DEFINITION
Annual percentage return is a rate of return on an investment for a period of 12 months that takes into consideration the compounding effect.
The Key Takeaways
- The annual percentage yield is a rate that you pay for borrowing money or earning it over a period of one year.
- This is a handy metric, especially if it can be distinguished from simple interest.
- You can make the most of your money in a bank once you understand APY.
- When calculating APY by hand, this is your formula: APY = 100 [(1 + Interest/Principal)^(365/Days in term) – 1]
What is Annual Percentage Yield? Definition and examples
The annual percentage yield is the rate of interest charged to borrow or earn money for a full year.
If you have ever opened a savings account you may have heard the term “annual percent yield” (APY).
- Acronym: APY
What is Annual Percentage Yield?
You earn interest when you deposit money into a savings, money-market, or Certificate of Deposit (CD). APY is a way to estimate how much interest will be earned on an account in a year. This is based on interest rates and compounding frequency. It shows the interest that you’d earn on your principal deposit plus interest earned on your earnings. 1
Why Annual Percentage Return is Unique
Compounding is when you earn interest both on the principal (or money invested) as well as on the returns (or past accumulated interest). 2
Simple Annual Payment Example
Imagine you deposit $1,000 into a savings account with a simple annual rate of 5%. If your bank only calculates interest and pays it once a year at the end, they would add $50 to the account. You would end up with $1,050 at the end of the calendar year (assuming that your bank only pays interest once a year).
Monthly Compounding Example
Assume that the bank calculates monthly and pays interest. You’d receive little additions each month. You would then end the year with 1,051.16 which is greater than the 5% interest rate.
It may not seem like much, but it adds up over time (or if you make larger deposits). Notice how earnings are increasing every month in the table below.
| Period | Earnings | Balance |
| 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 percent rate is the simple rate of interest that banks charge you on loans and credit card products over the course of a year. This is similar to the annual percentage yield, but does not take into account compounding.
Credit Card Loans show the importance of comparing APR with APY. You’ll pay a higher APY if you have a credit card balance because the issuer adds interest to your account each month. You’ll be charged interest on the interest in the next month. 4 It is the same as earning interest on the interest that you earn on a savings account. It may not seem like much, but it is there. The difference gets bigger the larger the loan is and the longer the borrower takes to pay it off.
The APR for a mortgage is more accurate, because you don’t usually add interest charges to your loan balance. APR also accounts for the closing costs which are added to your borrowing costs. 5 Some fixed-rate mortgages actually increase in value (if interest charges are not paid as they accumulate).
Note:
In some cases, APY can be more accurate than APR because it shows you the cost of a loan as interest costs accumulate. When you borrow money you will usually only see the APR. You may actually pay an APY which is usually higher for certain types of loans.
Spreadsheet Calculation of APY
Banks will usually quote the APY, so you don’t need to calculate it yourself. Although it is difficult, you can calculate your APY yourself. Spreadsheet software such as Microsoft Excel or Google Sheets makes it easier. You can use a Google Sheets spreadsheet to calculate APY, or you can follow the steps below to create your own.
- Create a new Excel spreadsheet.
- Enter the interest rate in decimal format (cell A1).
- Enter the compounding frequency (either “1” or “12” if it is monthly) in cell B1.
- Paste the following formula into any other cell: =POWER((1+(A1/B1)),B1)-1
Enter “.05” for example, in the cell A1 if you want to calculate the annual rate. Enter “12” for the monthly compounding in cell B1. 1
Note:
You may use 360 or 365 for daily compounding depending on the lender or bank you are using.
In the above example, the APY comes out to 5.116%. If you want to know what the APY is, then you can use a 5% rate of interest with monthly compounding. You can change the frequency of compounding to see the effect on the APY. You could, for example, choose quarterly compounding (four payments per year), or the less desirable one payment per annum–resulting in a 5-percent APY.
Calculating APY with a Formula
You can calculate the APY manually by following these steps:
APY is 100 [(1+r/n)n]- 1, where r is expressed as an annual interest rate in decimal form and n is the compounding period per year. The carat (“^”) is “raised by a power of”. “)1
If you continue the previous example, and receive $51.16 in interest on a $1,000 account balance over the course of the year, calculate the APY as follows:
- APY = [(1 + (.05/12)12]12 – 1]
- APY = 5,116%
Note:
This calculation is known to financial experts as “effective annual rates” (EAR).
You can also calculate the annual percentage yield by using this formula:
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.1
Calculate the APY using the interest payment and the account balance in the above example:
- APY = 100 [(1 + 51.16/1000)^(365/365) – 1]
- APY = 5,116%
Maximizing APY
Compounding occurs more frequently, which increases the annual percentage yield. Find out how often interest is compounded in your bank account. It is better to have daily or quarterly compounding than annual compounding. However, you should check the APY of each account.
If you consider all of your assets as part a bigger financial picture, then it is possible to boost your “personal APY”. Don’t separate your Checking Account from one Investment. All investments should be aligned to help you achieve your goals.
If you want to maximize your APY, make sure that your money compounds as often as possible. Choose the CD that pays interest the most often. Reinvesting your interest payments is a great way to earn more interest.
