A homeowner can obtain a $250,000,30-year fixed-rate mortgage at a rate of 6.0 percent with zero points or at a rate of 5.5 percent with 2.25 points.
If you will keep the mortgage for 30 years,what is the net present value of paying the points (to the nearest dollar)?

Question

Quizplus · Accepted Answer

To calculate the net present value of paying points, you need to find out the total cost of the mortgage with points and without points and then discount the difference back to its present value.

Without points:
Monthly payment = $1,498.88 
Total cost of mortgage over 30 years = $539,596.80

With points:
Monthly payment = $1,418.53 
Total cost of mortgage over 30 years = $510,370.80 
Points paid upfront = $5,625

Difference in total cost = $539,596.80 - $510,370.80 = $29,226 
Present value of $29,226 over 30 years at a discount rate of 5.5% is $8,360 (rounded to the nearest dollar).

Therefore, the best choice is to pay the points and obtain the lower interest rate.

A Homeowner Can Obtain a $250,000,30-Year Fixed-Rate Mortgage at a Rate