The Rule of 72: The Only Compound Interest Maths You Need in Your Head

Compound interest is the one piece of financial mathematics that genuinely changes decisions, and almost nobody can do it in their head.

The rule of 72 is the shortcut. Divide 72 by an annual percentage rate and you get the number of years for the amount to double.

At 6%, money doubles in 12 years. At 8%, in 9. At 3%, in 24. At 12%, in 6.

That is the whole rule, and it is accurate enough for nearly every decision you will use it for.

Why it works

Doubling means growing by a factor of 2, so you need the number of years where (1 + r)^n = 2. Taking logarithms gives n = ln(2) / ln(1 + r).

For small rates, ln(1 + r) is approximately r, and ln(2) is 0.693. So n is roughly 69.3 divided by the rate expressed as a percentage.

The number 72 is used instead of 69.3 for two reasons. It corrects slightly for the approximation at typical rates, making the answer more accurate in the range people actually use. And it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which is the entire point of a mental shortcut.

Accuracy is within about 1% for rates from 4% to 12%, and within a few percent from 1% to 20%. Beyond that it drifts, and 69.3 becomes the better numerator for continuously compounded rates.

Four things to point it at

Savings and investments. At a 7% long-run real return, money doubles roughly every 10 years. Someone investing at 25 gets four doublings by 65: a 16-fold increase. Starting at 35 gets three: 8-fold. That single decade of delay halves the outcome, and the rule of 72 makes this obvious in about five seconds, which no amount of general advice about starting early manages to do.

Debt. A credit card at 24% doubles the balance in three years if you pay nothing. A payday loan at 400% doubles it in about ten weeks. Seeing the doubling time is far more visceral than seeing the APR, which is exactly why it is worth converting.

Inflation. At 3%, prices double in 24 years. This is why costs from your childhood sound absurd and why fixed pensions decay. Someone retiring at 65 with an unindexed income will see its buying power roughly halve by 89 at 3% inflation, which is not an unusual lifespan.

Fees. This is the one people miss. A 1% annual fund fee does not cost you 1%. Over decades it changes the effective growth rate, and the rule shows the consequence: at a 7% return money doubles every 10.3 years, but at 6% after fees it takes 12 years. Over 40 years that is roughly one fewer doubling, which means ending with about a third less. For one percentage point.

The reverse direction

Divide 72 by the years you have and you get the rate you need.

Want to double your money in 8 years? You need about 9% a year. In 5 years? About 14.4%, which should immediately prompt scepticism about anything promising it safely.

This is a useful nonsense detector. Any investment promising to double your money in two years is claiming a 36% annual return. That is not impossible, but it is far outside what any reliable asset delivers, and the claim should be treated accordingly.

Related rules

The rule of 114 gives tripling time. At 6%, money triples in 19 years.

The rule of 144 gives quadrupling, which is just two doublings. At 6%, 24 years.

The rule of 70 is the more accurate version for low rates and continuous compounding, and it is what demographers use for population growth and physicists for exponential processes generally.

The real lesson

The rule of 72 is a party trick. What it is for is making exponential growth intuitive, and human intuition about exponential growth is famously terrible.

We think linearly. Told something grows at 7% a year, we imagine a gentle slope. The reality is that it doubles, then doubles again, then again, and the last doubling adds more than everything that came before it combined.

That is why compound interest sounds boring and turns out to be decisive. And it is why one rate that sounds nearly identical to another, 6% against 7%, produces outcomes that differ by half over a working life.

Twenty seconds of division makes that visible. Almost nothing else in personal finance offers a better return on that little effort.