APR vs APY — what does the difference actually cost?
APR is the nominal rate, ignoring compounding within the year. APY is the effective rate, including it. A card at 22% APR compounded monthly has an APY near 24.4% — that higher figure is what you actually pay.
Updated 2026-08-24
Two rates describing the same money
APR is the annual percentage rate. It is a nominal figure: the periodic rate multiplied by the number of periods in a year. A card charging 1.8333 percent a month quotes 22 percent APR, because 1.8333 times twelve is 22.
APY is the annual percentage yield, sometimes called the effective annual rate. It answers a different question: if this account compounds throughout the year, what single annual rate applied once would produce the same result? For that same card, the answer is closer to 24.4 percent.
The gap exists because interest charged in month one joins the balance that month two charges interest on. Multiplying the monthly rate by twelve ignores that entirely — it prices twelve independent months rather than twelve months where each builds on the last. APY prices the compounding in.
Both numbers are honest descriptions of the same arrangement. They are simply answers to different questions, and quoting one when the reader is thinking about the other is where the confusion — and occasionally the marketing — lives.
Which one gets quoted, and why
There is a reliable pattern. Lenders quote APR. Savings accounts quote APY. In both cases the institution is quoting the number that looks better from their side of the transaction.
For borrowing, APR is the smaller figure, so a card advertises 22 percent APR rather than 24.4 percent APY. For saving, APY is the larger figure, so a deposit account advertises 5.12 percent APY rather than 5 percent APR. Neither is a lie; both are a choice.
This makes direct comparison between products genuinely difficult, and that difficulty is not accidental. Comparing a loan quoted in APR against a loan quoted in APY is comparing two different measurements. Before choosing between anything, convert both to the same basis — normally APY, since it reflects what actually happens.
Regulation helps in places. Consumer credit disclosure rules in many countries require APR to include certain fees as well as interest, so a quoted APR on a mortgage may already be higher than the headline interest rate. That is a different adjustment from compounding, and the two are easy to conflate: a fee-inclusive APR still does not tell you the effective rate.
How much the frequency changes things
Compounding more often increases the effective rate, but the effect is heavily front-loaded and flattens fast — which surprises people who assume daily compounding is dramatically worse than monthly.
Take 12 percent nominal. Compounded annually, the APY is 12 percent exactly. Semi-annually, 12.36. Quarterly, 12.55. Monthly, 12.68. Daily, 12.747. Continuously — the mathematical limit — 12.749. The step from annual to monthly is worth 0.68 points; every further increase in frequency together is worth about 0.07.
The gap also widens with the rate itself. At 3 percent nominal, monthly compounding produces an APY of about 3.04 — a rounding error. At 24 percent it produces about 26.8, which on a five thousand balance is a difference of well over a hundred a year. Compounding frequency barely matters on a savings account and matters considerably on credit card debt.
The practical rule follows: compare effective rates and then stop thinking about frequency. Once you are looking at APY, the compounding interval has already been accounted for, and continuing to worry about it is double-counting.
Converting between them
The conversion is arithmetic rather than approximation, and worth knowing because it turns two incomparable quotes into one comparison.
To get APY from APR, divide the APR by the number of compounding periods, add one, raise to the power of that number, and subtract one. Written out: APY = (1 + APR ÷ n)ⁿ − 1. At 22 percent compounded monthly, that is (1 + 0.22 ÷ 12)¹² − 1, which comes to about 24.36 percent.
To go the other way, take the APY, add one, raise it to the power of one over n, subtract one, and multiply by n: APR = n × ((1 + APY)^(1÷n) − 1). An account advertising 5.12 percent APY compounded monthly is quoting a nominal rate of about 5 percent.
A rough shortcut for small rates: the gap between APR and APY is approximately the APR squared, divided by two, times a factor slightly under one. At 5 percent that predicts about 0.12 points, and the true answer is 0.12. At 22 percent the approximation breaks down badly, which is a useful reminder that the error grows exactly where the money does.
Where it actually costs you
For most savings decisions the distinction is small enough to ignore. At five percent, the difference between nominal and effective is around a tenth of a point — real, but not decision-changing on any ordinary balance.
On credit card debt it is substantial and permanent. A 22 percent APR card is charging an effective 24.4 percent, so a five thousand balance carried for a year accrues roughly twelve hundred and twenty rather than eleven hundred. Over the multi-year payoff periods that minimum payments produce, that difference compounds into a meaningful sum, and it never appears on a statement as a separate line.
It also distorts comparisons between structurally different products. A personal loan quoted at 14 percent APR compounded monthly has an effective rate near 14.9. A credit card quoted at 15 percent APY is genuinely cheaper despite the larger headline number. Choosing on the headline picks the worse product roughly whenever the two are quoted on different bases.
The habit worth building is simply to ask which one is being quoted, and to convert before comparing. It is two questions and one calculation, and it is the difference between comparing products and comparing the way products describe themselves.