APR versus APY

U.S. consumer financial law requires banks to quote two different annualised rates depending on the product. For credit, the disclosure is the Annual Percentage Rate (APR), required by Regulation Z under the Truth in Lending Act. For deposits, the disclosure is the Annual Percentage Yield (APY), required by Regulation DD under the Truth in Savings Act. The two rates are computed differently and convey different information. Understanding the difference is a prerequisite to comparing products.

This article explains how each rate is defined, what it does and does not include, how compounding converts the nominal rate into the disclosed rate, and where the two rates can be misleadingly close or far apart.

APR: the cost of credit

The Annual Percentage Rate is a measure of the cost of credit, expressed as a yearly rate. For closed-end credit (a mortgage, an auto loan, a personal loan), APR is computed under Appendix J to Regulation Z as the rate that, applied to the amount financed using a standard actuarial formula, produces the disclosed finance charge over the term of the loan. The finance charge includes interest and most fees that are a condition of obtaining the credit — origination fees, points, mortgage broker fees, certain insurance premiums — but excludes certain other charges defined in the regulation.

For open-end credit (a credit card or a HELOC), APR is computed differently: the periodic rate (for example, the daily periodic rate of 0.0479%) is multiplied by the number of periods in a year (365) to produce the disclosed APR (17.50%). Open-end APR does not reflect compounding within the year, even when the underlying balance does compound; this is a deliberate feature of the disclosure, designed to give consumers a directly comparable number across cards.

For a closed-end mortgage, the APR is meaningfully higher than the contract rate (the "note rate") because the upfront fees are amortised over the term of the loan. A 30-year fixed mortgage at a 6.50% note rate with $4,000 in finance-charge-included closing costs on a $300,000 loan might disclose an APR of around 6.62%. The APR provides a single comparison number that captures both the rate and the upfront costs, although the comparison breaks down if the borrower prepays — the upfront cost is then spread over fewer years, raising the effective APR.

For a credit card, the APR appears in the Schumer box on every solicitation and on every monthly statement. A card may have multiple APRs: one for purchases, one for cash advances, one for balance transfers, and possibly a separate penalty APR triggered by late payment. Variable-rate cards (the typical structure) reference an index — usually the prime rate published in the Wall Street Journal — plus a margin; when the index moves, the APR adjusts within the next billing cycle.

APY: the yield on a deposit

The Annual Percentage Yield, required by Regulation DD, is the rate at which a deposit would grow over a year given the bank's stated nominal interest rate and its compounding frequency. The calculation formula is in Appendix A to 12 CFR Part 1030; for a deposit with a constant balance compounded n times per year at a periodic rate of r/n, the APY is:

APY = (1 + r/n)n − 1

Three numerical examples make the relationship concrete. A 5.00% nominal rate compounded annually produces an APY of 5.00% (no compounding effect over a single year). A 5.00% nominal rate compounded monthly produces an APY of 5.12%. A 5.00% nominal rate compounded daily produces an APY of 5.13%. As compounding frequency rises toward continuous, the APY converges on e^0.05 − 1, or about 5.1271%. For practical retail purposes, daily compounding is essentially continuous; the difference between daily and continuous is in the fourth decimal place.

Two important asymmetries between APR and APY follow from this construction.

First, APY does reflect compounding, while APR (in the open-end credit context) does not. A credit card with an 18.00% APR compounded daily has an effective annual yield (to the issuer) of about 19.72% — the disclosed APR understates the actual cost to a borrower who carries a balance for a full year. This is a regulatory choice, defended on the grounds that the APR is meant to be directly comparable across cards, and that all U.S. cards use the same daily-compounding convention so the APR is in fact comparable in practice.

Second, APY is calculated for a deposit assumed to remain in the account for the full year. A deposit that is withdrawn before a full year, or one that has an introductory bonus rate followed by a lower ongoing rate, may not actually produce the disclosed APY. Regulation DD addresses this by requiring that the disclosed APY be based on the deposit's actual terms, including any tiered structure or introductory promotion, and that the disclosure clearly indicate any rate change after a defined period. APY is the disclosed-yield convention; what you earn depends on what actually happens with the deposit.

