The Rule of 72: How to Estimate Doubling Time in Your Head

A friend once told me, over coffee, that his index fund "should roughly double by the time the kids finish high school." I asked how he knew. He didn't open an app. He said "seven and a half percent, call it nine and a half years," and went back to his sandwich. That casual arithmetic is the Rule of 72, and once it lives in your head you stop reaching for a calculator to answer the most common money question there is: how long until this doubles?

The shortcut in one line

Here is the entire rule:

years to double ≈ 72 ÷ interest rate (in whole percent)

That's it. At an annual return of 8%, your money doubles in about 72 ÷ 8 = 9 years. At 6%, it's 72 ÷ 6 = 12 years. At 2%, a sleepy savings account, you wait 72 ÷ 2 = 36 years. The rate goes in as a whole number — 8, not 0.08 — because the 72 already absorbs the scaling. You can run any of these by hand in the time it takes to say them, which is the whole point.

The rule also runs backwards. If you know the time you have and want the return you'd need, flip it: 72 ÷ years = the rate. Want to double a fund in six years? You need roughly 72 ÷ 6 = 12% a year. That single number instantly tells you whether your goal belongs in a savings account or in equities — a savings account will not hand you 12%, so now you know the risk you're signing up for before you commit a dollar.

Why the trick actually works

The rule isn't folklore. It's a clean approximation of real compound math. The exact doubling time at rate r is:

exact years to double = ln(2) ÷ ln(1 + r)

For small rates, ln(1 + r) is very close to r itself, and ln(2) ≈ 0.693. So the exact answer is approximately 0.693 ÷ r, which in whole-percent terms is 69.3 ÷ rate. That 69.3 is the "true" continuous-compounding constant. So why does everyone say 72 instead of 69.3?

Two reasons. First, discrete annual compounding (the kind a normal account actually uses) needs a slightly larger numerator than the continuous limit, which nudges the best constant upward. Second, and more practically, 72 is a gift for mental math: it divides evenly by 2, 3, 4, 6, 8, 9, and 12. So 72÷8, 72÷6, and 72÷9 all land on whole numbers, while 69.3÷8 makes you stop and think. The number trades a sliver of precision for speed, and it happens to be most accurate right around 8% — which is conveniently where a lot of long-run stock-market assumptions sit.

If you want to watch the constant trade off against accuracy, the Rule of 72 Calculator lets you flip between 69.3, 70, and 72 and shows the exact figure beside each estimate so you can see the error move in real time.

A worked example, doubling by doubling

Let me make the abstraction concrete with a single $1,000 deposit, untouched, at 8%.

Start: $1,000
~9 years: $2,000 (one double)
~18 years: $4,000
~27 years: $8,000
~36 years: $16,000
~45 years: $32,000

Five doublings, no new contributions, and the original $1,000 has become $32,000 — a 32× gain — purely from time. Drop the rate to 6% and each doubling stretches to 12 years, so over those same 45 years you get fewer than four doublings. The gap between 8% and 6% looks small on paper; the Rule of 72 makes it visceral. This is the single best argument for starting young: every extra doubling cycle you fit in roughly multiplies the ending number, and the early ones are "free" time you can never buy back later.

Inflation: the same math, running in reverse

The Rule of 72 doesn't only describe growth. It describes erosion just as well, because halving is just doubling viewed from the other side. At 6% inflation, prices double in 72 ÷ 6 = 12 years — which means the purchasing power of idle cash halves in those same 12 years. At a milder 3%, it takes 24 years for prices to double. At 2%, 36 years.

This is the number that should make anyone uneasy about leaving a large balance in a 0.5% checking account. If inflation runs 4% and your cash earns nothing meaningful, the rule says your real wealth is on a ~18-year track to half. To turn that doubling into an actual future price tag — what today's $40,000 car costs in 2040 — pair the estimate with the inflation calculator, which compounds the erosion year by year instead of just handing you the doubling milestone.

How accurate is it, really?

The honest answer: very accurate where it matters, and visibly off at the extremes. In the 4%–12% band that covers most savings rates, bond yields, and equity assumptions, the rule lands within a few tenths of a percent of the exact figure.

Take 8% again. The rule says 9 years. The exact ln(2) ÷ ln(1.08) works out to 9.006 years — an error under 0.1%. You would never notice that gap in a real plan. But push to the edges and the approximation strains. At 25%, the rule says 72 ÷ 25 = 2.88 years, while the true doubling time is about 3.11 years — roughly 7% off. At very low rates the continuous constant 69.3 (or 70) fits better than 72.

The practical rule of thumb for the rule of thumb: trust 72 between about 4% and 12%, lean toward 70 or 69.3 below that, and at extreme rates stop estimating and compute the exact figure. Two common mistakes trip people up. The first is entering the rate as a decimal — it's 72 ÷ 8, never 72 ÷ 0.08. The second is keeping the 72 when you switch goals: 72 is strictly for doubling. To triple your money you divide ~114 by the rate, and to quadruple it you divide 144, both of which fall out of the same logarithmic math (the constant scales with log₂ of the target multiple).

When to put the shortcut down

The Rule of 72 is a reconnaissance tool, not a final answer. It tells you the order of magnitude — "about a decade," "roughly 12% needed" — fast enough to keep a conversation moving or to sanity-check a sales pitch on the spot. When a fund manager promises 12% a year, dividing 72 by 12 gives you six years to double, and that reframes the whole pitch before you've opened a single spreadsheet.

But once you've decided a plan is worth pursuing, switch to exact compounding. The rule ignores contributions, taxes, fees, and varying returns — all the things that actually shape an ending balance. When you're ready for the precise number, run your full schedule through the compound interest calculator, which handles regular deposits and compounding frequency instead of assuming one lump sum left alone. Use 72 to decide whether the destination is worth the trip; use real compounding to map the route.

Made by Toolora · Updated 2026-06-13