About the Rule of 72 Calculator
The Rule of 72 is a mental-math shortcut: divide 72 by an annual interest rate and you get roughly how many years it takes an investment to double. At 6% money doubles in about 12 years; at 9% in about 8. This calculator gives you that quick estimate alongside the exact doubling time from the compound-interest formula, so you can see how close the shortcut really is.
It is useful for savers comparing a savings account with an index fund, for anyone checking whether a promised return is realistic, and for understanding how inflation halves purchasing power (at 3% inflation, prices double in about 24 years). You can also flip the question and find the rate you would need to double your money in a target number of years.
The exact figure assumes a steady rate and that all growth is reinvested. Pick the compounding frequency that matches your account — annual for most investment return figures, monthly or daily for many savings accounts. Real investment returns vary year to year, so treat results as estimates.
With the default inputs, the rule of 72 estimate is 10.3 years. Change any value above to recalculate instantly.
How to use the rule of 72 calculator
- 1Enter the annual interest rate or expected return.
- 2Optionally enter a starting amount to see the dollar value after doubling.
- 3Choose how often interest compounds for the exact figure.
- 4Compare the Rule of 72 estimate with the exact doubling time.
- 5Enter a target number of years to see the rate you would need to double in that time.
Formula and method
The Rule of 72 divides 72 by the annual rate written as a whole number (R = 8 for 8%). It works because ln(2) ≈ 0.693, and for typical rates ln(1 + r) is slightly less than r, so a numerator a little above 69.3 compensates; 72 does that at ordinary rates and divides evenly by 2, 3, 4, 6, 8, 9 and 12. It is most accurate between about 6% and 10%.
The exact doubling time solves (1 + r/k)^(k·t) = 2 for t, where r is the annual rate as a decimal and k is compounding periods per year. With continuous compounding the answer is simply ln(2) ÷ r. Tripling and quadrupling use ln(3) and ln(4) in place of ln(2). The rate needed to double in a set time reverses the same equation.
- t
- Years to double
- R
- Annual rate as a whole number (7 for 7%)
- r
- Annual rate as a decimal (0.07)
- k
- Compounding periods per year
Worked examples
$10,000 at 7% a year
72 ÷ 7 gives about 10.3 years. The exact answer with annual compounding is ln(2) ÷ ln(1.07) = 10.24 years, so the shortcut is off by only about two weeks. To double in 10 years you need about 7.2% by the rule, or 7.18% exactly.
12% compounded monthly
The Rule of 72 says 6 years. Because 1% is added every month, the exact doubling time is ln(2) ÷ (12 × ln 1.01) = 5.81 years — the rule slightly overestimates at higher rates with frequent compounding.
Low rate: 2% savings account
At 2% the rule gives 36 years while the exact figure is 35.0 years. At low rates the "Rule of 70" or 69.3 is closer, but either way the message is the same: low-yield savings take decades to double.
Frequently asked questions
How accurate is the Rule of 72?+
For annual compounding it is within a few months of the exact answer between roughly 4% and 12%, and most accurate around 8%. At very low or very high rates the error grows; use the exact doubling time shown above for precise planning.
What is the difference between the Rule of 72, 70 and 69.3?+
They are all approximations of ln(2) ≈ 0.693. 69.3 is best for continuous compounding, 70 is easy for low rates like inflation, and 72 is popular because it divides evenly by many common rates and fits annual compounding at typical returns.
How long does it take money to double at 10%?+
Using the rule, 72 ÷ 10 = 7.2 years. The exact answer with annual compounding is ln(2) ÷ ln(1.10) ≈ 7.27 years, so the rule is very close at 10%.
Can I use the Rule of 72 for inflation?+
Yes. Divide 72 by the inflation rate to estimate how long it takes prices to double — or, equivalently, for the purchasing power of cash to halve. At 3% inflation that is about 24 years.
Does the Rule of 72 work for debt?+
Yes. A credit card balance at 24% APR left unpaid would roughly double in 72 ÷ 24 = 3 years, before fees. It is a quick way to see why high-interest debt grows so fast.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.