Question

1. 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. How long must the owner stay in the house to make it worthwhile to pay the points if the payment saving is invested monthly?

Answer 1

Monthly payment without the points

N=360

I/Y=6/12=0.5

PV=-250,000

FV=0

CPT PMT=1,498.8763

Monthly payment with the points

N=360

I/Y =5.5/12=0.45833

PV=-250,000

FV=0

CPT PMT =1,419.47

Monthly payment savings = 1,498.87 - 1,419.47= 79.40

Present Value of Monthly Payment Savings

N=360

I/Y=5.5/12=0.4583

PMT=79.40

FV=0

CPT PV=

13,984.73

The Cost of Points: 0.0225*250,000=5,625

Now, I=5.5/12=0.4583

PMT=79.40

FV=0

PV= -5,625

CPT

N=85.8492 months

N = 85.8492 months / 12 = 7.15years