Understanding APR, APY, and EAR
Jake goes to the bank and borrows $1000. The loan is at an APR of 5% and compounding is done on a monthly basis. The loan term is one year and he makes monthly loan payments. What is the Effective Annual Rate (EAR) of the loan?
- (A) 5.0000%
- (B) 5.1932%
- (C) 5.1162%
- (D) 5.0999%
Correct answer is Option C, EAR = 5.1162%
APR = Annual Percentage Rate = this is the interest rate; however, it does not provide how often compounding is done per year.
EAR = Effective Annual Rate = this is the real rate of interest Jake pays on the loan.
In the above loan, here are the facts:
- Compounding is done on a monthly basis.
- Interest rate per month = 0.05/12
- Term = 1 year = 12 months
- PV of loan = $1000
Now remember the PV and FV lesson – Time Value of Money – we will apply this lesson here. Here we need to solve for FV. Now let us enter the following in an Excel cell: “=FV(0.05/12,12,0,1000)”.
If you type “=FV” in Excel, it will show you what each field is. In the above case, we don’t know what the PMT is, so I entered 0. We know the value for all the other fields.
You will get -$1051.162. The sign is negative because that is what Jake will end up paying the bank when he pays off the loan.
Now the interest amount = $1051.162 – $1000 = $51.162
Effective Annual Rate = (51.162/1000) * 100 = 5.1162%.
I took the long road to explain how it works.
Here is the formula to calculate EAR from APR:
k = number of times loan is compounded per year.
In the example above,
If you calculate, EAR = 5.1162.
If compounding was done only once per year, then EAR = APR.
Key Take Away’s:
- When you are shopping for CD’s, banks will always quote the Annual Percentage Yield (APY).
- When you are applying for a loan, banks will quote you the APR. You need to ask and understand what the EAR is. Always review and understand the EAR before you sign up for the loan.