*The Business Professor*, updated September 5, 2019, last accessed May 31, 2020, https://thebusinessprofessor.com/lesson/annual-percentage-yield-definition/.

Back to: ECONOMICS, FINANCE, & ACCOUNTING

### Annual Percentage Yield Definition

This refers to the effective annual interest rate using compound interest. Any is mathematically denoted as:

**APY = (1+r/n) * n-1**

### Understanding Annual Percentage Yield (APY)

Similar to the annual percentage rate (APR), the APY is used for calculating the interest rates for loans, credit cards, and investments. However, the APY, unlike the APR, focuses on compounding interests rather than account fees. This method is crucial to measuring varying interest rate and turning them into percentages for loan and investment agreements.

### Differences between APY and Rate of Return

Rate of Return is the amount of an investment’s growth over a given period of time. It is mostly denoted as a percentage of the initial capital. Rate of return has different difficulties calculating the interest rate of various investments, especially due to compounding. This is where the APY comes in, as it can easily calculate compounding interest without errors.

### How Annual Percentage Yield is Calculated

Let us assume that you wish to invest in a 2-year zero-coupon note with returns of 9.6% when it gets to maturity. You also have another option of investing in a high-risk money market that gives 0.8% with compounding interest on a monthly basis.

Merely looking at both investments, there are equal, since 0.8% monthly for one year is equal to 9.6%. However, when compounding interest is used, we can see that the second investment would yield a higher interest using the APY formula.

An investment offering an interest rate of 9.6% per year, with daily compounding interest would be bigger than one that offers such yield once a month or once a year. This is because a new percentage is added to the 9.6% each day, unlike that of monthly (which gets an increase once in a month), and yearly (which gets an increase per annum).

### Reference for “Annual Percentage Yield – APY”

https://www.investopedia.com/terms/a/apy.asp

https://www.thebalance.com › … › Banking and Loans › Certificates of Deposit

financeformulas.net/Annual_Percentage_Yield.html

https://en.wikipedia.org/wiki/Annual_percentage_yield

https://www.omnicalculator.com/finance/apy

### Academics research on “Annual Percentage Yield – APY”

Computing **yields **on enhanced CDs, **Brooks, R. (1996). Computing yields on enhanced CDs. ***Financial services review***, ***5***(1), 31-42. **In this paper, we seek to provide a framework for comparing certificates of deposit (CD) products that vary in their features. There are now fixed-rate CDs with no early withdrawal penalties as well as floating-rate CDs with guaranteed floors. With the model developed here, we examine the required change in the effective annual rate required in basis points to make CD products with embedded derivatives (called enhanced CDs) comparable with the standard CD products (ones with large early withdrawal penalties). This framework is beneficial for both retail customers seeking to make rational comparisons and bank executives seeking to provide optimal liability products and seeking to manage the resulting interest rate risk.

Truth in Saving, **Morse, R. L., & Fasse, W. R. (1973). Truth in Saving. ***Journal of Consumer Affairs***, ***7***(2), 156-164.**

Modified duration and convexity with semiannual compounding, **Cole, C. S., & Young, P. J. (1995). Modified duration and convexity with semiannual compounding. ***Journal of Economics and Finance***, ***19***(1), 1. **Both duration and convexity are a function of the curvilinear bond price: yield relationship. While duration measures the slope of the price:yield curve at a given yield-to-maturity, convexity measures the change in duration at this yield-to-maturity. Three shortcomings exist in the presentation of bond price volatility in financial education. First, modified duration and convexity should be used together as measures of bond price volatility. Second, these measures of bond price volatility should properly reflect semiannual compounding. Third, simple linear models for modified duration and convexity should be generally adopted in financial education literature.

Serving as an educator: A southern case in embedded librarianship, **Li, J. (2012). Serving as an educator: A southern case in embedded librarianship. ***Journal of business & finance librarianship***, ***17***(2), 133-152. **This is a case study at Mississippi State University where a business librarian taught a one-credit financial literacy course for undergraduate freshmen during the 2010 Fall term. In this case, the librarian acted as a faculty teacher and an instructional librarian to teach the students financial literacy as well as information literacy. The course curriculum was embedded with a library orientation to introduce the library services. Pre- and post-course assessments were conducted to analyze the students’ learning level in financial knowledge and the level of familiarity with various library services.

Statements to Congress, **Seger, M. R., Heller, H. R., & Loney, G. E. (1989). Statements to Congress. ***Federal Reserve Bulletin***, ***75***(7), 493.**