Question

# A homeowner can obtain on property valued at \$250,000, a 30-year fixed-rate mortgage, LTV=90%, at a...

A homeowner can obtain on property valued at \$250,000, a 30-year fixed-rate mortgage, LTV=90%, at a rate of 6.0 percent with zero points or at a rate of 5.5 percent with 2.25 points. If she will keep the mortgage for 30 years, what is the net present value of paying the points (to the nearest dollar)?

step1:
find monthly payment of loan without points

let X be the monthly payment

X * [1-(1+6%/12)^-360]/6%/12 = 250,000

X = 1498.88

step2:

find monthly payment of loan with points

let y be the monthly payment

y * [1-(1+5.5%/12)^-360]/5.5%/12 = 250,000

y = 1419.47

difference between the monthly payments = 1498.88 - 1419.47 = 79.41

step3:

Net present value of points = Present value of sum of montly payment saved - value of points payed

= 79.41 * [1-(1+5.5%/12)^-360]/5.5%/12 - (0.025 * 250000)

= 7735.83

= \$7736 .....ans

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