The Rule of 72 Explained (With Examples)

How to use it

The rule is one line: years to double ≈ 72 / rate, where rate is the annual percentage as a whole number (not a decimal). Some examples:

• 2%: 72 / 2 = 36 years. A savings account paying 2% doubles in 36 years.
• 4%: 72 / 4 = 18 years. A bond portfolio at 4% doubles in 18 years.
• 6%: 72 / 6 = 12 years. Real equity returns, roughly — stocks double in real terms every 12 years.
• 8%: 72 / 8 = 9 years. Nominal equity returns, roughly — stocks double in nominal terms every 9 years.
• 12%: 72 / 12 = 6 years. An aggressive growth assumption; if sustainable, doubles in 6.
• 18%: 72 / 18 = 4 years. Credit-card APR territory — debt doubles in 4 years if untouched.

Reverse it, too: if something has doubled in a known time, divide 72 by that time to estimate the growth rate. A 401(k) that went from $200,000 to $400,000 in 10 years has averaged roughly 72 / 10 = 7.2% annualised.

Why it works (the math)

Compound growth satisfies A = P × (1 + r)^t. Setting A = 2P and solving for t:

2 = (1 + r)^t → t = ln(2) / ln(1 + r)

ln(2) is about 0.693. For small r, ln(1 + r) ≈ r. So t ≈ 0.693 / r, which in percentage terms is 69.3 / rate. The true formula is the "Rule of 69.3".

But 69.3 divides cleanly by very few whole numbers. 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12 — exactly the integer rates people encounter most. Swapping 69.3 for 72 introduces a small error (about 4%) that is roughly cancelled by the ln(1 + r) approximation at rates around 8%. It is a rare case of two approximation errors lining up to produce an answer that is more useful than either alone.

Comparison for a few rates: true doubling time vs Rule of 72 estimate.

• 2%: true 35.0 years, rule 36.0 (off by 1.0)
• 4%: true 17.7 years, rule 18.0 (off by 0.3)
• 6%: true 11.9 years, rule 12.0 (off by 0.1)
• 8%: true 9.0 years, rule 9.0 (exact)
• 10%: true 7.3 years, rule 7.2 (off by 0.1)
• 15%: true 5.0 years, rule 4.8 (off by 0.2)
• 20%: true 3.8 years, rule 3.6 (off by 0.2)

Across the realistic range for investing and debt, the rule is within half a year of reality.

Practical applications

The rule is most useful when you need a fast intuition for compound processes that span decades. Some examples:

Retirement planning sanity check. A 30-year-old with $100,000 in a retirement account expecting 7% real returns will, with no further contributions, have about $100,000 × 2^(35 / 10.3) = roughly $1,000,000 by age 65. Without the rule you are reaching for a calculator; with it, you can estimate in your head. The key computation: 72 / 7 ≈ 10, so money doubles every 10 years → roughly 3.5 doublings in 35 years → 2^3.5 ≈ 11× growth.

Inflation intuition. At 3% inflation, the purchasing power of a dollar halves every 24 years. A $50,000 income today will need to be $100,000 in 24 years just to buy the same basket of goods. This is why cash-heavy retirement portfolios are risky on long horizons.

Debt awareness. Credit card debt at 22% APR doubles in about 72 / 22 ≈ 3.3 years if untouched. A $5,000 balance becomes $10,000 in roughly 40 months. Student loans at 6% double in 12 years — a long-enough horizon that deferred payment during graduate school can meaningfully inflate balances.

Economic and political reading. A country's GDP growing at 2% real doubles every 36 years — about a generation. At 7% (rapid developing-economy growth) it doubles every 10 years. The rule lets you quickly interpret claims like "we will double GDP within a generation" and see whether the implied growth rate is plausible.

Variants worth knowing

• Rule of 114 — tripling time. 72 × (ln 3 / ln 2) = about 114.
• Rule of 144 — quadrupling time. 72 × 2 = 144.
• Rule of 69.3 — more accurate for low rates (near-zero interest environments, slow growth).
• Eckart-McHale rule — 69.3 / r + 0.33, accurate across a wider range but not a mental shortcut any more.

Where it does not apply

The rule assumes constant annual compounding. Real investments have variable returns, down years, and contributions added mid-period. The rule will not tell you when your actual portfolio doubles; it tells you when a hypothetical portfolio compounding smoothly at r% would double.

It is also not useful for non-compounding processes. Simple interest does not "double" in the compounding sense — at 5% simple interest, money takes exactly 20 years to double (100% of principal in 20 × 5%). The Rule of 72 would incorrectly suggest 14.4 years.

For situations with regular contributions — the typical retirement-savings case — the rule works for the existing principal but does not capture the additional growth from new savings. For a fuller picture, use a proper compound-interest calculator with a monthly-contribution input.

The point

The Rule of 72 is not a substitute for doing the real math on important decisions. It is a shortcut that lets you screen ideas, sanity-check claims, and build intuition for exponential processes — three things most people never develop because they reach for a spreadsheet instead. Memorise it, use it on every news article that mentions a percentage, and the financial world will start making a lot more sense.