Question

In: Finance

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

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)

Solutions

Expert Solution

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


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