The Rule of 72: A 5-Second Mental Math Trick for Compound Interest

The Rule of 72 is the most useful mental math trick in personal finance. It estimates how long it takes any investment to double in value, given a fixed rate of return — and it works in your head, in seconds, with no calculator.

The rule in one sentence

Years to double = 72 ÷ annual interest rate

At 6%, money doubles in 12 years (72÷6). At 8%, 9 years. At 12%, 6 years. At 4%, 18 years. Memorize it once, use it forever.

Worked examples

• $10,000 at 8%: doubles to $20,000 in 9 years, $40,000 in 18, $80,000 in 27, $160,000 in 36.
• $50,000 at 6%: doubles to $100,000 in 12 years, $200,000 in 24, $400,000 in 36.
• Credit card debt at 24% APR: doubles in 3 years if you make no payments.

Why 72?

It's an approximation derived from the natural log of 2 (about 0.693) divided by the typical interest rate. The exact formula uses ln(2) ≈ 0.693, but 72 is divisible by more numbers (2, 3, 4, 6, 8, 9, 12) making mental math easier.

When the rule is accurate

The Rule of 72 is most accurate between 4% and 12% interest rates. Below 4%, use the Rule of 70 for slightly better precision. Above 12%, the Rule of 76 fits better. For everyday use, 72 covers virtually every investment rate you'll encounter.

Three powerful applications

1. Inflation: At 3% inflation, prices double in 24 years. A $50 dinner today costs $100 in 2050.
2. Salary: A 4% annual raise doubles your income in 18 years.
3. Debt: 18% credit card interest doubles your balance in 4 years if untouched.

The doubling cascade is the real lesson

Money doesn't just double — it doubles, and doubles again, and again. The 4th doubling produces more wealth than the previous three combined. This is why decades of compounding produce balances that look unreal compared to the contributions. The Rule of 72 is your shortcut for visualizing the cascade.