Rule of 72

About Rule of 72

Estimate years for money to double at a given annual rate — classic rule of 72 next to the exact ln formula.

The rule of 72 is the napkin version of compound doubling: years ≈ 72 ÷ rate%. At 8% that is nine years. It is famous because it is close enough for a hallway conversation and wrong enough that serious planners should check the exact math.

This page shows both. Approximate uses 72 / rate. Exact uses ln(2) / ln(1 + r) so you can see how far the shortcut drifts. Mid-single-digit rates are where the rule feels sharpest; very low or very high rates stretch the error band.

Nothing here forecasts markets. You type an assumed return; you get a doubling time under continuous annual compounding of that return. For full future-value tables with a starting principal, open the compound interest calculator. For regular deposits toward retirement, use the retirement calculator.

How to use Rule of 72

1. 1Enter an annual return as a percent.
2. 2Compare approximate years (rule of 72) with exact doubling time.
3. 3Change the rate to see how sensitive the estimate is.

What it won't do

• ·Doubling time only — no principal or contribution schedule.
• ·Assumes a constant rate; real returns vary.

Common questions

Related tools

• Compound interest calculatorFuture value with compounding schedule and a simple growth chart.
• Simple interest calculatorInterest = principal × rate × time. Cross-links to compound.
• ROI calculatorReturn on investment and annualized ROI over years.