The Rule of 72: Calculating How Fast Your Investments Will Double

What Is the Rule of 72?

The Rule of 72 is an elegant mathematical approximation derived from the natural logarithm of 2:

\ln(2) \approx 0.693147

For compound interest compounding annually, calculating the exact doubling time requires:

t = \frac{\ln(2)}{\ln(1 + r)}

Because 72 has many divisors (2, 3, 4, 6, 8, 9, 12, 18, 24, 36), it serves as a fast mental calculation shortcut for interest rates between 5% and 12%:

\text{Years to Double} \approx \frac{72}{\text{Annual Rate of Return (\%)}}

Doubling Timelines Across Asset Classes

The Silent Hazard: How a 1.5% Expense Ratio Cuts Your Wealth in Half

Consider two investors, Maya and Liam, who each invest $20,000 at age 25. Both achieve an underlying gross market return of 8.0% per year over a 36-year horizon:

• Maya invests in an ultra-low-cost index fund charging 0.05% (net return 7.95%).
• Liam invests in an actively managed fund charging a 1.55% fee (net return 6.45%).

Applying the Rule of 72:

• Maya's money doubles every: 72 ÷ 8.0 = 9.0 years.

Over 36 years, Maya experiences 4 complete doublings:

$20,000 → $40,000 → $80,000 → $160,000 → $320,000!

• Liam's money doubles every: 72 ÷ 6.45 = 11.16 years.

Over 36 years, Liam experiences only 3.2 doublings:

His final portfolio reaches approximately $190,000.

The Result: That seemingly small 1.5% management fee cost Liam over $130,000 in uncollected compound gains!

Reverse Rule of 72: Inflation's Purchasing Power Erosion

The Rule of 72 works symmetrically in reverse to show how quickly inflation cuts your currency's purchasing power in half:

• At 3.0% annual inflation, purchasing power halves in: 72 ÷ 3 = 24 years.
• At 6.0% elevated inflation, purchasing power halves in: 72 ÷ 6 = 12 years.

Run precision compounding simulations with multiple contribution frequencies using our Compound Interest Calculator.