By knowing how to calculate the AER, you can accurately compare savings accounts, investments, and loans that have different compounding periods to see which one earns (or saves) you the most money.
Definition and Examples of the Annual Equivalent Rate
The AER is an interest rate that tells you exactly how much interest you’ll accrue on an investment or a debt based on how often it compounds (in other words, how often you accumulate interest on your interest). It’s typically used to determine the annual percentage yield (APY) for a savings account, the yield of a bond, or the effective annual percentage rate (APR) of a loan.
Acronym: AER, EAR, APY Alternate names: Effective annual interest rate, effective interest rate, annual percentage yield, effective APR
Here’s an example of when you might see AER used. Say you took out a loan with 12 monthly payments and an APR of 12%, which compounds monthly. When you get your first monthly statement, you see that you were charged 12% interest, which was added to your balance. On your second statement, you see that you were charged interest again, but it doesn’t match the original loan amount multiplied by the stated interest rate. This is because the previous month’s interest was added to your balance and interest charged, then added to your balance again. This is because of compounding interest—which on a 12-month loan (at a 12% APR) makes your AER 12.68%. You can figure out how much you’ll pay on this loan by calculating the AER and applying it to the original loan balance.
How Do You Calculate the Annual Equivalent Rate?
There are two variables you need to know to calculate the annual equivalent rate: Here’s what the equation looks like: For n, you’ll enter 1 if the investment compounds annually, 2 for semi-annually, 4 for quarterly, 12 for monthly, and 365 for daily.
How the Annual Equivalent Rate Works
The AER levels the playing field of all investments, giving you an accurate way to determine which one would earn more interest if you never took any withdrawals and let your balance compound indefinitely.
Using the AER To Compare Investments
For example, let’s say you’re deciding between two certificates of deposit (CDs). Option A has a stated interest rate of 7%, compounded semi-annually. Option B has a stated interest rate of 6.95%, compounded daily. Assume that both CDs have terms of 10 years. (Note: These rates and terms are not real and are only being used for this example. Actual CD terms and rates may be much shorter and lower.) At face value, you might assume Option A is better because the interest rate is higher. But when you calculate the AER, you find out Option B earns more interest:
Option A: (1 + (0.07 / 2))2 – 1 = 7.12%Option B: (1 + (0.0695 / 365))365 – 1 = 7.20%
If you wanted to know how much more you’d earn in interest with Option B, you could use the compound interest calculator for that. For example, if you deposited $50,000 into Option A, you’d have $100,649.32 at maturity (10 years). Not bad. But if you went with Option B instead, you’d have $102,714.37 at maturity—over $2,000 more even though it has a lower stated interest rate. This is because of the AER. These differences may not seem like much when you’re dealing with small amounts. When you’re talking about hundreds of thousands of dollars compounded for years, however, they start to add up—and can make a significant difference in your overall wealth.
Using the AER To Compare Loans or Credit
The AER is a good tool for comparing the amount of interest you’ll end up paying on credit card debt or loans. For instance, say you have two loans, A and B. They have the same stated interest rate, but loan B compounds more often. When you calculate the AER, you’ll see that you’ll owe more interest with loan B. Likewise, suppose you’re considering two credit cards with the same stated interest rate, but card B compounds more often. When you calculate the AER, you’ll find that you’ll pay more interest on credit card B debt (and should therefore go with credit card A).
How To Calculate the Annual Equivalent Rate in Excel
Although you can calculate the AER by hand, you might save time if you use an online calculator or spreadsheet instead. For example, Google Sheets and Excel have built-in formulas for AER wherein the nominal rate is the interest rate given along with the total number of compounding periods in a year:
Do I Need To Calculate the AER?
Financial institutions will typically advertise whichever rate is more attractive to consumers. If it’s for a credit card or loan, they’ll likely advertise the nominal rate because it’s lower than the AER and makes it look better. In other words, they’ll tell you a credit card has a 15% APR even though you’ll end up paying 16.18% if compounded daily. For a savings account, the institution may advertise the AER or APY so it looks like they’re paying you the highest rate possible for your money. Calculating the AER is important so you know the exact rate you’re paying (or getting paid) on your money.
