Rule of 72 Explained: How Long to Double Your Money

The Rule of 72 provides a quick approximation without a calculator:

Years to double = 72 ÷ Annual return rate

Examples:

• 6% return → 72 ÷ 6 = 12 years
• 8% return → 72 ÷ 8 = 9 years
• 10% return → 72 ÷ 10 = 7.2 years
• 12% return → 72 ÷ 12 = 6 years

The formula works because of how logarithms relate to compound growth. The exact formula is ln(2) / ln(1 + r), but 72 ÷ r gives remarkably close results for rates between 2% and 20%, making it one of the most useful financial shortcuts ever devised.

Comparing Rule of 72 estimates to exact doubling times:

• 2% → Rule of 72: 36 years | Exact: 35.0 years (off by 1.0)
• 4% → Rule of 72: 18 years | Exact: 17.7 years (off by 0.3)
• 6% → Rule of 72: 12 years | Exact: 11.9 years (off by 0.1)
• 8% → Rule of 72: 9 years | Exact: 9.0 years (perfect)
• 10% → Rule of 72: 7.2 years | Exact: 7.3 years (off by 0.1)
• 15% → Rule of 72: 4.8 years | Exact: 5.0 years (off by 0.2)
• 20% → Rule of 72: 3.6 years | Exact: 3.8 years (off by 0.2)

For rates above 20%, the "Rule of 69.3" (using 69.3 instead of 72) is more accurate but less convenient for mental math. The number 72 was chosen because it has many divisors (2, 3, 4, 6, 8, 9, 12), making division easy.

Practical applications beyond basic investing:

Inflation erosion: At 3% inflation, your money's purchasing power halves in 72 ÷ 3 = 24 years. A dollar today buys only 50 cents worth of goods in 2050.

Comparing accounts: A savings account at 1% doubles in 72 years. A high-yield account at 4.5% doubles in 16 years. The difference is stark when you see it this way.

Debt growth: Credit card debt at 18% APR doubles in just 4 years if unpaid. This shows why carrying balances is so destructive.

Salary negotiations: If your salary grows at 3% annually, it doubles in 24 years. At 5% growth, it doubles in 14.4 years—a decade faster.

Quick investment comparison: If someone pitches you an investment returning 6% vs another at 9%, the first doubles in 12 years while the second doubles in 8 years. Over 24 years, the 9% investment quadruples while the 6% one only doubles twice.

Important caveats:

1. Constant returns assumed: Real investments fluctuate. A fund averaging 8% might return 20% one year and -5% the next. Volatility actually slows real growth compared to a smooth 8%.

1. No taxes or fees: Investment fees of 1% and capital gains taxes reduce your effective rate. An 8% gross return might be 6% net, changing doubling time from 9 to 12 years.

1. No contributions: The rule only applies to a single lump sum. If you're adding money regularly, use an investment growth calculator for accurate projections.

1. Extreme rates: Below 2% or above 20%, accuracy drops. For very high rates, use 69.3 ÷ rate instead.

1. Not a guarantee: Just because the math says your money should double in 9 years doesn't mean it will. Sequence of returns, market conditions, and economic factors all introduce uncertainty.