What is the Rule of 72?
The Rule of 72 is a mental shortcut for compound growth: divide 72 by the annual rate in percent and you get the approximate number of years it takes for an amount to double. At 6% a year, 72 / 6 = 12 years. At 9%, 72 / 9 = 8 years. It works the other way too: divide 72 by the number of years you have, and you get the yearly rate needed to double in that time.
The rule applies to anything that compounds at a steady rate: savings interest, an investment growth rate you assume, inflation pushing up prices, or a debt left unpaid. It is an estimate, and this page shows exactly how good an estimate it is at the rate you type.
How do you calculate the Rule of 72, and what is the exact formula?
The estimate is one division: years to double = 72 / rate, with the rate written as a whole number (8 for 8%, not 0.08).
The exact answer comes from solving (1 + r)^t = 2 for t, which gives t = ln 2 / ln(1 + r) for yearly compounding, with r as a decimal. At 8% that is 0.693147 / 0.076961 = 9.006 years. With monthly compounding the exact time is ln 2 / (12 x ln(1 + r / 12)), and with continuous compounding it is simply ln 2 / r.
That last form explains the numbers. ln 2 is 0.693, so with continuous compounding the exact rule is the Rule of 69.3. Yearly compounding is slower than continuous, which stretches the doubling time and pushes the numerator up. Near 8% the numerator that gives the exact answer is 72.05, which is why 72 lands so close there.
Rule of 72, 70 or 69.3: which is more accurate?
It depends on the rate and the compounding. The table below uses yearly compounding. The 69.3 column is shown unrounded because 69.3 divided by these rates comes out exact.
| Rate | Exact years | Rule of 72 | Rule of 70 | Rule of 69.3 |
|---|---|---|---|---|
| 2% | 35.00 | 36 | 35 | 34.65 |
| 4% | 17.67 | 18 | 17.50 | 17.325 |
| 6% | 11.90 | 12 | 11.67 | 11.55 |
| 8% | 9.01 | 9 | 8.75 | 8.6625 |
| 10% | 7.27 | 7.20 | 7 | 6.93 |
| 12% | 6.12 | 6 | 5.83 | 5.775 |
| 20% | 3.80 | 3.60 | 3.50 | 3.465 |
With yearly compounding, 72 is exact at about 7.85% and 70 is exact at about 1.98%. Of the three, the Rule of 70 is closest from about 1% to 4.9%, and the Rule of 72 is closest at every rate above that, even where its own error grows large. The Rule of 69.3 is about a third of a year short at every rate in the table, because it is the continuous-compounding answer applied to yearly growth. Switch the calculator to Continuously and 69.3 becomes almost exact everywhere.
How does the error change as the rate rises?
The rules divide a fixed number by the rate, but the exact numerator drifts upward as the rate climbs. With yearly compounding it is 69.66 at 1%, 72.05 at 8%, 76.04 at 20% and 79.26 at 30%. So at low rates the Rule of 72 overstates the doubling time, and at high rates it understates it.
In percentage terms, the Rule of 72 is 3.4% too long at 1%, within 1% of the exact answer from about 6% to 10%, 5.3% too short at 20% and 9.2% too short at 30%. The chart under the calculator plots this for every whole rate from 1% to 30%, with a marker at your rate.
As a piece of arithmetic, a numerator of 69.3 plus one third of the rate follows the drift closely. At 8% that is 71.97, giving 8.996 years against the exact 9.006. At 20% it is 75.97, giving 3.798 years against 3.802. It appears here only to show the drift, and the calculator gives the exact numerator for your inputs.
Worked examples in dollars, pounds and dirhams
The doubling time does not depend on the amount or the currency, only on the rate. The examples use yearly compounding.
- US dollars. $10,000 at 8% a year: the rule says 9 years. After exactly 9 years the balance is $19,990.05, just short of $20,000, which matches the exact doubling time of 9.006 years.
- Pounds. £5,000 at 6% a year: the rule says 12 years. After 12 years the balance is £10,060.98, already past £10,000, because the exact doubling time is 11.90 years.
- UAE dirhams. AED 20,000 at 9% a year: the rule says 8 years. After 8 years the balance is AED 39,851.25; the exact doubling time is 8.04 years.
- Euros. €15,000 at 4% a year: the rule says 18 years, the exact answer is 17.67 years, and after 18 years the balance is €30,387.25.
How do you find the rate needed to double money in a set time?
Flip the rule: rate = 72 / years. To double in 10 years you need about 7.2% a year. The exact yearly rate is 2^(1/10) - 1 = 7.177%, so the rule is 0.02 percentage points high. Over 5 years the rule gives 14.4% against an exact 14.87%, and over a single year it says 72% when the true answer is plainly 100%.
The Rate to double tab works this out for any period from 1 to 100 years. The rate it returns is arithmetic, not a forecast: it tells you what a goal implies, not whether any investment or account will deliver it.
How do you work out doubling time in Excel or Google Sheets?
The exact doubling time is =LN(2)/LN(1+8%), which returns 9.006. Excel's NPER function gives the same answer when there is no regular payment: =NPER(8%, 0, -1, 2) asks how many periods it takes for 1 paid in to grow to 2, and also returns 9.006. For monthly compounding use =NPER(8%/12, 0, -1, 2), which returns months, and divide by 12.
