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 the homeowner keeps the mortgage for 30 years, what is the net present value of paying the points?

. $8629.386

Explanation:

P = 250,000

r = 6%

r with point = 5.5%

Points = 2.25%

N = 30years × 12 = 360months

1. Paying the points (Loan)= p × point

=$250,000 x .2.25 / 100 = $5,625 (CF0)

Payments with 6% loan

I = p/ (1 + r)^n

= $250000 / (1 + 0.06)^360

= $1940.11

Payments with 5.5% loan

I = p/ (1 + r)^n

= $250,000/ ( 1 + 0.055)^360

= $1064.276

Savings = $1940.11 - $1064.276

= $875.834

Net present value of paying the points.

= $5625 + $1940.11 + $1064.276

= $8629.386

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