APR vs APY vs Interest Rate
A 22.99% card APR costs you 25.84% a year. A mortgage APR understates the cost of a loan you sell in five years. Neither is a mistake in the disclosure.
Two savings accounts sit side by side. One advertises 4.50% APR. The other advertises 4.50% APY. Deposit $10,000 in each and leave it alone for a year. The APY account pays exactly $450. The APR account, if it compounds monthly, pays $459.40. Same headline number, different money — and the account with the larger payout is the one whose advertised figure looks less impressive to anyone who does not know the difference.
That gap is small at 4.5% over one year. It is not small at 22.99% on a credit card, and it points in the opposite direction there: the number in the disclosure is lower than what you will actually pay. Understanding which rate is which, and what each one legally has to include, is the difference between comparing offers and guessing.
What each term legally means
These are not marketing words. Both are defined in federal regulation, and the definitions are not symmetrical.
Annual percentage yield (APY) is defined under Regulation DD, which implements the Truth in Savings Act, as "a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period." The regulation requires it to be rounded to the nearest one-hundredth of a percentage point. The important clause is and the frequency of compounding: APY has compounding baked in by construction. Two accounts quoting the same APY pay the same interest over a year regardless of whether one compounds daily and the other annually.
Annual percentage rate (APR) lives under Regulation Z, which implements the Truth in Lending Act. Regulation Z has separate machinery for open-end credit such as credit cards and closed-end credit such as mortgages and auto loans, with different sections governing how the rate is determined in each case and an entire appendix devoted to the closed-end computation. What APR does not do, in either case, is annualize by compounding. It annualizes by simple multiplication.
The interest rate — the "note rate" on a mortgage, the "nominal rate" on an account — is the periodic rate multiplied out to a year with no compounding and no fees at all. It is the rawest of the three numbers and by itself tells you almost nothing about cost.
Compounding frequency is the whole gap
For a given nominal rate, APY rises with compounding frequency, and it rises faster the higher the rate. Here is the same nominal rate converted to effective annual yield at three frequencies:
| Nominal rate | Compounded annually | Compounded monthly | Compounded daily |
|---|---|---|---|
| 5.00% | 5.000% | 5.116% | 5.127% |
| 4.50% | 4.500% | 4.594% | 4.603% |
| 22.99% | 22.990% | 25.574% | 25.838% |
| 24.99% | 24.990% | 28.061% | 28.379% |
Two things jump out. First, the jump from annual to monthly compounding captures nearly all of the effect; going from monthly to daily adds very little. At 5%, monthly compounding adds 11.6 basis points and daily adds only one more. Anyone marketing "daily compounding!" as a differentiator over monthly is selling you a rounding error.
Second, the gap explodes at high rates. At 5% the spread between nominal and daily-compounded effective is 0.13 percentage points. At 22.99% it is 2.85 percentage points — more than twenty times larger. Compounding is a convexity effect, and convexity does not scale linearly.
Why your card's APR understates what carrying a balance costs
A credit card issuer typically converts the disclosed APR to a daily periodic rate by dividing by 365, then applies that rate to the balance each day. At a 22.99% APR the daily periodic rate is about 0.062986%. Because yesterday's interest is part of today's balance, the arithmetic compounds.
Carry $5,000 for a full year with no payments and no new charges. Simple interest at 22.99% would be $1,149.50. Daily compounding produces $1,291.92 — $142.42 more, an effective rate of 25.84%. The disclosed APR is accurate as a disclosure and understates your actual annual cost by nearly three percentage points, because that is what the disclosure standard is: an annualized periodic rate, not an effective yield.
There is a second asymmetry worth knowing. For closed-end credit, Regulation Z requires certain fees to be folded into the APR, which is why a mortgage's APR usually exceeds its note rate. For a credit card, the disclosed APR is essentially the periodic rate annualized; an annual fee is disclosed separately rather than rolled in. So a 22.99% card APR and a 6.46% mortgage APR are not the same kind of number, and stacking them in a spreadsheet as if they were is a category error.
The mortgage APR trap nobody mentions
Here is the claim most rate comparisons will not make: a mortgage's disclosed APR systematically understates the cost of a loan you do not hold to maturity, and most people do not hold to maturity.
Work it through. Borrow $300,000 on a 30-year fixed at a 6.25% note rate with $6,500 in finance-charge fees. The monthly principal and interest payment is $1,847.15. Spreading those fees across all 360 payments gives a disclosed APR of about 6.46%. That figure is correct, and it is genuinely more useful than the note rate for comparing two 30-year offers.
But suppose you sell or refinance after five years, which is closer to typical behavior than holding for three decades. The balance at that point is $280,011.72. Solve for the rate that equates your $293,500 in net proceeds with sixty payments plus that payoff, and the effective annual cost is 6.78% — a third of a percentage point above the disclosed APR, because the same $6,500 in fees was amortized over five years of use rather than thirty.
The practical consequence: when comparing a low-rate-with-points offer against a higher-rate-no-points offer, APR tilts the comparison toward paying points, because it assumes you will be around long enough to recover them. If your realistic horizon is five to seven years, model both loans over that horizon with the Loan Payment Calculator rather than letting the APR column decide.
Where the difference is genuinely noise
Not every version of this distinction is worth your attention, and pretending otherwise is how financial content wastes people's time.
- Small balances at moderate rates. On $2,000 held for one year at 5%, the difference between annual and monthly compounding is $2.32. Choosing a bank over that is not a decision, it is a hobby.
- Monthly versus daily compounding, at any rate under about 6%. Roughly one basis point of difference. Ignore it.
- Any account you will not hold for long. Compounding is a function of time; over three months the effect is a quarter of an already-small annual number.
And where it genuinely matters: revolving debt at 20% or more, where three points of effective rate is real money every month; long-horizon accumulation, where a small annual difference compounds for decades (run it through the Compound Interest Calculator over thirty years and the gap stops being cosmetic); and any comparison where one institution quotes APY and the other quotes a nominal rate, because that is not a fair fight.
The rule that resolves all of it
Compare like to like. On deposits, insist on APY, which is what Regulation DD requires be disclosed for exactly this reason — the standard exists so consumers can compare accounts without doing compounding arithmetic themselves. On loans, compare APR to APR, but only within the same product type and only over a holding period you actually expect. If a lender quotes a nominal rate on savings, convert it before comparing, and use the Savings Goal Calculator with the effective figure rather than the headline one.
None of this is a claim that disclosure rules are misleading. They are unusually well designed, and both APY and APR do real work in making offers comparable. The failure mode is assuming that a number designed to be comparable within its own category is also comparable across categories, or that a disclosure computed under one set of assumptions applies when your behavior differs from those assumptions. It usually does not.
Related tools
- Loan Payment Calculator — model payments and total cost over your real holding period
- Compound Interest Calculator — change the compounding frequency and watch the effective rate move
- Savings Goal Calculator — plan contributions using an effective annual yield
Sources and further reading
Figures and definitions on this page are drawn from the following primary sources. If you find something out of date, tell us and we will correct it.