Differences between Annual Percentage Rate and Annual Percentage Yield
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Annual percentage rate vs. Annual percentage yield[edit]
In financial services, annual percentage rate (APR) and annual percentage yield (APY) are two standard methods for calculating and expressing interest over a one-year period. While both terms describe interest, they serve different functions in the context of borrowing and saving. The primary distinction between the two is that APR represents simple interest, whereas APY accounts for the effects of compounding interest.[1]
Comparison table[edit]
| Category | Annual percentage rate (APR) | Annual percentage yield (APY) |
|---|---|---|
| Primary application | Loans, credit cards, and mortgages | Savings accounts, CDs, and investments |
| Compounding | Does not include compounding | Includes compounding |
| Calculation basis | Simple interest + fees | Compound interest |
| Relative value | Usually lower than APY | Usually higher than APR |
| U.S. Regulation | Truth in Lending Act (TILA) | Truth in Savings Act (TISA) |
| Goal for consumer | Lower rate is better for the borrower | Higher rate is better for the saver |
| Inclusions | Includes interest and upfront fees | Primarily reflects interest earned |
APR and borrowing[edit]
Lenders use APR to disclose the cost of credit to consumers. Under the United States Truth in Lending Act of 1968, creditors must provide the APR in a clear, standardized format before a loan agreement is signed.[2] This requirement allows borrowers to compare different loan products on equal terms.
In many lending scenarios, such as mortgages or auto loans, the APR is higher than the base interest rate. This is because the APR calculation incorporates additional costs of borrowing, such as loan processing fees, mortgage insurance, and discount points. Because APR does not factor in the compounding of interest during the year, it may understate the total amount of interest a borrower pays on a revolving balance, such as a credit card.
APY and savings[edit]
APY is the standard measure used by banks and financial institutions to show the potential return on deposit accounts. The Truth in Savings Act of 1991 requires the disclosure of APY on consumer savings products to prevent misleading advertisements.[3]
The frequency of compounding—whether daily, monthly, or quarterly—determines the difference between the nominal interest rate and the APY. When interest is added to the principal balance more frequently, the earner receives interest on the previously earned interest in subsequent periods. This cumulative effect means that as the frequency of compounding increases, the APY also increases. For example, a 5% nominal interest rate compounded monthly results in a 5.116% APY, while daily compounding results in a 5.127% APY.
Mathematical relationship[edit]
The mathematical relationship between these two figures is defined by the compounding frequency. The formula to convert a periodic interest rate into APY is:
APY = (1 + r/n)^n - 1
In this formula, "r" represents the stated annual interest rate (or APR) and "n" represents the number of compounding periods per year. If interest compounds only once per year, the APR and APY are identical. In any other scenario where interest compounds more than once annually, the APY will always be higher than the APR. Financial institutions often advertise the APR for loans to make the debt appear less expensive and the APY for savings accounts to make the returns appear more lucrative.[4]
References[edit]
- ↑ Investopedia. (2024). "APR vs. APY: What's the Difference?"
- ↑ Consumer Financial Protection Bureau. "What is the difference between a mortgage's interest rate and its APR?"
- ↑ Federal Reserve Bank of San Francisco. "What is the difference between APR and APY?"
- ↑ Office of the Comptroller of the Currency. "Answers about Interest Rates and APY."
