Rule of 72

The Rule of 72 is an approximation of compound growth that estimates the doubling time of an investment: 72 divided by the annual percentage rate of return equals the approximate number of years required for the value to double. It substitutes simple division for the logarithmic formula that exact compound-interest math requires, trading a small amount of precision for the ability to run the calculation in your head.

The exact doubling time comes from solving (1 + r)ⁿ = 2, which gives n = ln(2) ÷ ln(1 + r). The natural log of 2 is about 0.693, so a "Rule of 69.3" would be mathematically purer for continuous compounding — but 72 wins in practice because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12, and the slight upward nudge happens to correct for annual rather than continuous compounding across the rate range most investors care about. At 8%, the rule says 9.0 years; the exact answer is 9.006. The approximation drifts at the extremes: at 1% the rule says 72 years versus a true 69.7, and at 20% it says 3.6 versus a true 3.8.

The less obvious uses are often the most valuable. Run the rule on inflation to see purchasing power erode — at 3% inflation, prices double (and a fixed income's buying power halves) in about 24 years, well within a single retirement. Run it on investment costs: a portfolio earning 7% gross but paying 1% in annual fees compounds at 6%, stretching its doubling time from about 10.3 years to 12 — a gap that widens with every doubling.

Take the annual growth rate as a whole number and divide it into 72. The quotient is the approximate doubling time in years. To find the rate needed to double within a deadline, divide 72 by the years instead.

A hypothetical example: Sam, 35, has $100,000 in retirement savings and wants a feel for where it could be at 65 without touching a calculator. At an assumed 7% return, 72 ÷ 7 ≈ 10 — call it a doubling every decade. Three decades means roughly three doublings: $100,000 → $200,000 → $400,000 → $800,000 by 65, before any new contributions. If Sam instead assumes a more conservative 5%, doubling takes about 72 ÷ 5 ≈ 14.4 years — barely two doublings in 30 years, landing near $400,000. The exact compound math gives $761,226 and $432,194 — the shortcut got within striking distance in seconds, which is precisely its job.

Pros

• Fast enough to use mid-conversation — no calculator, no spreadsheet.
• Builds real intuition for compounding, which most people otherwise underestimate badly.
• Works on anything that compounds: returns, inflation, fees, debt balances, even college-cost growth.

Cons

• It is an approximation — accuracy degrades below about 4% and above about 12%, and it assumes a steady rate real investments never deliver.
• Estimates doublings only; it cannot answer more precise questions like "how much will I have in 23 years?"
• Easy to misuse with gross returns — ignoring fees, taxes, and inflation makes doubling look faster than a saver's real experience.