๐ Rule of 72 Calculator
A quick approximation using "72 รท annual rate" โ use a compound interest calculator for an exact figure.
Use the "Rule of 72" (72 รท annual rate (%) โ years to double), a commonly used approximation for compound growth, to estimate how many years it takes an investment to double at a given annual rate โ or, in reverse, the rate needed to double within a target number of years.
How to use
- Choose "From rate" or "From years".
- Enter the annual rate (%), or the target number of years.
- The result is calculated automatically.
How the calculation works
The rule of 72 is a mental-math approximation for how long money takes to double with compound interest. Years to double โ 72 รท annual rate (%) Required rate (%) โ 72 รท target years Exactly, with annual compounding, the doubling time t solves (1 + r)^t = 2, giving t = ln 2 รท ln(1 + r). Since ln 2 โ 0.693, "69.3 รท rate" is closer at very low rates, but for the few-percent to 10% rates people usually deal with, 72 gives a smaller error โ and 72 divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes it easy to use in your head. Alongside the rule-of-72 estimate, this tool shows the value from the exact formula.
Worked example
At 6% a year Rule of 72: 72 รท 6 = 12 years Exact: ln 2 รท ln 1.06 โ 11.90 years At 1% a year Rule of 72: 72 years Exact: about 69.66 years (the error grows at low rates) To double in 10 years Rule of 72: 72 รท 10 = 7.2% Exact: 2^(1/10) โ 1 โ 7.18%
Things to be aware of
- The rule is most accurate at rates of about 6โ10% and less accurate at very low or very high rates.
- It works for debt too. An unpaid card balance at 15% a year doubles in about 5 years (72 รท 15 โ 4.8).
- Applied to inflation, 2% a year halves the value of money in about 36 years.
FAQ
What is the Rule of 72?
A commonly used financial rule of thumb that approximates the number of years it takes an investment to roughly double under compound growth, using the simple formula "72 รท annual rate (%)".
Why is the number 72 used?
The exact compound-growth formula ln(2)/ln(1+r) is close to 72 for typical interest rates (roughly a few percent to the low teens), and 72 has many convenient divisors, making it easy to calculate by hand.
What if I need an exact compound interest calculation?
The Rule of 72 is only an approximation. For a precise future value, use a compound interest calculator that accounts for the exact principal and time period.