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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)

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jepessoa

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

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