Answer:
the NPV of paying the points = $7,619.31
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
