About the Rule of 72 Calculator
The Rule of 72 is the classic mental shortcut: divide 72 by your annual rate and you get the years to double, accurate within a whisker for rates between 4% and 15%. It is how investors size up growth rates at a glance — and how savers quantify what inflation eats.
It cuts both ways: at 8%/yr your money doubles every 9 years; at 8% inflation, prices double every 9 years too, and purchasing power halves per doubling on the “real side.”
The formula behind it
The rule and the exact math it approximates:
Years = 72 / rate • Exact: ln(2) / ln(1+r)r = the annual rate as a percentage (8 for 8%). The exact answer is ln(2)/ln(1+r); the 72-version is within 1% or less for typical consumer rates, and slightly less accurate at high rates — 10% → 7.2 years (exact 7.27), 15% → 4.8 (exact 4.96).
Worked example
Defaults — an 8% annual return:
- 72 / 8 = 9 years per doubling.
- Exact: ln(2)/ln(1.08) = 9.01 years.
- At 7% instead: doubling time ~10.3 years — you gain a whole extra year of waiting for one point less return.
Takeaway: At 72/rate, a 6% account doubles in 12 years while an 8.5% portfolio doubles in 8.5. The table the tool prints shows the whole doubling ladder for you.
What moves the result
- Rate magnitude — accuracy degrades somewhat above ~15%; below 4% the rule still works beautifully.
- Compounding frequency — the exact answer assumes annual compounding; the rule works across all frequencies for typical rates.
- Inflation — the same rule halves the real value of cash at the inflation rate (that is a halving, not the same as doubling).
- Fees — subtract fund expense ratios from the rate before using the rule.
Practical tips
- Use it as a sizing number, not a forecast: it frames “how mind-shakingly long 20 years of 3% is” in seconds
- For fee-comparison thinking at the fund level — 0.5% fees subtracted from every doubling every, not just once — the tool can show the compounding drag.
- Compare 72/rate across candidates: at 72-rate scale, small percentage differences in your yield carry huge future-time effects.
- Always subtract inflation to assume real purchasing power doubling; otherwise the number only tells the happy half.
- Teach this tool as the greatest mental-math on-ramp to finance: 70% of planning intuitions flow from it.
Frequently asked questions
How accurate is the Rule of 72?
Within a fraction of a percent for rates between 4% and 15%. Past ~20% it drifts and cooling toward exact ln(2)/ln(1+r) methods is warranted, but for almost all consumer-intended rates it’s remarkably precise.
What about the “Rule of 70” or “Rule of 69”?
Simpler variants of the same concept, using 70 and 69 for faster mental math and continuous compounding respectively. 72 has more precise results for common consumer rates like 6–10%.
Can it be used for inflation?
Yes: divide 72 by an inflation rate and get the years to halve purchasing power. At 3% inflation, cash loses half its purchasing power every 24 years, regardless of whether you are spending or not.