72 / rate = years to double. That's the whole rule. One division, and you have a useful answer to every "how long until my money doubles" question in personal finance.
The table
- At 3% — doubles in 24 years.
- At 4% — 18 years.
- At 5% — 14.4 years.
- At 6% — 12 years.
- At 7% — ~10 years. (The stock-market real-return anchor.)
- At 10% — ~7 years.
- At 12% — 6 years.
- At 24% (credit card) — 3 years. Debt doubles fast.
Why 72?
The precise formula is ln(2) / ln(1 + r), which at small rates is approximately 69.3 / rate. The 72 version is less accurate but easier to divide mentally — 72 is divisible by 2, 3, 4, 6, 8, 9, 12. Useful for quick back-of- envelope math; the small accuracy cost doesn't matter for any real decision.
The power of stacking doublings
A 7% return for 30 years means 3 doublings. $10,000 → $20,000 → $40,000 → $80,000. A 40-year horizon adds a 4th doubling: $160,000. The difference between starting at age 25 vs 35 is one extra doubling — which is enormous.
When you want the exact number instead of the estimate. Year-by-year projections with contributions.