From APR and quoted interest rate to loan fees…

I received positive feedback after emailing the following write-up on mortgage loans to students.  Perhaps it will move more people closer to understanding mortgage APRs, fees, and “rates” (quoted interest rates).:

Let loan amount = PV = 80,000
Let QIR =  4.250%
Let APR = 4.464%

We saw in class how to calculate the fees embedded in the APR:
Step 1: PV = -80,000; I = APR = 4.464/12; N = 30×12; FV = 0; -> PMT=403.64
Step 2: PMT = 403.64; I = QIR = 4.250/12; N = 30×12; FV=0; -> PV=-82,050
Step 3: fees in APR = 82,050 – 80,000 = 2,050

Another way to look at Steps 1 and 2:
1. Loan amount with APR -> PMT if fees are included in loan amount
2. Loan amount + fees with QIR -> PMT if fees are included in loan amount (same PMT as step #1)

Step one is an implicit inclusion of fees, step 2 is an explicit inclusion of fees.  Of course, you could pay the fees with a check at closing, but that is a cost that you incur.  You must account for it somehow.  A convenient way is to go by the APR that does include fees.

Now, should you pay the fees at closing [or roll them into the loan]?  Guess what, it depends.  It depends on (a) if you can afford to pay the fees at closing and (b) if there are better alternative instruments to put those fee dollars.

Right now, 30 year T-bonds return 3.80% per year.  So, presuming you have the cash, it would not make sense to roll the fees into the loan.  You would be borrowing \$2,050 at 4.25% to invest in T-bonds that yield only 3.80%.  Thus, pay the fees with a check at closing.

However, if you think you can earn 5% on average over the next 30 years, roll the fees into the loan (i.e., borrow \$2,050), invest the \$2,050, and pray you do earn 5%!

May you be enlightened.