APR vs APY: the difference that quietly costs you money

APR and APY are both “annual percentage” something, both printed next to financial products, and both routinely mistaken for each other. The difference is not pedantic: on the same underlying rate, the two numbers diverge, and the divergence is money — paid or earned — every single year. This guide explains what each one measures, the formula that converts between them, and why the financial industry quotes savings one way and debt the other. It is educational only, not financial advice.

What is APR?

APR — annual percentage rate — is a yearly rate stated without intra-year compounding. A 12% APR billed monthly simply means 1% per month; the APR is the periodic rate multiplied by the number of periods, full stop. For consumer loans there is a second ingredient: under the Truth in Lending Act’s Regulation Z, a loan’s disclosed APR must also fold certain mandatory fees — origination charges, points, some closing costs — into the rate, so it approximates the total yearly cost of borrowing, not just the interest. That is why a mortgage’s APR is usually a little higher than its interest rate, and why a large gap between the two is worth interrogating.

What is APY?

APY — annual percentage yield — answers a different question: if this rate compounds at its stated frequency for one year, what does the balance actually grow by? It is the effective annual rate, interest-on-interest included. A savings account paying a 5% nominal rate compounded daily doesn’t grow your balance 5% in a year — it grows it about 5.13%, and 5.13% is the APY the bank advertises. Compounding is the entire difference between the two conventions; if interest is credited exactly once a year, APR and APY are the same number.

How to convert APR to APY

The conversion is one formula:

APY = (1 + r/n)^n − 1

where r is the nominal annual rate as a decimal and n is how many times per year it compounds. Here is a 6% nominal rate at increasing frequencies:

Two things to notice. The gap grows with frequency but flattens quickly — daily compounding buys only a hair more than monthly, because the formula converges toward a mathematical ceiling (continuous compounding, e^r − 1 ≈ 6.184% here). And the gap grows with the rate itself: at 2% the APR/APY difference is rounding error; at 25% it is more than two full percentage points. The mechanics behind this are covered in depth in our compound interest guide. One caution: the formula converts a nominal rate to a yield. A loan APR that already has fees baked in can’t be pushed through it to recover a “true rate” — the fee component isn’t interest.

Why banks quote APY on savings but APR on loans

Once you know APY ≥ APR for any compounding rate, the industry’s quoting habits stop looking like coincidence. Deposit products are advertised by APY — the larger number — which makes a savings rate look its best. Credit products are disclosed by APR — the smaller convention — which makes debt look its cheapest. Each side of the balance sheet leads with the figure that flatters it.

The quoting rules themselves, though, exist for a pro-consumer reason: standardization. The Truth in Lending Act(implemented as Regulation Z, 1968) forced every consumer lender to disclose cost as an APR computed the same way, so a borrower could compare two loans without reverse-engineering each lender’s fee structure. The Truth in Savings Act(implemented as Regulation DD, 1991) did the same for deposits, mandating a uniformly computed APY so “5.25% compounded daily” and “5.35% compounded annually” could be compared at a glance. Within each category the disclosures are honest and comparable. The trap is only acrosscategories: an APR and an APY are computed on different conventions, so comparing a loan’s APR directly against a savings account’s APY quietly tilts the comparison.

Credit cards: where the gap actually bites

Credit cards are the sharpest real-world example, because most cards compound daily. The issuer takes the APR, divides by 365 to get a daily periodic rate, and applies it to your balance every day — so each day’s interest is charged on a balance that already includes yesterday’s interest. A 24% APR carried for a full year is an effective rate of (1 + 0.24/365)³⁶⁵ − 1 ≈ 27.1%. The disclosed number understates the cost of carrying a balance by about three percentage points, entirely legally, because the disclosure convention is APR. (The CFPB’s consumer materials walk through how card APRs are applied in practice.)

Mortgages: where APR means something extra

On a mortgage, the APR-vs-interest-rate gap is mostly about fees, not compounding. Regulation Z requires the APR to absorb points, origination charges, and certain closing costs, amortized over the full loan term. That makes APR useful for comparing total cost between lenders — but only if you’ll actually keep the loan for its full term, since selling or refinancing early means you paid the upfront fees but never spread them over 30 years. Your monthly payment, meanwhile, is computed from the interest rate alone; our guide on reading an amortization schedule shows exactly where that rate shows up payment by payment.

The practical rules

Compare savings accounts by APY and loans by APR — within each category, the regulated disclosure is the comparable number. Never compare an APR to an APY directly; convert first with (1 + r/n)^n − 1 so both sides speak the same convention. Treat a credit card’s APR as a floor on the true cost of carrying a balance, not the cost itself. And on a mortgage, read the gap between interest rate and APR as a fee meter: the wider it is, the more you are paying upfront. None of this requires new math — just knowing which of the two questions each number is answering.