Question

a homeowner can obtain 250,000, 30 year fixed mortgage at a rate of 6% 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)

Answer 1

Calculation of monthly payment on first loan:

PV = 250000
Nper = 30 * 12 = 360
Rate = 6% / 12 = 0.5%
FV = 0

Monthly payment can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(0.5%,360,-250000,0)
= $1,498.88

Calculation of monthly payment on second loan:

PV = 250000
Nper = 30 * 12 = 360
Rate = 5.5% / 12
FV = 0

Monthly payment can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(5.5%/12,360,-250000,0)
= $1,419.47

Monthly savings = $1,498.88 - $1,419.47 = $79.40

Present value of monthly savings can be calculated by using the following excel formula:
=PV(rate,nper,pv,fv)
=PV(5.5%/12,360,-79.40)
= $13,984.74

Value of points in dollar = Loan amount * points = $250,000 * 2.25% = $5,625.

Net present value of savings = Present value of savings - value of points in dollar
= $13,984.74 - $5,625
= $8,359.74

Net present value of savings = $8,359.74