How does the rule of 72 calculator work?
The calculator divides 72 by your rate to estimate doubling time, then calculates the exact doubling time with logarithms for comparison. The two usually agree within a few tenths of a year for everyday rates.
If you enter a starting amount and a time horizon, it also compounds the amount once a year at your rate to find the future value. The growth multiple is that future value divided by the starting amount, and the number of doublings is the horizon divided by the rule's doubling time.
Because 2 raised to the number of doublings is only an approximation of the growth multiple, the two will differ slightly. The future value and growth multiple are computed exactly; the doublings figure is a quick mental-math aid.
Years to double ≈ 72 ÷ R Exact doubling time = ln(2) ÷ ln(1 + R/100) Future value = P × (1 + R/100)^t Growth multiple = (1 + R/100)^t Number of doublings = t ÷ (72 ÷ R)
- R
- annual return rate in percent
- P
- starting amount
- t
- time horizon in years
Example: $15,000 at 6% for 30 years
Scenario: Alex invests $15,000 and wants to see how a steady 6% annual return, compounded yearly, would play out over 30 years.
- Rule of 7272 ÷ 6 = 12 years to double
- Exact doubling timeln(2) ÷ ln(1.06) = 0.69315 ÷ 0.05827 = 11.90 years
- Number of doublings30 ÷ 12 = 2.5
- Growth multiple1.06^30 = 5.743491
- Future value$15,000 × 5.743491 = $86,152.37
Alex's $15,000 would grow to about $86,152.37 in 30 years, roughly 5.74 times the starting amount.
Two and a half doublings would suggest a multiple of 2^2.5 = 5.66; the exact multiple is a bit higher because 6% actually doubles money in slightly under 12 years.
When is the rule of 72 handy?
Comparing two rates quickly
A 4% account doubles in about 18 years and a 6% account in about 12. Turning rates into doubling times makes the difference easier to feel.
Seeing what inflation does to cash
At 3% inflation, prices double in about 24 years, so a dollar's buying power halves in that time. That frames why idle cash loses ground.
Understanding a growing debt
An unpaid balance at 24% interest would double in about 3 years if nothing were paid. The rule makes high rates concrete.
Rough retirement projections
Knowing how many doublings fit before retirement gives a fast sense of what early savings could become, before using a detailed calculator.
What mistakes do people make with the rule of 72?
Entering the rate as a decimal
Use 6, not 0.06. Dividing 72 by 0.06 gives 1,200, which is clearly not the doubling time.
Trusting it at extreme rates
At 1% the rule says 72 years against an exact 69.66. At 20% it says 3.6 against 3.80. Check the exact figure for very low or high rates.
Assuming returns are steady
Investment returns vary year to year. The rule describes a constant rate, so it is a planning illustration, not a forecast.
Forgetting taxes, fees and inflation
A 7% return after a 1% fee is 6%, and inflation reduces the real gain further. Use the rate you actually keep for a more honest doubling time.
How accurate is the rule of 72 at different rates?
The rule is an approximation of the exact formula, chosen because 72 divides evenly by many common rates. It is almost exact around 8%, gives slightly too many years below that, and too few above it.
Some people use 69.3 or 70 for low rates or continuous compounding, since ln(2) is about 0.693. For annual compounding at everyday rates, 72 is usually close enough for mental math, and the calculator shows the exact figure either way.
| Annual rate | Rule of 72 (years) | Exact (years) | Rule minus exact |
|---|---|---|---|
| 1% | 72.00 | 69.66 | +2.34 |
| 2% | 36.00 | 35.00 | +1.00 |
| 3% | 24.00 | 23.45 | +0.55 |
| 4% | 18.00 | 17.67 | +0.33 |
| 6% | 12.00 | 11.90 | +0.10 |
| 8% | 9.00 | 9.01 | -0.01 |
| 10% | 7.20 | 7.27 | -0.07 |
| 12% | 6.00 | 6.12 | -0.12 |
| 15% | 4.80 | 4.96 | -0.16 |
| 20% | 3.60 | 3.80 | -0.20 |
Terms used on this page
- Rule of 72
- The Rule of 72 is a mental-math shortcut for estimating how long money takes to double at a fixed compound rate: divide 72 by the annual percentage rate. At 8%, money doubles in about nine years. It works best for rates between roughly 4% and 12% and can also estimate how fast debt or inflation doubles.
