Question

Mortgage loan commercials and bank banners can be a little confusing due to the fact they report two rates: 1) the stated nominal annual rate that we usually think of as APR which is compounded monthly and is the rate that is used on the actual loan amount to determine the monthly payment, and 2) the "APR" which is somewhat higher and in some ads significantly higher than the first rate. This second "APR" is a stated nominal annual rate but assumes the borrower will finance all closing costs necessary to get the loan (instead of paying them in cash when closing the loan) in addition to the amount the borrower needs to complete the purchase of their home. Here's how this second "APR" is determined. First, the first stated annual rate is used to figure the monthly payment on the loan amount plus closing costs. Then, the monthly interest rate that equates the present value of these monthly payments with the loan amount without closing costs is found. Finally, this monthly rate is multiplied by 12 to get this second "APR". The larger the difference between the two rates the larger the closing costs and fees for the loan. The mortgage ads usually use some fixed loan amount like $100,000, $150,000, or $200,000. Whether the borrower decides to finance the closing costs or not, this second APR can give the borrower a truer cost of borrowing once the closing costs are factored in. Let's look at a couple of examples of how this works. Imagine the Prof. Fin finds a $280,000 condo he wishes to buy and has a $90,000 down payment and will need to borrow $190,000 before any closing costs. Use this information to answer the questions below.

1. Friendly Mortgage offers a 30-year fixed rate mortgage with a nominal annual rate of 3.25% with $500 in closing costs.

a. What would be Prof. Fin's monthly mortgage payment if he pays the closing costs in cash?

b. What would be Prof. Fin's monthly mortgage payment if he finances the closing costs?

c. What is the second "APR" for this loan as described above?

2. Rapid Loans offers a 30-year fixed rate mortgage with a nominal annual rate of 3.0% with $4000 in closing costs.

a. What would be Prof. Fin's monthly mortgage payment if he pays the closing costs in cash?

b. What would be Prof. Fin's monthly mortgage payment if he finances the closing costs?

c. What is the second "APR" for this loan as described above?

3. Which of the two mortgage options would you recommend to Prof Fin? Explain why.

Answer 1

Q#1: Friendly Mortgage

Part (a): Monthly mortgage payment if closing costs is paid in cash= $826.80

Part (b): Monthly mortgage payment if closing costs is financed= $829.07

Part (c): Second “APR” as described= 3.270852%

Q#1: Rapid Loans:

Part (a): Monthly mortgage payment if closing costs is paid in cash= $801.05

Part (b): Monthly mortgage payment if closing costs is financed= $817.91

Part (c): Second “APR” as described= 3.163626%

Q#3: Loan from Rapid Loans is recommended to Prof. Fin since the truer cost which is second ‘APR’ is lower at 3.16% compared to 3.27% with Friendly Mortgage.

Details of calculation as below: