Annual Percentage Yield

The annual percentage yield (APY) helps a business or investor to understand how much they are earning from the money they have invested with compounded interest. In other words, how much are you earning on your invested money over the course of a year if the interest is compounded?

The term, “compound interest”, essentially means the interest has been reinvested. Your cash contributions earn interest, which stays in the investment and becomes part of the principal balance. As time goes on, the value of your interest earned will be greater because of all the prior interest added to the principal. 

For example, if you invest $100 with a 10% interest rate per month, then after the first month you will have $110. The second month’s interest earned would be $11, totalling to $121. The third month’s interest earned would be $12.10, totalling to $133.10, and so on. As you can see, the more time your capital has to spend with its compound interest, the more money you can make. With accounts like these, the earlier you can begin investing, the better.   

Annual Percentage Yield Formula

$$APY = \bigg( 1 + \dfrac{r}{n} \bigg)^{n} - 1$$

  • r = interest rate
  • n = number of compounded periods

APY should always be expressed in a percentage. Also, this formula looks at the percentage yield for one year at a time. 

Consequently, you should be looking at the annual interest rate for the variable r. Now, there are different types of interest rates. Different accounts and banks will have differing terms set on their interest rates. Some may compound monthly while others compound annually. Your annual percentage yield will be higher if your interest is compounded more frequently. 

Annual Percentage Yield Example

Frank just received a $5000 award for an art competition. He wants to invest this money in an account with compounded interest. He is comparing 3 different banks. Bank A has an account with an interest rate of 9% and compounds quarterly. Bank B has an account with an interest rate of 9% and compounds monthly. Bank C has an account with a 9% interest rate and compounds daily. Which bank’s account will give Frank the best return on his investment in 1 year?

Let’s break it down to identify the meaning and value of the different variables in this problem. 

Bank A

  • Interest Rate (r): 9% or 0.09
  • Number of compounded periods per year (r): 4

Bank B

  • Interest Rate (r): 9% or 0.09
  • Number of compounded periods per year (n): 12

Bank C

  • Interest Rate (r): 9% or 0.09
  • Number of compounded periods per year (n): 365

We can apply the values to our variables and calculate the annual percentage yield for each bank. 

Bank A

$$APY = \bigg( 1 + \dfrac{9\%}{4} \bigg)^{4} - 1 = 9.31\%$$

The APY for Bank A would be 0.930 or 9.31%.

Bank B

$$APY = \bigg( 1 + \dfrac{9\%}{12} \bigg)^{12} - 1 = 9.38\%$$

The APY for Bank B would be 0.0938 or 9.38%.

Bank C

$$APY = \bigg( 1 + \dfrac{9\%}{365} \bigg)^{365} - 1 = 9.42\%$$

The APY for Bank C would be 0.0941 or 9.42%.

In this case, Frank would be most likely to choose Bank C because it would offer daily compounding, which would give him a higher APY than the other two account options. 

Because of these formulas, Frank can make the best choice for his investment. Unfortunately, unless you are investing a significant amount of money, a change in the compounding frequency won’t necessarily give one interest rate an edge over another. Usually, a higher interest rate will be better than a lower interest rate with a more frequent rate. Still, you never know, which is why you should always remember to check out the APY.

Annual Percentage Yield Analysis 

The annual percentage yield is a means to understand how much money you will actually be taking home from an investment where interest is compounded. It can be very useful in comparing different accounts that you are considering. 

Typically, if you are the one who is investing, then a higher APY is better. If you are deciding on a CD or savings account, you can calculate the APY to figure out which will ultimately give you the better return. On the other hand, APY can also mean additional money you are charged. If you have a balance on your credit card, you can be charged a compounded interest on your balance, meaning that you pay more over time.   

You may be tempted to confuse APY with APR, or annual percentage rate, which is similar except that it only looks at a basic interest rate, not a compounded one. Depending on the type of investment you’ve made, the annual percentage yield can be more accurate since it will tell you the actual value at the end of the investment period. If you have two investments with the same interest rate, the actual value of their return could be very different if one of the accounts had compounding interest.

However, with all the intricate legal jargon that comes with bank account documents, it can be difficult to identify these variables. Thankfully though, in the U.S. it is a federal law that banks have to disclose their interest rates, including APY, along with any potential fees associated with the account. This is meant to help individuals more accurately compare the future of their investment. 

Annual Percentage Yield Conclusion

  • The annual percentage yield is the cash earned from an investment over a year. 
  • The annual percentage yield includes compounded interest in its calculation. 
  • The annual percentage yield formula requires 2 variables: interest rate and the number of compounded periods per year. 
  • A higher APY is better for investments, like savings accounts, while a lower APY is better for loans or credit, like a credit card. 

Annual Percentage Yield Calculator

You can use the annual percentage yield calculator below to get a quick estimate of your investment’s return with compounded interest by entering the required numbers.

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