Definition and Examples of Annual Percentage Yield
Annual percentage yield can be defined as the rate charged for borrowing or earning money over the course of a year.
For example, if you've ever signed up for a savings account, you've likely heard or seen the term "annual percentage yield" or "APY."
- Acronym: APY
How Annual Percentage Yield Works
When you deposit funds into a savings account, money market, or certificate of deposit (CD), you earn interest. APY can help you tell how much interest you'd earn on the account over one year. It's based on the interest rate and the frequency of compounding, and it shows you the interest you would earn on the principal (original deposit) plus interest on earnings.
Why Annual Percentage Yield Is Unique
Compared to a simple interest rate (no compounding), APY provides a more accurate indication of how much you will earn on a deposit account, because it factors in compounding.
Compounding happens when you earn interest on both the money you invest (or the original principal) and on your returns (or on past accumulated interest).
Single Annual Payment Example
Suppose you deposit $1,000 in a savings account that pays a 5% simple annual interest rate. If your bank calculates and pays interest only once at the end of the year, the bank would add $50 to your account. At the end of the year, you would have $1,050 (assuming your bank pays interest only once per year).
Monthly Compounding Example
Now, assume that bank calculates and pays interest monthly. You would receive small additions every month. In that case, you would end the year with $1,051.16, which is more than the quoted interest rate of 5%.
The difference may seem small, but over many years (or with bigger deposits), it can be substantial. In the table below, notice how the earnings increase slightly every month.
|1||$ 4.17||$ 1,004.17|
|2||$ 4.18||$ 1,008.35|
|3||$ 4.20||$ 1,012.55|
|4||$ 4.22||$ 1,016.77|
|5||$ 4.24||$ 1,021.01|
|6||$ 4.25||$ 1,025.26|
|7||$ 4.27||$ 1,029.53|
|8||$ 4.29||$ 1,033.82|
|9||$ 4.31||$ 1,038.13|
|10||$ 4.33||$ 1,042.46|
|11||$ 4.34||$ 1,046.80|
|12||$ 4.36||$ 1,051.16|
APR vs. APY
Annual percentage rate (APR) is the simple interest rate that a bank charges you over a year on products including loans and credit cards. It's similar to annual percentage yield but doesn't take compounding into account.
Credit card loans demonstrate the importance of differentiating between APR and APY. If you carry a balance, you'll often pay an APY that is higher than the quoted APR, because card issuers typically add interest charges to your balance each month. In the following month, you’ll have to pay interest on top of that interest. This is similar to earning interest on top of the interest you earn in a savings account. The difference might not be significant, but there is a difference. The larger your loan and the longer you borrow, the bigger that difference becomes.
With a fixed-rate mortgage, APR is more accurate because you usually don’t add interest charges and increase your loan balance. What’s more, APR accounts for closing costs, which add to your total borrowing cost. However, some fixed-rate loans actually grow (if you don’t pay interest costs as they accrue).
APY is more accurate than APR in some situations, because it tells you how much a loan costs as interest costs compound. But when you borrow money, you typically only see the APR. In reality, you might pay APY, which is almost always higher with certain types of loans.
Calculating APY With a Spreadsheet
You will almost always see the APY quoted from banks, so you generally don’t have to do any calculations yourself. You can calculate APY on your own, though it can be challenging. Spreadsheet software like Microsoft Excel or Google Sheets can make it easier. Use a Google Sheets spreadsheet for APY calculation, or follow the process below to make your own:
- Create a new spreadsheet.
- Enter the interest rate (in decimal format) in cell A1.
- Enter the compounding frequency in cell B1 (use "12" for monthly or "1" for annually).
- Paste the following formula into any other cell: =POWER((1+(A1/B1)),B1)-1
For example, if the stated annual rate is 5%, type “.05” in cell A1. Then, for monthly compounding, enter “12” in cell B1.
For daily compounding, you might use 365 or 360, depending on your bank or lender.
In the example above, you’ll find that the APY is 5.116%. In other words, a 5% interest rate with monthly compounding results in an APY of 5.116%. Try changing the compounding frequency, and you’ll see how the APY changes. For example, you might show quarterly compounding (four times per year) or the less advantageous one payment per year—resulting in a 5% APY.
Figuring APY With a Formula
If you prefer to do the math the old-fashioned way, manually calculate APY as follows:
APY = 100 [(1 + r/n)^n] – 1 where r is the stated annual interest rate as a decimal, and n is the number of compounding periods per year. (The carat ("^") means "raised to the power of.")
Continuing the earlier example, if you receive $51.16 of interest over the year on an account balance of $1,000, figure the APY this way:
- APY = 100 [(1 + .05/12)^12] – 1]
- APY = 5.116%
Financial experts might recognize this as the "effective annual rate" (EAR) calculation.
You can also calculate annual percentage yield as follows:
APY = 100 [(1 + Interest/Principal)^(365/Days in term) – 1] where Interest is the amount of interest received, and Principal is the initial deposit or account balance.
Using the interest payment and account balance from the example above, calculate the APY as follows:
- APY = 100 [(1 + 51.16/1000)^(365/365) – 1]
- APY = 5.116%
Annual percentage yield increases with more frequent compounding periods. If you're saving money in a bank account, find out how often the interest compounds. Daily or quarterly compounding is usually better than annual compounding, but check the APY for each account to be sure.
You can also pump up your own “personal APY” if you look at all of your assets as part of a larger financial picture. In other words, don’t think of one CD investment as separate from your checking account—all investments should work together in helping you meet your goals, and they should each be positioned accordingly.
To maximize your personal APY, ensure that your money is compounding as frequently as possible. If two CDs pay the same interest rate, pick the one that pays out interest more often (and therefore has the higher APY). You can automatically reinvest your interest earnings—the more frequently, the better—and you'll start earning more interest on those interest payments.
- Annual percentage yield is the rate charged for borrowing or earning money over the course of a year.
- It's a useful metric to have on hand, especially if you can differentiate it from simple interest and understand how to calculate it.
- Once you have a grasp on APY, you can decide how to make the most out of the money you hold in a bank.
- When calculating APY by hand, this is your formula: APY = 100 [(1 + Interest/Principal)^(365/Days in term) – 1]
Federal Deposit Insurance Corporation. "Appendix A to Part 1030—Annual Percentage Yield Calculation." Accessed Nov. 29, 2021.
U.S. Securities and Exchange Commission. "What Is Compound Interest?" Accessed Nov. 29, 2021.
American Express. "APY vs. APR: The Basics About How Interest Is Calculated." Accessed Nov. 29, 2021.
Consumer Financial Protection Bureau. "What Is a Credit Card Interest Rate? What Does APR Mean?" Accessed Nov. 29, 2021.
Consumer Financial Protection Bureau. "What Is the Difference Between a Mortgage Interest Rate and an APR?" Accessed Nov. 29, 2021.
University of Wisconsin. "Cheat Sheet 2," Page 1. Accessed Nov. 29, 2021.