Rule of 72 Calculator

Estimate how long it takes to double your money, what rate of return you need, or how many times your investment can double using the Rule of 72 – with an instant accuracy check against the exact compound interest formula.

Rule of 72 – Interactive Calculator

Choose 72 for quick mental math, 69–70 for more accuracy.

Used only for the exact comparison; the Rule of 72 itself ignores compounding frequency.

%

Expected average annual return (e.g., 7 for 7% per year).

$

Used to show the approximate doubled value.

What is the Rule of 72?

The Rule of 72 is a classic mental-math shortcut used in personal finance and investing. It estimates:

  • How many years it takes for an investment to double at a given annual return, or
  • What annual return you need to double your money in a given number of years.

Instead of using logarithms or a financial calculator, you simply divide a constant (usually 72) by the interest rate or the number of years.

Core Rule of 72 formulas

  • Doubling time (years) ≈ 72 ÷ annual rate (%)
  • Required rate (%) ≈ 72 ÷ years to double
  • Number of doublings ≈ years ÷ (72 ÷ rate)

Exact formula vs. Rule of 72

The Rule of 72 is an approximation to the exact compound interest formula. For an investment growing at rate r per year (as a decimal) with n compounding periods per year, the exact doubling time is:

Exact doubling time:

\[ t_{\text{double}} = \begin{cases} \dfrac{\ln 2}{\ln(1 + r/n)} & \text{(discrete compounding)}\\\\ \dfrac{\ln 2}{r} & \text{(continuous compounding)} \end{cases} \]

The Rule of 72 replaces this logarithmic expression with a simple division. It works best for “normal” investment returns between about 4% and 15% per year.

Why 72?

72 is popular because:

  • It has many small integer factors (2, 3, 4, 6, 8, 9, 12), making mental math easy.
  • At around 8% annual return, it is surprisingly close to the exact doubling time.

For example, at 8%:

  • Rule of 72: 72 ÷ 8 = 9 years
  • Exact (annual compounding): about 9.01 years

How to use this Rule of 72 calculator

1. Time to double

  1. Select Time to double.
  2. Enter your expected annual return (e.g., 6% or 8%).
  3. Optionally enter an initial amount to see the approximate doubled value.
  4. Click Calculate.

The calculator shows:

  • Approximate years to double using your chosen rule constant (72, 70, or 69.3).
  • Exact years to double using the compound interest formula and your compounding frequency.
  • The difference between the two in both years and percentage error.

2. Required rate to double

  1. Select Required rate.
  2. Enter how many years you want it to take to double.
  3. Optionally enter an initial amount.
  4. Click Calculate.

You’ll see the approximate rate from the Rule of 72 and the exact rate needed to double in that time.

3. Number of doublings

  1. Select Number of doubles.
  2. Enter your investment horizon in years and your expected annual return.
  3. Optionally enter an initial amount.
  4. Click Calculate.

The calculator estimates how many times your money can double and what that means for your approximate final value.

When is the Rule of 72 accurate?

The Rule of 72 is a rule of thumb, not a precise financial planning tool. Its accuracy depends on:

  • Interest rate level – best between about 4% and 15%.
  • Compounding frequency – it assumes simple annual compounding.
  • Stability of returns – it assumes a constant rate over time.

For very low rates (e.g., 1–2%) or very high rates (e.g., 25%+), the error can be large. In those cases, rely on the exact compound interest result shown by the calculator.

Practical examples

Example 1 – Long-term stock market investing

Suppose you expect a long-term average return of 7% per year.

  • Rule of 72: 72 ÷ 7 ≈ 10.3 years to double.
  • Over 30 years, that’s about 30 ÷ 10.3 ≈ 2.9 doublings.
  • $10,000 could grow to roughly $10,000 × 2.9 ≈ $76,000 (exact compound interest will differ).

Example 2 – Required rate to double in 10 years

You want your money to double in 10 years:

  • Rule of 72: 72 ÷ 10 = 7.2% per year.
  • Exact rate (annual compounding) is about 7.18%.

Limitations and cautions

  • The Rule of 72 ignores volatility and sequence of returns risk.
  • It assumes reinvestment of all earnings and no withdrawals.
  • It does not account for taxes, fees, or inflation.

Use it for quick back-of-the-envelope estimates and intuition, then rely on full compound interest calculations and, where appropriate, professional advice for real financial decisions.

FAQ

Is the Rule of 72 the same as the Rule of 70 or 69?

They are closely related shortcuts. 72 is convenient for mental math. 69 or 69.3 is more accurate for continuously compounded interest, and 70 can be slightly better at higher rates. This calculator lets you switch between them and compare to the exact result.

Can I use the Rule of 72 for inflation?

Yes. If inflation averages 3% per year, the Rule of 72 suggests prices will double in about 72 ÷ 3 = 24 years. That also means your money’s purchasing power halves in roughly the same time if your returns don’t keep up.

Can I use it for negative returns?

Conceptually, you can think about “halving time” with a negative rate, but the Rule of 72 becomes less intuitive and less accurate. For losses or very low returns, use the exact compound interest formula instead of the shortcut.

This calculator is for educational and illustrative purposes only and does not constitute financial advice. Always consider consulting a qualified professional for personalized investment decisions.