For the reverse question, Excel's RRI function returns the equivalent rate for growth from a present value to a future value over a number of periods. =RRI(10, 1, 2) returns 0.0718, the 7.18% a year that doubles money in 10 years.
Using the Rule of 72 for inflation, debt, tripling and quadrupling
Inflation. At 3% a year, prices double in about 72 / 3 = 24 years (exactly 23.45), so a sum of money buys half as much. The inflation calculator works with any amount and period.
Debt. An unpaid balance at 24% a year doubles in about 3 years by the rule. Compounded yearly the exact answer is 3.22 years; charged at 2% a month it is 2.92 years.
Tripling and quadrupling. Quadrupling is two doublings, so at 8% it takes about 2 x 9 = 18 years (exactly 18.01). For tripling, the matching continuous-compounding numerator is 100 x ln 3 = 109.9, and with yearly compounding at 8% a numerator of 114 lands close: 14.25 years against an exact 14.27.
Common mistakes, and what the rule leaves out
- Typing the rate as a decimal. 72 / 0.08 is 900, not 9. Use the rate in percent.
- Using it for very high rates. Above about 20% the Rule of 72 is more than 5% short; use the exact answer.
- Ignoring compounding. The same 8% compounded monthly doubles in 8.69 years, not 9.01.
- Treating it as a forecast. The rule assumes one steady rate. Real growth rates vary from year to year and can be negative.
- Forgetting costs. Tax, fees and money taken out all lengthen the doubling time; the rule ignores them.
Glossary
Doubling time: the time for an amount growing at a steady rate to reach twice its size. Numerator: the number divided by the rate, such as 72, 70 or 69.3. Natural logarithm (ln): the logarithm used in the exact formula; ln 2 is 0.693147. Continuous compounding: growth added constantly rather than in steps, the limit of ever more frequent compounding. Percentage point: the plain difference between two rates, so 7.20% minus 7.18% is 0.02 points.
Frequently asked questions
How does the Rule of 72 work?
Divide 72 by the annual rate in percent to estimate how many years it takes money to double. At 8% that is 72 / 8 = 9 years. Divide 72 by a number of years instead to estimate the rate needed to double in that time.
How accurate is the Rule of 72?
With yearly compounding it is within 1% of the exact answer from about 6% to 10%. At 8% it gives 9 years against an exact 9.006. It is 3.4% too long at 1% and 5.3% too short at 20%.
What is the exact formula for doubling time?
For yearly compounding it is ln 2 / ln(1 + r), where r is the rate as a decimal. For continuous compounding it is ln 2 / r, which is where the Rule of 69.3 comes from, since ln 2 is 0.693.
Should I use the Rule of 72, 70 or 69.3?
Each is closest in a different range. With yearly compounding, 70 is closest from about 1% to 4.9% and 72 at higher rates, though 72 is more than 5% short above about 20%. With continuous compounding, 69.3 is almost exact at every rate.
How long does it take to double money at 7%?
The Rule of 72 gives 72 / 7 = 10.29 years. The exact answer with yearly compounding is 10.24 years. With monthly compounding it is a little shorter.
What rate doubles money in 10 years?
The Rule of 72 gives 7.2% a year. The exact rate with yearly compounding is 2^(1/10) - 1 = 7.177%. In Excel, =RRI(10, 1, 2) returns the same 7.18%.
Does the Rule of 72 work for inflation?
Yes. Divide 72 by the inflation rate to estimate how long it takes prices to double, which is also how long it takes money to lose half its buying power. At 3% inflation that is about 24 years; the exact figure is 23.45 years.
Why 72 and not another number?
72 sits close to the exact numerator for yearly compounding at common rates: the exact figure is 72.05 at 8% and crosses 72 at about 7.85%. 72 also divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the mental arithmetic easy.
Does the Rule of 72 work for debt?
It works for any balance that compounds at a steady rate. An unpaid balance at 24% a year doubles in about 3 years by the rule, or 3.22 years exactly with yearly compounding and 2.92 years if interest is charged at 2% a month.
Is there a rule for tripling money?
Divide about 110 to 115 by the rate. The continuous-compounding figure is 100 x ln 3 = 109.9; with yearly compounding at 8%, 114 / 8 gives 14.25 years against an exact 14.27 years.
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Last reviewed 14 November 2026 by the NIFM Academy editorial team. Next review by 14 November 2027.
- Doubling-time arithmetic, exact doubling time ln 2 / ln(1 + r) for yearly compounding, ln 2 / (12 ln(1 + r/12)) monthly, ln 2 / r continuous; reverse rate 2^(1/n) - 1; every figure on this page computed from these formulas. Checked 14 November 2026.
- Microsoft Support, NPER function, NPER(rate, pmt, pv, [fv], [type]): the number of periods for an investment from a constant rate; fv optional, type 0 end or 1 beginning. Checked 14 November 2026.
- Microsoft Support, RRI function, RRI(nper, pv, fv) returns an equivalent interest rate for the growth of an investment. Checked 14 November 2026.