16.07.2022 - 17:53

A homeowner can obtain a $250,000, 30-year fixed-rate mortgage at a rate of 6.0% with zero points or at a rate of 5.5% 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:

A homeowner can obtain a $250,000, 30-year fixed-rate mortgage at a rate of 6.0% with zero points or at a rate of 5.5% 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)?

Answers (0)
  • Bertha
    April 11, 2023 в 17:37
    The net present value of paying the points can be calculated using a present value formula. First, we need to calculate the total cost of each loan option over 30 years: Option A: Loan amount = $250,000 Interest rate = 6.0% Number of years = 30 Monthly payment = $1,498.88 Total payments over 30 years = 12 * 30 * $1,498.88 = $539,596.80 Option B: Loan amount = $250,000 Interest rate = 5.5% Number of years = 30 Points = 2.25% of loan amount = 0.0225 * $250,000 = $5,625 Loan amount after points = $250,000 - $5,625 = $244,375 Monthly payment = $1,386.07 Total payments over 30 years = 12 * 30 * $1,386.07 = $498,385.20 Next, we need to calculate the present value of the cost of each option: Option A: Interest rate = 6.0% Number of years = 30 Total cost = $539,596.80 Present value = $539,596.80 / (1 + 0.06/12)^(12*30) = $174,955.87 Option B: Interest rate = 5.5% Number of years = 30 Total cost = $498,385.20 + $5,625 (points) = $503,010.20 Present value = $503,010.20 / (1 + 0.055/12)^(12*30) = $169,641.87 The net present value of paying the points is the difference between the present value of Option A and Option B: Net present value = $174,955.87 - $169,641.87 = $5,314 Therefore, the net present value of paying the points is $5,314 to the nearest dollar.
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