How the Rule of 72 Works and When It Fails

The rule of 72 is the most useful piece of mental arithmetic in personal finance. Divide 72 by a growth rate and you get, near enough, the number of periods it takes for something to double. Seven percent doubles in about ten years. Nine percent in eight. Three percent in twenty-four.

It takes two seconds, requires no device, and is accurate enough for almost every decision it gets used for. It is also a genuine approximation with a range where it works and edges where it drifts.

Why the number is 72

Doubling time is properly given by the natural logarithm of 2 divided by the growth rate — roughly 0.693 divided by the rate.

Working in percentages rather than decimals, that becomes about 69.3 divided by the percentage. So the theoretically pure version is a rule of 69.3, which is a poor number to divide by in your head.

Two adjustments produce 72. First, most real-world compounding is annual rather than continuous, which pushes the correct constant slightly upward. Second, and more practically, 72 is divisible by 2, 3, 4, 6, 8, 9 and 12, which makes the mental arithmetic clean for exactly the rates people care about.

So 72 is a deliberate trade: marginally less exact than 69.3 at very low rates, far easier to compute, and closer to correct across the middle of the range where it is actually used.

Where the rule of 72 is sharpest

The rule is most accurate around 8%, where it is nearly exact. It stays within a few percent of the true answer roughly between 4% and 15%, which happily covers most investment returns, most inflation rates, and most loan rates.

Outside that band it drifts.

At very low rates it understates the time. At 1%, the rule says 72 years; the true figure is around 70. Not a large error proportionally, but the answer is a long time either way.

At high rates it understates badly. At 30% the rule says 2.4 years; the truth is closer to 2.6. At credit-card rates the drift is enough to matter, and the credit card payoff calculator is the right tool rather than mental arithmetic.

Practitioners sometimes adjust: use 70 for very low rates, 78 for high ones. That is more precision than the rule was meant to deliver, and if you need it the rule of 72 calculator gives both the approximation and the exact doubling time side by side.

What it is genuinely good for

The value is not precision. It is that it makes the shape of compounding intuitive at conversational speed.

Judging a fee. This is the best use. If a portfolio grows at 7% and doubles every ten years, a 1% fee means it grows at 6% and doubles every twelve. Over forty years that is four doublings instead of three and a bit — the difference between sixteen times and roughly eleven times. Suddenly a "small" fee is visibly enormous. The expense ratio drag calculator confirms it, but the mental version is what changes behaviour.

Understanding inflation. At 3%, prices double in 24 years. Anyone planning a 30-year retirement should expect the cost of living to more than double during it. The inflation calculator puts real figures on that, and what a raise is worth after inflation covers the working-life version.

Seeing why starting early wins. The last doubling is the one that adds the most money, and you only get it by having started early enough to reach it. This single fact explains most of the advice given to young savers, and the compound interest calculator shows the curve.

Spotting nonsense. An investment promising to double in three years is claiming about 24% annually, sustained. Naming the implied rate is often enough to end the conversation.

The version for the other direction

The same arithmetic works on decline, which is less familiar and equally useful.

Divide 72 by an inflation rate and you get how long until money halves in purchasing power. At 4%, cash loses half its value in eighteen years. That reframing tends to be more motivating than a percentage, particularly for anyone holding a large cash balance for safety.

It also works for depreciation and for any recurring drag. The depreciation calculator handles the asset version properly.

What it cannot do

The rule assumes one thing: a constant rate applied to a fixed sum. Every limitation follows from that.

It ignores contributions. Most real savings involve adding money regularly, and the rule says nothing about that. The savings goal calculator handles the accumulation case.

It assumes a steady rate. Real returns vary, and the order matters once you are withdrawing. Two portfolios with the same average return can end up very far apart — the reason sequence risk exists as a concept.

It ignores tax. A taxable account does not compound at its gross rate. The rate to use is the after-tax one, which can extend the doubling time considerably.

It ignores fees, unless you subtract them from the rate first — which is exactly the adjustment that makes the fee example above so striking.

It says nothing about risk. A rate is not a promise. Dividing 72 by an expected return gives a doubling time for a scenario, not a schedule.

Used within those limits it is excellent. The rule of 72 will not tell you what your portfolio will be worth, but it will tell you, instantly and closely enough, whether a fee is worth arguing about, whether a rate of return is plausible, and how badly inflation is going to treat a pile of cash over a couple of decades. Those are three questions worth being able to answer without reaching for anything.