Rule of 72: How Long to Double Your Money
By Tools Star Hub Editorial Team · Published
Quick answer: divide 72 by the annual interest rate to estimate how many years it takes money to double with compound interest. At 7.2% a year, 72 ÷ 7.2 = 10 years. Checking that in the Compound Interest Calculator with 10,000 at 7.2% compounded annually for 10 years gives a final balance of 20,042.31, just over double. The SEC's investor.gov describes the rule the same way: a shortcut for estimating how long an investment takes to double at a fixed annual rate of return.
Knowing doubling time makes rates easier to compare. A 6% return doubles money in about 12 years, a 3% return in about 24. That gap is hard to feel from the percentages alone. The rule also works in reverse for costs: at a fixed rate, debt and inflation-driven prices double on the same timetable.
What is the rule of 72 formula?
Years to double ≈ 72 ÷ annual rate, with the rate written as a whole number, so 8% is 8, not 0.08. You can also rearrange it: the rate needed to double in a set number of years ≈ 72 ÷ years. To double in 9 years you need about 72 ÷ 9 = 8% a year.
The rule assumes the rate stays fixed and returns are reinvested, which is what compound interest means. It does not include deposits, withdrawals, fees or taxes. For those, run the full numbers in a calculator.
How accurate is the rule of 72?
Close for typical rates. Each row below starts with 10,000 compounded annually for the number of years the rule predicts, using the Compound Interest Calculator. A perfect rule would give exactly 20,000 every time.
The estimate is within about 1.5% across 3% to 12%. It is slightly generous at low rates, where the money ends up a little over double, and slightly short at high rates, where 12% for 6 years leaves you just under double.
| Rate | Rule of 72 years | Exact balance | Result |
|---|---|---|---|
| 3% | 24 | 20,327.94 | A bit over double |
| 6% | 12 | 20,121.96 | Just over double |
| 7.2% | 10 | 20,042.31 | Almost exactly double |
| 8% | 9 | 19,990.05 | Just under double |
| 12% | 6 | 19,738.23 | Under double |
Why 72?
The exact doubling time with annual compounding is ln 2 ÷ ln(1 + r), and ln 2 is about 0.693. For small rates, ln(1 + r) is close to r, which gives about 69.3 ÷ rate. Using 72 instead nudges the estimate up to fit the most common rates of roughly 6% to 10% better.
72 is also easy to divide: 2, 3, 4, 6, 8, 9 and 12 go into it evenly. That makes it practical for mental arithmetic, which is the whole point of the shortcut.
Does compounding frequency matter?
Yes, a little. More frequent compounding grows money slightly faster. In the calculator, 10,000 at 6% for 12 years gives 20,121.96 compounded annually but 20,507.51 compounded monthly. The tool offers annual, semiannual, quarterly, monthly and daily compounding.
The rule of 72 does not distinguish between them, so treat it as a rough guide. When frequency matters, for a savings account or loan quote, use the calculator with the frequency in the account terms.
How is this different from simple interest?
Simple interest pays only on the original amount, so money does not grow on its earlier gains. At 7.2% simple interest, 10,000 earns 720 a year and is 17,200 after 10 years, not doubled. Simple interest takes 100 ÷ 7.2, or about 13.9 years, to double.
The rule of 72 only applies to compound growth, where each year's interest earns interest in later years. That is why the gap between simple and compound results widens over time.
Does the rule of 72 work for debt and inflation?
The arithmetic is the same for anything that grows at a fixed compound rate. An unpaid balance growing at 24% a year would double in about 72 ÷ 24 = 3 years if no payments were made. At 3% inflation, prices would double in about 24 years.
For real debts, payments change the picture, so use the Debt Payoff Calculator or Loan Calculator to see payoff time and interest. The rule is a warning sign for how fast high rates compound, not a payoff plan.
When should I not rely on the rule of 72?
It is less accurate at very high rates. At 25% or more the estimate drifts further from the exact answer. It also assumes a steady rate; investment returns vary from year to year, so a doubling time based on an average return is only a rough picture.
The rule ignores contributions. If you add money every month, your balance will double sooner than the rule predicts. A savings goal calculator or compound interest calculator with regular deposits gives a better estimate.
Are there other versions like the rule of 70 or 69?
Yes. Some people use 70, and 69.3 is closer to the exact figure for continuous compounding. They differ only slightly: at 7%, the rule of 70 says 10 years and the rule of 72 says about 10.3 years.
Whichever number you use, check important decisions against the exact compound result rather than the shortcut.
