🔢 The Rule of 72: Mental Math for Investing

The Rule

Divide 72 by the annual interest rate to find approximately how many years it takes to double your money at compound interest.

• 2% (savings account): 72 ÷ 2 = 36 years to double • 6% (conservative portfolio): 72 ÷ 6 = 12 years • 8% (moderate portfolio): 72 ÷ 8 = 9 years • 10% (aggressive, historical S&P avg): 72 ÷ 10 = 7.2 years • 22% (credit card APR): 72 ÷ 22 = 3.3 years for debt to double

Why 72?

The exact answer to "how long to double at rate r" is ln(2) ÷ ln(1+r) ≈ 69.3 ÷ r for small r. But 72 is used because it's easily divisible by 1, 2, 3, 4, 6, 8, 9, and 12 — the most common interest rates. It's accurate within a few percent for rates between 3% and 15%, which covers the range relevant to most investors.

For very low rates (below 2%), the Rule of 69 is slightly more accurate. For very high rates (above 20%), use 70.

Applying It Beyond Investments

The Rule of 72 works for any compounding quantity:

• Debt: At 22% APR, credit card debt doubles in 3.3 years without payments • Inflation: At 4% inflation, prices double in 18 years • GDP growth: At 3% growth, an economy doubles in 24 years • Population: At 2% growth, a city doubles in 36 years

It's a universal tool for intuitively understanding exponential growth and decay.

Practical Uses

When evaluating a financial decision, the Rule of 72 gives immediate intuition:

"My advisor says this fund returns 5%." → It doubles every 14.4 years. Starting at 35 with $50,000, you'll have ~$200,000 at 64 (two doublings). Is that enough?

"Should I pay off my 18% store credit card?" → At 18%, that balance doubles in 4 years. Yes.

"My high-yield savings pays 4.5%." → Money doubles every 16 years. For an emergency fund, that's fine. For 30-year retirement savings, you need more.