The simple version

Annual percentage rate appears on credit products. Annual percentage yield appears on deposit products. Both are expressed as a percentage per year, which makes them look interchangeable.

They are computed differently. Annual percentage yield reflects the effect of compounding within the year, meaning interest earning interest. Annual percentage rate generally does not incorporate that effect in the same way, which means the two numbers describe different things even when they are the same size.

The numbers

• Regulation Z, which implements the Truth in Lending Act, states that the annual percentage rate is a measure of the cost of credit, expressed as a yearly rate, that relates the amount and timing of value received by the consumer to the amount and timing of payments made (Consumer Financial Protection Bureau, 12 CFR 1026.22)
• Regulation DD, which implements the Truth in Savings Act, states that annual percentage yield means 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 (Consumer Financial Protection Bureau, 12 CFR 1030.2)
• Regulation DD defines a deposit account's interest rate as the annual rate of interest paid on an account which does not reflect compounding, and permits that rate to also be referred to as the annual percentage rate in account disclosures (Consumer Financial Protection Bureau, 12 CFR 1030.2)
• For open-end credit such as credit cards, Regulation Z states that the annual percentage rate is determined by multiplying the periodic rate by the number of periods in the year (Consumer Financial Protection Bureau, 12 CFR 1026.14 and its official commentary)
• Regulation Z states its purpose as promoting the informed use of consumer credit by requiring disclosures about its terms and cost; Regulation DD states its purpose as enabling consumers to make informed decisions about accounts at depository institutions (Consumer Financial Protection Bureau, 12 CFR 1026.1 and 12 CFR 1030.1)
• Regulation DD applies to depository institutions except for credit unions, which follow the National Credit Union Administration's parallel Truth in Savings rule (12 CFR 1030.1; 12 CFR part 707)
• Stated hypothetical, our arithmetic: a nominal rate of 12 percent compounded once a year is 12.00 percent for the year. Compounded monthly it accumulates to about 12.68 percent, and compounded daily to about 12.75 percent, because each period's interest earns interest in the periods that follow (arithmetic; hypothetical figures, not any product's rate)

What compounding does to a number

Compounding is interest earning interest. If a balance earns interest monthly, the second month's interest is calculated on a slightly larger balance, because the first month's interest was added to it.

Over a year that produces a total larger than the simple rate would suggest. A rate quoted without accounting for compounding describes the rate applied at each period. A yield accounting for it describes what actually accumulates across the year. Regulation DD draws exactly that line: the interest rate on a deposit account does not reflect compounding, and the annual percentage yield does.

That is the entire difference, and it means the gap between the two grows with how frequently compounding occurs. In the stated hypothetical above, 12 percent compounded annually is 12 percent, compounded monthly it is about 12.68 percent, and compounded daily it is about 12.75 percent. Compounded annually, the two figures are the same. Compounded monthly or daily, they diverge.

The credit side is built the other way. For a credit card, Regulation Z computes the disclosed annual percentage rate by multiplying the periodic rate by the number of periods in the year, which is the simple annualization that leaves compounding out. Neither is a more honest number. They answer different questions, they are required by different laws, and both are disclosed exactly as those laws specify.

Two laws, two disclosures

The reason these are separate measures rather than one is that they come from separate statutes addressing separate problems.

The Truth in Lending Act governs credit disclosure, so that a borrower can compare the cost of borrowing across lenders on a common basis. We covered what that standardization is for in the piece on converting a payday fee to an annual rate. Its measure is built for comparing what credit costs.

The Truth in Savings Act governs deposit disclosure, and Regulation DD states its purpose as enabling consumers to make informed decisions about accounts at depository institutions. Its measure is built for comparing what deposits earn, which is why it incorporates compounding: what a saver actually receives depends on how often interest is credited.

Each measure is standardized within its own domain. Neither was designed to be compared against the other, which is exactly what people do when they put a loan rate and a savings rate side by side. Regulation DD even permits a deposit account's non-compounded interest rate to be labeled annual percentage rate in account disclosures, which is one more reason the abbreviation alone does not settle what a number is.

The Real Cost lens on comparing like with like

The practical value is knowing which comparison is valid. Every figure in this article is a stated hypothetical.

• Comparing one credit product's annual percentage rate to another credit product's is valid, because the measure was standardized for exactly that
• Comparing one deposit account's annual percentage yield to another's is equally valid for the same reason
• Comparing a credit product's rate to a deposit account's yield is not a like comparison, because the two figures are constructed differently
• The more frequently interest compounds, the further a yield figure sits from the underlying nominal rate, which is why compounding frequency appears in disclosures at all

None of that says anything about which products anyone should use, which depends on circumstances no article can assess. It is a statement about which numbers can be placed next to each other.

What this means

When a rate appears on a financial product, the abbreviation attached to it tells you which measure it is and therefore what it can be compared against. Both are required disclosures with defined meanings, and the definitions are published.

The broader habit is checking that two numbers were constructed the same way before comparing them. Standardized disclosures make comparison possible within a category and create a trap across categories, because the standardization is what makes them look alike.

What this is NOT

This is not advice about borrowing, saving, or choosing any product, and no institution, lender, or product is named. This is not a comparison of any real products' rates. This is not a claim that either measure is more accurate or more favorable: each is standardized for its own purpose under its own law. This is not a statement of any product's terms, which are in that product's own disclosures. The rate figures are stated hypotheticals used to show the arithmetic. This is not investment or financial advice of any kind.

Sources

• Consumer Financial Protection Bureau, Regulation Z, 12 CFR 1026.22, determination of annual percentage rate (the definition of the annual percentage rate as a measure of the cost of credit): https://www.consumerfinance.gov/rules-policy/regulations/1026/22/
• Consumer Financial Protection Bureau, Regulation Z, 12 CFR 1026.14, determination of annual percentage rate for open-end credit (periodic rate multiplied by the number of periods in the year): https://www.consumerfinance.gov/rules-policy/regulations/1026/14/
• Consumer Financial Protection Bureau, Regulation Z, 12 CFR 1026.1, purpose: https://www.consumerfinance.gov/rules-policy/regulations/1026/1/
• Consumer Financial Protection Bureau, Regulation DD, 12 CFR 1030.2, definitions (annual percentage yield and interest rate): https://www.consumerfinance.gov/rules-policy/regulations/1030/2/
• Consumer Financial Protection Bureau, Regulation DD, 12 CFR 1030.1, purpose and coverage: https://www.consumerfinance.gov/rules-policy/regulations/1030/1/
• National Credit Union Administration, 12 CFR part 707, Truth in Savings (the parallel rule for credit unions): https://www.ecfr.gov/current/title-12/chapter-VII/subchapter-A/part-707