How do I use the rule of 72 to compare two offers?
Turn each rate into a doubling time and compare the years. An account paying 4% doubles in about 18 years, one paying 6% in about 12. Over a long horizon that six-year gap means the faster account can double roughly three times in 36 years while the slower one doubles only twice.
The same trick shows the cost of fees. If an investment returns 7% before a 1% annual fee, the net 6% doubles in about 12 years instead of about 10.3. Small differences in rate become large differences in outcome over decades, which is exactly what the rule makes visible.
How do I find the exact answer in the calculator?
Enter your principal, the annual rate and the compounding frequency in the Compound Interest Calculator, then try the rule's estimate as the number of years. If the balance is a little under double, add a year; if it is well over, take one away. With whole-year terms you will land on the first year the balance passes twice the principal.
The calculator also shows the total interest earned, which at the doubling point is roughly equal to the original principal. That is another quick check that you have found the doubling year.
How do I use the rule of 72 step by step?
- Find the annual rate. Write it as a whole number, such as 6 for 6%.
- Divide 72 by the rate. 72 ÷ 6 = 12 years to double.
- Open the calculator. Enter a principal such as 10,000, the rate and the years from step 2.
- Pick the compounding. Choose annual to match the rule, or the account's real frequency.
- Compare the result. See how close the final balance is to double, for example 20,121.96.
Example
Savings at 3%
72 ÷ 3 = 24 years. The calculator shows 10,000 growing to 20,327.94 over 24 years with annual compounding.
Target rate
To double money in 9 years you need about 72 ÷ 9 = 8%; the exact result is 19,990.05, just under 20,000.
Simple vs compound
At 7.2% for 10 years, compound interest gives 20,042.31 while simple interest gives 17,200.
What should I keep in mind?
Estimate only
The rule assumes a fixed rate with no deposits, fees or taxes.
High rates
Above about 20%, check the exact figure in the calculator.
Limits of the tool
The calculator accepts rates up to 100% and terms up to 100 years.
FAQ
- What is the rule of 72?
- A shortcut: divide 72 by the annual rate to estimate the years needed to double money.
- How long does it take to double money at 6%?
- About 12 years. The exact result for 10,000 compounded annually is 20,121.96 after 12 years.
- How long at 8%?
- About 9 years, giving 19,990.05 on 10,000 with annual compounding.
- Is the rule of 72 accurate?
- It is within about 1.5% for rates from 3% to 12% in the table above.
- Why is it 72 and not 70?
- 72 fits common rates slightly better and divides evenly by many numbers.
- Does it work with monthly compounding?
- Roughly. Monthly compounding doubles a little faster than the rule suggests.
- Does it work for simple interest?
- No. Simple interest takes longer to double, for example about 13.9 years at 7.2%.
- Can I use it for credit card debt?
- It shows how fast an unpaid balance would double, but payments change the real result.
- Who recommends the rule of 72?
- Investor.gov, from the US SEC, describes it as a way to estimate doubling time.
- How do I find the exact doubling time?
- Run the numbers in a compound interest calculator and adjust the years until the balance doubles.
- How do I estimate years to double at 9%?
- Divide 72 by 9 to get about 8 years—a quick approximation of compounding growth.
- Can I reverse the rule to find a needed return?
- Yes—divide 72 by your target years to estimate the annual rate that roughly doubles money.
- Does inflation need a separate rule-of-72 pass?
- You can apply it to inflation to see purchasing-power half-life, separate from investment doubling.
- Why do fees change the doubling story?
- Net return after fees is what matters—run the rule on the rate you actually keep.
- Is the rule useful for irregular contributions?
- It assumes a lump sum compounding; new deposits need a savings schedule calculator instead.
- How far off is it at very high rates?
- Error grows as rates get extreme; use exact compound formulas when precision matters.
- Can I apply it to population or traffic growth?
- Any steady percentage growth can use the same mental math, with the same caveats.
- Does daily compounding break the rule?
- More frequent compounding raises effective yield slightly—adjust the rate or switch to exact math.
- How should students remember 72 vs 69.3?
- 72 is friendlier for mental division; 69.3 ties to the natural-log rule of 70 for continuous growth.
- Where does the rule fail for debt snowballs?
- Minimum payments and changing balances need amortization tools, not a single doubling shortcut.
Check any doubling estimate with the free Compound Interest Calculator.
Plan deposits with the Savings Goal Calculator.
Compare rates correctly in Percentage Points vs Percent.
See growth rates in How to Calculate Percentage Change.