Guides · Money foundations
APR, APY, and the Rule of 72
Two accounts advertise 'the same rate' and pay different amounts. The gap is compounding, and it's the single most important piece of math in this entire app.
Two ways to quote the same rate
APR is the simple annualized rate — the rate before you count the fact that interest itself earns interest. APY is what you actually end up with once compounding is included.
The formula is APY = (1 + r/n)^n − 1, where r is the annual rate and n is how many times a year it compounds. The more often it compounds, the further APY pulls ahead of APR.
US banks must disclose APY on savings accounts under Regulation DD precisely so you can compare offers on the same footing. Lenders, meanwhile, typically quote you APR. That asymmetry is worth noticing.
An APR and an APY are different units. Convert to APY before comparing two offers.
The Rule of 72
Divide 72 by the annual rate and you get, roughly, the number of years it takes money to double. At 8%, that's 72 ÷ 8 = 9 years.
It's an approximation — most accurate between about 6% and 10% — but it's accurate enough to do in your head while someone is talking, which is the entire point of it.
Move the sliders below. Watch how little the doubling time changes between 6% and 8%, and how much it changes between 2% and 4%. Rate differences matter most at the low end, which is the opposite of most people's intuition.
The same math, running against you
Compounding has no opinion about which side you're on. The arithmetic that doubles savings also doubles a debt, and credit card rates are far higher than savings rates.
At a 22% APR, 72 ÷ 22 is about 3.3 years to double — if you never paid a cent. Nobody actually does that, but it explains why a balance you're making minimum payments on can feel like it never moves: most of each payment is going to interest.
This is why the order of operations in personal finance usually puts high-rate debt ahead of investing. You're comparing a guaranteed 22% against a hoped-for 8%.
APY includes compounding, APR doesn't. Rule of 72: divide 72 by the rate to get years to double.