupling time. At 7 percent, 144 / 7 = 20.57 years. The exact answer is ln(4) / ln(1.07) = 20.49 years. Same pattern, same accuracy. There is also a rule of 114 for tripling: at 7 percent, 114 / 7 = 16.29 years against the exact ln(3) / ln(1.07) = 16.24 years. You do not need to memorize all three constants. Just remember 72 for doubling and stack it: two doublings for quadrupling, and so on.

Why 72, and not 70 or 100?

The true constant in the doubling formula is about 69.3, which is why a "rule of 70" also floats around. The number 72 won because of arithmetic convenience: it divides cleanly by 3, 4, 6, 8, 9, and 12, which are the rates people actually estimate with. For rates under 6 percent, 70 is technically closer to the truth, and for the 6 to 10 percent range, 72 edges ahead. In practice the two rules differ by a fraction of a year, so use whichever divides cleanly and move on.

Where the rule breaks down

At very high rates, compounding accelerates faster than the linear shortcut assumes. At 20 percent, the rule says 3.6 years to double while the exact answer is 3.80 years: still close. At 50 percent, the rule says 1.44 years and the exact answer is 1.71 years: the gap is growing. By 100 percent, the rule claims 0.72 years but money truly doubles in 1 year at 100 percent interest. Below 20 percent, you are safe. Above that, use the exact formula or a calculator.

The rule also assumes compounding. For simple interest, where interest is paid out instead of reinvested, doubling takes exactly 100 / rate years, not 72 / rate. At 8 percent simple interest, money doubles in 12.5 years; at 8 percent compounded, in 9 years. That 3.5-year gap is compounding doing its work.

The rule of 72 as a planning tool

The real value of the rule is comparison speed. A savings account at 4 percent doubles money in 18 years. An investment at 7 percent does it in 10.3. That 7.7-year gap, visible in two seconds of mental math, is often what convinces someone to move idle cash. Run the same check on fees: a 1 percent fee drag that drops your return from 7 to 6 percent stretches doubling from 10.3 to 12 years. Fees and rate gaps compound too, and the rule of 72 shows the cost instantly.

Try the full calculator

The rule of 72 gives you doubling time, but it ignores monthly contributions, and contributions are where most real savings plans live. A monthly deposit changes the math completely: $500 a month at 7 percent becomes $86,542 in 10 years, and the rule of 72 alone would never tell you that. For the full picture with your own numbers, run them through the free future value calculator below.