- Compound Interest
- Compound interest is interest earned or charged on both the original principal and the interest that has already built up. Each period's interest is added to the balance, so the next period's interest is a little larger. Over long stretches, compounding makes savings grow faster and unpaid debts grow faster too.
- APY (Annual Percentage Yield)
- APY is the amount you actually earn on savings in one year, expressed as a percentage, after accounting for how often interest compounds. A higher compounding frequency pushes APY above the stated interest rate. Banks must disclose APY under federal Truth in Savings rules, so it is the fairest way to compare accounts.
- Inflation
- Inflation is the general rise in prices over time, which reduces how much a dollar can buy. In the US it is most often measured by the Consumer Price Index, published monthly by the Bureau of Labor Statistics. When your savings earn less than inflation, their purchasing power shrinks even though the dollar balance grows.
Rule of 72 Calculator: common questions
How long does it take to double money at 6%?
About 12 years by the rule of 72, since 72 ÷ 6 = 12. The exact figure with annual compounding is about 11.90 years. Either way, $10,000 growing at a steady 6% would be roughly $20,000 after 12 years and roughly $40,000 after 24, before taxes and fees. The small gap between 12 and 11.90 years is typical for rates in this range.
Why is it 72 and not 70?
The true constant for continuous compounding is about 69.3, but 72 has two advantages for mental math: it divides evenly by 2, 3, 4, 6, 8, 9 and 12, and it happens to be more accurate than 69.3 for annual compounding at common rates around 6% to 10%. Some people use 70 for low rates, which is also reasonable.
Is the rule of 72 accurate?
It is very close for typical rates and less so at the extremes. At 8% it gives 9.00 years against an exact 9.01. At 2% it gives 36.00 against 35.00, and at 20% it gives 3.60 against 3.80. The calculator shows the exact figure beside the estimate so you can see the gap.
Can I use the rule of 72 for credit card debt?
Yes. Any balance growing at a steady rate follows the same math. A card balance at 24% APR with no payments and no new charges would roughly double in 72 ÷ 24 = 3 years. Actual card interest compounds monthly and minimum payments reduce the balance, so the real path differs, but the rule shows how quickly high rates build.
How can I use the rule of 72 for inflation?
Divide 72 by the inflation rate to estimate how long it takes prices to double, which is also how long it takes the buying power of a dollar to fall by half. At 3% inflation, that is about 24 years; at 4%, about 18 years. The inflation calculator on this site projects the exact amounts.
What is the number of doublings?
It is the time horizon divided by the doubling time. If money doubles every 12 years and you hold it for 36 years, it doubles three times, ending at roughly eight times the start. Each doubling adds more dollars than the last, which is why the final years of a long horizon contribute so much.
Does the rule of 72 work with monthly compounding?
It still gives a close estimate, but more frequent compounding shortens the true doubling time slightly. The exact figure for monthly compounding uses the monthly rate and counts months instead of years. For most everyday rates, the difference is a few months at most, so the rule remains a useful shortcut.
How do I find the rate needed to double money in a set time?
Flip the rule: divide 72 by the number of years. To double money in 10 years, you would need about 7.2% a year; in 8 years, about 9%. The exact rate for 10 years is about 7.18%, so the reverse shortcut works well too. The exact formula is 2 raised to the power of one divided by the years, minus 1.
Does the rule of 72 apply to savings accounts and CDs?
Yes, as long as you use the account's annual percentage yield, which already reflects compounding. A CD with a 4% APY doubles in about 18 years if interest stays in the account and the rate holds, which a single CD term rarely covers. Taxes on interest would stretch the timeline in a taxable account.
Sources
- Rule of 72 (glossary) — U.S. Securities and Exchange Commission (Investor.gov). Accessed October 17, 2026.
- Compound interest (glossary) — U.S. Securities and Exchange Commission (Investor.gov). Accessed October 17, 2026.
- Compound Interest Calculator — U.S. Securities and Exchange Commission (Investor.gov). Accessed October 17, 2026.
We cite primary sources: regulators, central-bank data and federal agencies. Worked examples on this page are our own calculations, last checked October 17, 2026. See our methodology.