Question

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)

Answer 1

the NPV of paying the points = $7,619.31

Step-by-step explanation:

if the homeowner gets the loan at 6%, his/her monthly payment = $1,498.88

the present value of the 360 monthly payments at 6% is $250,000

if the homeowner gets the loan at 5.5%, his/her monthly payment = $1,419.47

in order to compare both loans, I will discount the 360 payments by 6%, instead of 5.5%:

PV = $1,419.47 x 166.79161 (PV annuity factor, 0.5%, 360 periods) = $236,755.69

the NPV of paying the points = -($250,000 x 2.25%) - $236,755.69 + $250,000 = $7,619.31