Annual Percentage Yield, or APY, tends to throw off a lot of people. There seems to be three major points of confusion: 1) Why is the APY different than the interest rate? 2) How is this different from APR? and 3) Trying to calculate the APY on a term less than 12 months. I’ll explain each of these on this page.
First, APY is a formula that includes the interest rate, but that isn’t all. The formula is: APY = interest rate + compounded interest. I’ll explain this by illustrating it with an example:
Let’s say you have a CD that is paying a 5% interest rate for 12 months. You deposit $10,000 into the CD. The interest is credited monthly. So, here is how you figure out your interest after one month:
$10,000 x .05 = $500(annually); $500 / 12(mos) = $41.67(first month); $10,000 + $41.67 = $10,041.67
In your first month, you gained $41.67 in interest based off your balance of $10,000. To figure out month two, would you do the exact same thing? No, you would change your starting balance, but then the rest would match. Let’s do it:
$10,041.67 x .05 = $502.08(annually); $502.08 / 12(mos) = $41.84(per month); $10,041.67 + 41.84 = $10,083.51
Your second month interest earned is $41.84, which was higher than $41.67 your first month. The reason is because you are compounding your interest. That means each time your interest is applied to your balance, your interest rate is drawing off a higher number. This happens every month during the 12 month cycle. That means your applied interest goes up 12 consecutive months. At the end of the term, you look at your total interest earned, which in this case would be $511.62, and you would do the math backwards to calculate your APY for the year.
$511.62 / $10,000 = .055162 = 5.116% This is your APY, compared to your interest rate of 5%
This is why APY and interest rate are not the same thing. APY accounts for the magic of compounded interest. Therefore, your interest rate will always be lower than your APY. If you aren’t allowing your interest to compound inside the CD, then your rate and APY should be equal.
This is all assuming your bank does not add any other kind of credit or interest to the CD. If it does, then that is factored into the APY as well. I could even amend the formula to say: APY = interest rate + compounded interest + any other credit from institution. Most institutions don’t add any other credits, but it isn’t unheard of.
Second, how is APY different from APR? APR stands for Annual Percentage Rate. It is specific to loans, not savings accounts or CDs. It is calculated like this: APR = interest rate + fees + any other charges applied to the loan.
The easiest way to explain it is this way: they are essentially the same thing, but the APY benefits YOU while the APR benefits the BANK. Imagine a scenario where you and the bank swapped roles. The bank is now giving YOU their money and YOU are paying them to keep it. When that happens, you replace APY with APR and it works the same way. Here are the formulas stacked together:
APY = interest rate + compounded interest + any other credits
APR = interest rate + fees + any other charges
I’ve seen some people apply the term APR to mean exactly the same thing as APY, even telling the customer who purchased a CD that their APR is going to be x% but that simply isn’t accurate. APR is for loans and it benefits the bank. A CD customer should always be told that the rate they are getting is the APY.
As an important point, you should know that whenever a person calls multiple banks to shop rates on CDs, that person will always be told what the APY on that CD is. The reason is because it’s the law. It used to be that Bank A could tell a shopper they are paying 10% on a CD and leave off the details about added fees that reduce the true interest rate to 6%. Congress got complaints about this being misleading, and they stepped in and created the Truth in Savings Act in 1991, which levels the playing field in this scenario. Now, when a customer calls multiple banks, they all quote the APY so the shopper gets a true apples-to-apples comparison to make a sound decision.
Third, how do you calculate your interest yield on a CD that isn’t 12 months?
Here is what constantly happens to customers. They find out a bank is offering a CD special that pays 5% for 7 months. The customer is wanting to deposit $10,000 into this CD and they do some quick math to figure out what they’ll have at the end of 7 months. Here is the formula the customer uses:
$10,000 x .05 = $500 The customer is then expecting to have a total CD value of $10,500 at maturity 7 months later
But, they are leaving out a very important step! Remember, the A in APY stands for “Annual,” meaning it is a 12 month assumption. So, if a CD lasts for 7 months, that means you can’t use the above formula to determine your yield. You must consider the fact that you are only in it for 7 out of 12 months. How do you do that? The good news is that it’s quite simple. You add the step: x (number of months/12). Here is what I mean: $10,000 x .05 x (7/12) = $291.67
Do you understand what happened? You aren’t holding the CD for the full A of the APY, so you have to factor in how long you’re actually holding it. Since A is always 12 months, you divide your actual number of months by 12 and that is your answer.
It may be easier to explain this by using a 6 month CD. That’s easy because 6/12 = .5 or half of your term.
So, $10,000 x .05 = $500 x .5 = $250
Since 6 months is HALF of a year, you multiple your annual yield by HALF as well, which is also expressed with (.5). If you are told to add a dollar to a cookie jar every day for 12 days, but then get pulled from it on day 6, you will have $6 dollars in the jar, but your rate will still be $1/day. The only reason it didn’t reach $12 is because you didn’t get the full 12 days to fulfill your obligation. However, your RATE was still the same. You simply ran out of time. It’s no different with CDs with terms less than 12 months. Your rate is still what was quoted to you, but you won’t have the full 12 months at your disposal. APY is an annual number required by law(see previous question) so that’s what you’re always going to be quoted when you ask for CD rates.
Long form video
"Even the smallest compounded interest can change the course of the future."