The Rule of 72 Explained: Estimating Investment Growth

The Rule of 72 is a mental-math shortcut for estimating how long it takes an investment to double in value at a given annual rate of return: divide 72 by the annual percentage rate, and the result is roughly the number of years to double. At an 8% annual return, 72 divided by 8 gives 9 years — no calculator, spreadsheet, or logarithm required.

The formula

Years to double ≈ 72 / annual rate of return (as a whole number, not a decimal)

A few worked examples:

Annual return	Years to double (Rule of 72)
2%	36 years
4%	18 years
6%	12 years
8%	9 years
12%	6 years

The relationship is inverse and roughly linear at this scale: double the rate, and the doubling time roughly halves. That intuition — small differences in sustained annual return compound into large differences in outcome over long horizons — is the entire reason the rule is worth having memorized, even in an age of instant calculators.

Where the 72 comes from

The rule is an approximation of the actual formula for compound growth. Exact doubling time is ln(2) / ln(1 + r), where r is the rate as a decimal — not something most people compute in their head. Because ln(2) is about 0.693, and 72 is a number with a lot of small integer divisors (2, 3, 4, 6, 8, 9, 12, and more all divide evenly into it), 72 turns out to be a convenient stand-in for 69.3 that trades a small amount of precision for numbers that divide cleanly by hand. That’s also why you’ll occasionally see “Rule of 70” or “Rule of 69.3” used instead — they’re the same idea with a different tradeoff between accuracy and ease of mental division.

How accurate is it

The approximation is closest in the 6% to 10% range, which happens to cover a lot of realistic long-run return assumptions for diversified stock portfolios. Outside that band, the error grows:

• At very low rates (1-2%), the rule is still reasonably close, off by a matter of months.
• At very high rates (above 20%), the approximation starts to drift more noticeably from the exact compound-interest answer, though it stays in the right ballpark for a quick estimate.

For back-of-envelope planning — “roughly how long until this doubles” — the rule is accurate enough. For anything where the exact number matters, the real compound interest formula is one calculator away.

Related shortcuts

The Rule of 72 has siblings built the same way, swapping the numerator for a constant better suited to a different question:

• Rule of 114 estimates years to triple an investment — divide 114 by the annual rate.
• Rule of 144 estimates years to quadruple — divide 144 by the annual rate, which is really just two doublings, since 144 is twice 72.
• Applied to inflation, the same math estimates how long it takes purchasing power to halve at a given inflation rate — 72 divided by a 3% inflation rate suggests roughly 24 years before today’s dollar buys half of what it buys now. This is the same doubling-time approximation pointed at a shrinking quantity instead of a growing one, since a constant percentage decline is just compounding growth with a negative sign.

All of these share the same underlying approximation of natural-log-based compound growth, just scaled to a different multiple than doubling.

A worked comparison

Two investments with different fees illustrate why the rule is more than a party trick. An index fund charging a low expense ratio versus an actively managed fund charging meaningfully more in fees, both otherwise earning the same gross return, don’t just differ by “a percent or two” in outcome — the fee difference directly slows the net rate the Rule of 72 is dividing into, which stretches out doubling time disproportionately over a long enough horizon. This is exactly the mechanism behind the common advice to pay attention to fees when comparing an ETF or index fund — a seemingly small, constant annual drag compounds the same way returns do, just in the opposite direction, and the Rule of 72 makes that compounding visible without needing a spreadsheet.

What the rule assumes

The Rule of 72 estimates doubling time under a constant, compounding annual rate of return — it doesn’t model any of the real-world texture that determines an actual investment’s outcome:

• No contributions or withdrawals. It assumes a single lump sum growing untouched, not a portfolio being added to over time — which is how most retirement accounts, including a typical 401(k) or Roth IRA, actually grow.
• No volatility. Real returns vary year to year; the rule assumes a smooth, constant average rate, so it’s an estimate of a long-run average outcome, not a promise about any specific year.
• Pre-tax and pre-fee. It doesn’t account for taxes on gains or fund expense ratios, both of which reduce the effective rate actually compounding.

It’s also sometimes applied in reverse — dividing 72 by a desired number of years to find the rate of return that would be needed to double an investment in that time — which is a useful sanity check on whether a target is realistic before committing to it.

The takeaway

The Rule of 72 turns a logarithm into a division problem: 72 divided by the annual rate gives a fast, good-enough estimate of doubling time, most accurate in the high-single-digit to low-double-digit return range. It’s a mental-math tool for building intuition about how compounding rates translate into time, not a substitute for a real compound-interest calculation once contributions, withdrawals, taxes, and fees actually matter to the answer.