When searching for a loan or savings product, you are quoted with the annual percentage rate (APR) and the annual percentage yield (APY). Many consumers are unaware of which one they should be paying the most attention to. Some even mistake the two for the same thing when making comparisons between two different products and unfortunately, arriving at an incorrect conclusion. In this post I will show you what each calculation means, how to perform the calculation, and when to use it.
Annual Percentage Rate (APR)
The APR is the interest rate without taking into account compounding. You will sometimes hear it referred to as the nominal interest rate as well. For the most part, loan products such as you mortgage or car loan will quote you with the APR.
To calculate the APR you take the rate and multiply it by the number of periods in a year. For example, a car loan with a 2% monthly interest rate would be calculated as follows:
2% x 12 = 24% APR
Annual Percentage Yield (APY)
The APY is the effective interest rate when compounding is taken into account. Most investing products such as savings accounts and certificates of deposit will quote you with the APY. This is actually a requirement so that you can correctly compare a certificate of deposit between two different banks. Sometimes you will see the APY referred to as the effective annual rate, or EAR.
The formula for the APY is a little more involved:
(1 + nominal APR/n)^n-1
n is the compounding periods per year (if compounded quarterly, n would equal 4; if compounded monthly, n would equal 12, etc.)
Nominal APR is the number from the calculation above. When performing this calculation, be sure to use the APR as a decimal as opposed to a percent (0.24 vs. 24%)
Let’s say that car loan from above with a 24% APR is compounded monthly. The calculation would be:
(1 + .24/12)^12-1 = 26.82% APY
Why Loans are Quoted with APR and Deposits with APY
When you stop and think about it, it makes perfect sense. As a borrower, you are looking for the lowest rate possible. Since the APR does not take into account compounded interest, this rate is the lowest number they can quote you.
On the flip side, as a lender, you want the highest return for your money so banks quote you with the APY, which takes into account compound interest.
Importance of Understanding Both Calculations
It is very important to pay attention to both of these numbers when they are quoted to you as well as making sure which number is being quoted to you. For example, when looking for a new car, both lender may offer you 4% APR. Even though they both offer the same APR, what you pay could be different. Let’s say the first lender compound that loan monthly while the other lender compounds that loan semi-annually. You have to do the math (thank goodness for excel!) to know which is the better deal. The answer is the 4% that is compounded semi-annually. That APY is 4.04% while the other APY is 4.07%. This may not seem like much, but over time it adds up; especially when we are talking about a 30 year mortgage.
When shopping for a savings or loan product, make sure you are comparing apples to apples when it comes to loan rates. Also be mindful of the compounding periods of each product as well. As we have seen, an APR can be the same but what you actually pay when compounding is taken into account can be different, costing you money in the end.