APY Earned: the after-the-fact number

Periodic statements for an interest-bearing deposit account must disclose the "APY Earned" for the statement cycle: the actual yield expressed as a yearly rate based on the actual interest paid and the days in the cycle. APY Earned can differ from the APY disclosed at account opening for several reasons: the bank may have changed the rate, the customer's balance may have moved through rate tiers, fees may have been deducted from interest, or the account may have been open for only part of the cycle. APY Earned is the canonical number for checking whether the bank actually paid what it promised; APY is the canonical number for comparison across products.

How the two rates differ in use

For deposits, APY is the comparison number. A bank advertising a 5.00% APY savings account is committing to a yield that includes the effect of compounding; a depositor comparing two savings accounts can directly compare APYs. The nominal rate without compounding information is, by itself, not enough information to determine the actual yield.

For closed-end credit (mortgages, auto loans), APR is the comparison number. It combines the rate and the upfront costs into a single figure that allows direct comparison across loans of the same term and structure. A 6.50% APR mortgage from one lender is, in principle, the same cost over the full term as a 6.50% APR mortgage from another, even if the upfront fee structures differ.

For open-end credit (credit cards, HELOCs), APR is the comparison number, but it does not capture the compounding effect; a borrower planning to carry a balance for a full year would want to compute the implied effective annual rate from the daily periodic rate, which is the more accurate measure of cost. For a transactor (a borrower who pays the statement balance in full each month within the grace period), the APR is largely irrelevant because no interest accrues; what matters then is the fee structure (annual fee, foreign-transaction fee) and the rewards-program details.

Truth in Lending and Truth in Savings in detail

The legal authority for the two disclosures lives in separate statutes. APR is required by the Truth in Lending Act and implemented by Regulation Z; APY by the Truth in Savings Act and implemented by Regulation DD. The two statutes were enacted decades apart (TILA in 1968, TISA in 1991) and reflect different policy concerns: TILA's purpose was to make credit costs comparable across lenders by forcing them into a single yearly-rate convention; TISA's purpose was to do the same for deposit yields, after the deregulation of deposit rates in the early 1980s produced wide variation in how banks advertised yields.

Both statutes empower the CFPB (since the 2011 transfer of authority from the Federal Reserve under Dodd-Frank) to write and enforce the implementing rules. Both regulations contain detailed methodologies in their appendices; both have been the subject of many years of interpretive guidance and enforcement.

Edge cases

A handful of common product structures produce rates that need careful reading:

• Promotional CDs. A bank may advertise a CD with a 5.00% APY for a "special" 7-month term, while the same bank's standard 6-month and 12-month CDs pay materially less. The disclosure must reflect the actual term and the actual rate; any rate change after the promotional period must be flagged.
• Tiered savings rates. A money market deposit account may pay 4.50% on balances below $100,000 and 4.75% above. The disclosed APY must reflect the tier structure; the actual APY Earned depends on which tier the average balance falls in during the cycle.
• Introductory credit-card APRs. A 0% APR for 12 months followed by a 22.99% standard APR is disclosed under Regulation Z with both rates and the date of the change. Promotional balance transfers are subject to the same disclosure.
• Mortgage APR with discount points. A 6.25% note rate purchased down by 1.5 points produces a lower APR than the same loan without points, because the upfront point cost is part of the finance charge and the lower note rate produces less interest over the term. The APR comparison correctly reflects the trade-off only if the borrower keeps the loan to maturity; for borrowers who prepay early, the APR-with-points understates the effective cost.

Limits and uncertainty

The APR-versus-APY distinction is durable; the underlying calculation methodologies have been stable for decades. What changes more often is the regulatory treatment of specific fees: which fees count toward the APR finance charge, what disclosures are required on what timeline, how penalty APRs are restricted. The CARD Act of 2009 substantially restricted credit-card APR changes; recent CFPB rulemaking has addressed credit-card late fees. Where this article cites a specific computational treatment, it is based on the current rule; readers should check the relevant regulation for any specific fee or charge they are trying to attribute to APR or APY.