Guides · Money foundations
APR, APY, and the Rule of 72
Two accounts advertise the same rate and pay you different amounts. Nobody is lying. The gap is compounding, and once you can see it you can't unsee it.
One number that tells you how long doubling takes
Divide 72 by an annual rate and you get, roughly, the years it takes money to double at that rate. At 8%, that's 72 ÷ 8 = 9 years. At 4% it's 18. At 2% it's 36.
It's an approximation — closest between about 6% and 10% — but it's accurate enough to do in your head while somebody is still talking, which is the entire point of it.
Move the sliders below and watch where the doubling time actually moves. Going from 6% to 8% barely changes it. Going from 2% to 4% cuts it in half. Small rate differences matter most at the low end, which is the opposite of what most people expect.
Two ways of quoting one rate, and only one counts compounding
APR is the plain annualised rate: what you'd earn if interest never earned interest. APY is what you actually end up with once it does. The more often an account compounds, the further APY pulls ahead of the APR it came from.
So an APR and an APY are different units, like miles and kilometres. Comparing 5% of one against 5% of the other and calling it a tie is the mistake — the numbers look identical and the money isn't.
US banks must disclose APY on savings accounts under Regulation DD, precisely so you can put two offers side by side honestly. Lenders, meanwhile, typically quote you APR. That asymmetry is not an accident, and it's worth noticing which one you're being shown.
APY = (1 + r/n)ⁿ − 1, where r is the annual rate and n is compounding periods per year. You never need to compute it — banks publish it — but this is where the gap comes from.
The same arithmetic, running against you
Compounding has no opinion about which side of it you're on. The maths that doubles savings also doubles a debt, and card rates are far higher than savings rates.
At 22%, 72 ÷ 22 is a bit over 3 years to double — if you never paid a cent. Nobody does that, but it explains the feeling people describe as a balance that never moves: most of an early payment is going to interest, so the principal barely shifts.
This is why the usual order of operations puts high-rate debt ahead of investing. Paying off a 22% balance is a guaranteed 22% return. No investment offers that, and any that claims to is the subject of a later lesson.
APY already counts compounding; APR doesn't. Convert before you compare — and divide 72 by a rate to know how long money takes to double at it.