Question

You are buying a house and will borrow $225,000 on a 30-year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of 4.3 percent. Alternatively, she tells you that you can “buy down” the interest rate to 4.05 percent if you pay points up front on the loan. A point on a loan is 1 percent (one percentage point) of the loan value. How many points, at most, would you be willing to pay to buy down the interest rate?

Answer 1

This question can be solved easily in excel.

APR is the annual Percentage rate . It denotes the percentage of principal given as interest payment per year.

Here PV =$225,000 (Principal)

PMT = 4.3% * PV= -9675 (negative means will pay) This amount is paid annually as per definition of APR

NPER(years)= 30

We can get the rate of discount by using RATE function in Excel. Use RATE( NPER,PMT,PV) . You will get 1.7284%

Now as we know rate of discount. Lets find out the upfront payment we have to make to get 4.05%. We have to choose an amount for upfront payment such that (upfront payment + Present Value of Interest payment @ 4.05% APR) should not exceed $225,000 , otherwise we are overpaying i.e effectively paying more than 1.7284% as per original deal.

So Maximum Upfront Payment= $225,000 - Present value of total interest paid @ 4.05% APR

To get Present value use excel function =PV(1.7284%, NPER, 4.05%*PV) = $211,918.6

Thus Maximum upfront payment= $13,081.4 which is 5.81% of $225,000. So the consumer must pay approximately 6 points upfront to buy down the interest rate to 4.05%