Question

When you buy a house, you also "buy" an interest rate. That is, depending on the conditions of the housing market and the current federal interest rate, you get locked into a rate for the duration of your loan agreement by the bank that sells you the loan. Though there are many home loan durations (often terminating at the time called the "pay-off" date), the most typical for home-buyers is 30 years.

Suppose you buy a new home for $200,000 at 4.5% APR. After having owned the home for 5 years, you are offered a refinance for 4.25% APR for the remainder of your loan duration. Of course, this reduces your payment... but, there are closing costs which amount to 3% of what you owe on the loan at the time of refinance. After the refinance, how long would you have to own the home for in order to "break even" with the closing cost fees you paid to refinance? (Assume you pay the refi costs out-of-pocket at the time of refinance.)

NOTE: The APR is calculated in a more complicated way than we will let-on here. Assume APR is the same rate concept developed in our modules on interest rates. Also, we can assume the interest is compounded monthly on a mortgage.

TO DO:

1. Provide a response that thoughtfully addresses each of the questions above by Wednesday, 11/7, 11:59PM.

2. Respond thoughtfully to the posts of at least two other classmates by Saturday, 11/10, 11:59PM.

Answer 1

Solution:
Computation of how long to own house after refince to break even the closing cost fee
Closing Cost fee ($200,000 x 3%)	$6,000
Savings in APR Rates per annum (4.5% - 4.25%)	0.25%
Savings in interest per annum ($200,000 x 0.25%)	$500
Break even years ($6,000 / $500)	12
Therefore we have to own the home another 12 years to break even the closing costs fee we paid to refinance.
(Note: we have ignored present value of money in closing costs fee and saving in annual interest per annum to calculate the break even)