Ethan Scott is a licensed CFP® specializing in compounding, investment projections, and retirement planning, ensuring all rules of thumb are applied accurately.
The **Rule of 72 Calculator** provides a simple estimate of how long it takes for an investment to double at a fixed annual rate of return, or what rate is required to double an investment in a given timeframe. It is a quick mental shortcut for analyzing compounding growth. Enter the Annual Rate or the Years to Double to solve for the missing variable.
Rule of 72 Calculator
*The Rule of 72 is an approximation that works best for rates between 6% and 10%.
Rule of 72 Formula
The Rule of 72 uses a simple division to estimate exponential growth. While the more complex logarithmic formula provides the exact answer, the Rule of 72 is invaluable for quick estimates.
Solve for Years to Double (Q):
$$ Q \approx \frac{72}{V} $$Solve for Annual Rate (V):
$$ V \approx \frac{72}{Q} $$*Note: V is used here as the annual rate percentage (not decimal).
Formula Source: Investopedia: The Rule of 72
Variables Explained
- F (Initial Investment): The starting capital. (Used for context, not directly in the Rule of 72 calculation).
- P (Target Doubling Value): The target amount, assumed to be twice the Initial Investment (P=2F). (Used for context).
- V (Annual Rate of Return): The expected compound interest rate, expressed as a whole number percentage (e.g., 8, not 0.08).
- Q (Years to Double): The estimated number of years it takes for the initial investment to reach the target value.
Related Calculators
For more exact analysis of your investment growth, use these tools:
- Compound Interest Calculator (For exact, non-doubling growth)
- Exact Time to Double Calculator (Uses the logarithmic formula)
- Future Value Calculator (Finds the final value given time and rate)
- Present Value Calculator (Finds today’s worth of a future amount)
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 return, by dividing 72 by the annual rate. The result is the approximate number of years required. It operates on the principles of compound interest but simplifies the complex logarithmic math into a quick mental shortcut.
For example, if you expect an 8% annual return, the rule suggests it will take $72 \div 8 = 9$ years for your money to double. While it’s an approximation (the exact figure for 8% is 9.006 years), it’s remarkably accurate for interest rates commonly found in the market (between 5% and 15%).
How to Calculate Rule of 72 (Example)
Let’s find the **Annual Rate (V)** required to double an investment in 12 Years (Q).
- Determine the Known Variable:
$Q = 12$ Years (Term).
- Apply the Formula:
We use the formula to solve for the rate: $V \approx \frac{72}{Q}$.
- Perform the Calculation:
$V \approx \frac{72}{12} = \mathbf{6.0}$.
- Final Result:
The estimated Annual Rate (V) required to double the investment in 12 years is approximately **6.0%**.
Frequently Asked Questions (FAQ)
How accurate is the Rule of 72?
It is most accurate for an annual compounding rate of 8%. The approximation error increases as the interest rate deviates significantly from this level (e.g., less than 4% or greater than 15%). For higher accuracy outside this range, the “Rule of 70” or “Rule of 69.3” may be marginally better.
Does the Rule of 72 work for inflation?
Yes. The Rule of 72 can be used to estimate how long it will take for the purchasing power of your money to be cut in half. Simply divide 72 by the annual inflation rate.
Why is the number 72 used instead of 70 or 69?
The number 72 has more divisors (1, 2, 3, 4, 6, 8, 9, 12, etc.) than 70 or 69, making it easier to perform the mental division for common investment rates (like 6%, 8%, 9%, 12%). Mathematically, 69.3 is more accurate for continuous compounding, but 72 is preferred for its practicality.
Does this rule apply to simple interest?
No. The Rule of 72 is specifically designed to approximate the growth of **compound interest**, where returns are reinvested and generate their own earnings over time. For simple interest, the time to double is just $100 / R$ years.