Economist and financial educator specializing in compound growth and long-term financial modeling.
The **Rule of 72 Calculator** is a simple mental math shortcut used to quickly estimate the time it takes for an investment or debt to double in size, given a fixed annual rate of return. Use this tool to solve for the missing variable: Rate of Return, or Doubling Time. The Starting and Ending Values are fixed for the Rule of 72, but we include them for validation.
Rule of 72 Calculator
Instructions: Enter either the **Annual Rate of Return** (R) or the **Doubling Time** (T) to solve for the other. The Starting and Ending Values are only needed for consistency checks against the exact formula.
Rule of 72 Parameters
The Rule of 72 Formula
The Rule of 72 is an approximation, not a mathematically exact formula. It works best for rates between 6% and 10%.
To Solve for Doubling Time ($t_{72}$):
$$t_{72} \approx \frac{72}{r}$$To Solve for Rate of Return ($r_{72}$):
$$r_{72} \approx \frac{72}{t}$$The Exact Doubling Time Formula (for Comparison):
$$t = \frac{\ln(2)}{\ln(1 + r/100)}$$ Formula Source: InvestopediaVariables Explained (P, F, V, Q – Parameters)
- $V_{start}$ (Starting Value, $P$): The initial investment amount. (Only for exact comparison.)
- $V_{end}$ (Ending Value, $F$): The value required to double the starting amount. (Only for exact comparison.)
- $r$ (Annual Rate, $V$): The estimated annual compounded growth rate (as a percentage, e.g., 8 for 8%).
- $t$ (Doubling Time, $Q$): The time (in years) required for the value to double.
Related Compound Growth Calculators
For more exact calculations of time and value:
- Compound Annual Growth Rate Calculator
- Compound Interest Calculator
- Future Value Calculator
- Inflation Rate Calculator
What is the Rule of 72?
The Rule of 72 is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a quick, rough estimate of the number of years required. It’s not a precise mathematical rule but an approximation that is surprisingly accurate for common interest rates (those between 6% and 10%).
The rule can also be used in reverse: dividing 72 by the number of years one wants the investment to double in will give the necessary annual rate of return. It is also often applied to debt to estimate how long debt will take to double if no payments are made (e.g., credit card debt at a high rate).
How to Use the Rule of 72 (Example)
Suppose you have an investment earning an average annual return of 8%. We are solving for the Doubling Time ($t_{72}$):
- Step 1: Identify the Rate
The rate ($r$) is 8 (not 0.08, as 72 is used instead of 100). $r = \mathbf{8}$.
- Step 2: Divide 72 by the Rate
$t_{72} = 72 / r = 72 / 8 = \mathbf{9}$.
- Step 3: Compare with the Exact Formula (Optional)
The Rule of 72 estimates 9 years. The exact formula yields $\ln(2) / \ln(1 + 0.08) \approx 9.006$ years. The approximation is very close!
The estimated Doubling Time is 9 years.
Frequently Asked Questions (FAQ)
While the exact formula is closest to the “Rule of 69.3,” 72 is chosen because it has many small divisors (2, 3, 4, 6, 8, 9, 12), making the mental calculation much easier and more accurate across a common range of rates (6% to 10%).
Yes. If your credit card charges 24% interest and you make no payments, your debt would roughly double in $72 / 24 = 3$ years. This demonstrates the powerful negative effect of compounding debt.
No. It is a mental estimation. For higher rates (above 10%), the “Rule of 70” or “Rule of 69” may provide a slightly more accurate estimate, but the Rule of 72 is the most widely used standard.
No. The Rule of 72 only estimates the compounding effect based on the *gross* annual rate. Any taxes, fees, or inflation must be accounted for separately by reducing the rate you input.