Banks often quote the annual percentage rate when you apply for a loan, but this figure ignores the effect of compound interest and therefore could be misleading. In comparison, the annual percentage yield offers a true representation of the interest you pay by factoring in periodic compounding.
Annual Percentage Rate
APR refers to the interest rate on a loan and ignores the effect of compounding. Multiplying the period interest rate by the number of periods in a year produces the APR. However, the result does not accurately depict the interest you encounter unless no compounding occurs, which might be the case when you pay off accumulated interest each period. If interest compounds, then APY provides a more realistic estimation of interest you pay.
Annual Percentage Yield
You'll encounter APY when discussing investment options, such as savings accounts or mutual funds. However, loans and investments are two sides of the same coin, because your loan is also an investment for the bank -- the APY the bank receives comes from the interest you pay. To fully appreciate the loan you are offered, you need to consider the APY and not just the APR.
As part of the Truth in Lending Act, financial institutes must fully disclose the terms of your loan, including how interest is calculated. The loan documents provide the necessary data for the calculation, for which you'll need to know how often interest is compounded and the periodic interest rate. You can also calculate the periodic interest rate by dividing the APR by the number of compounding periods in a year. As an example, if the interest on your credit card compounds daily with a 21.9 percent APR, divide 21.9 by 365 days to get the daily interest rate of 0.06 percent.
Calculating the APY
Divide the periodic interest rate by 100 to convert it to decimal format and then add 1. Raise the result to the number of compounding periods in a year and then subtract 1 to calculate the APY in decimal format. Multiply by 100 to convert it to a percentage. To continue with the example, divide 0.06 by 100 to get 0.0006 and then add 1. Raise the resulting 1.0006 to the power of 365 to get 1.2447. Subtract 1 to get 0.2447 and divide by 100 to find the APY of 24.47 percent.
- Bank Rate: What's the Difference Between APR and APY?
- Experian. "What Is APR and How Does It Affect Me?" Accessed Sept. 15, 2020.
- Inc. “Why Einstein Considered Compound Interest the Most Powerful Force in the Universe.” Accessed Sept. 15, 2020.
- Corporate Finance Institute. “What is the Compound Interest Formula?” Accessed Sept. 15, 2020.
- Corporate Finance Institute. “What is the Annual Percentage Yield?” Accessed Sept. 15, 2020.
- Office of the Comptroller of the Currency. "Truth in Lending." Accessed Sept. 15, 2020.
- American Express. "APY vs. APR: The Basics About How Interest Is Calculated." Accessed Sept. 15, 2020.