Question

a homeowner can obtain a 500,000 thirty year fixed rate mortgage at a rate of 3.0% with zero points or at a rate of 2.75% with 2 points. if you will keep the mortgage for 30 years what is the net present value of paying the points to the nearest dollars

1.)9,475

2.)8,360

3.) 6,366

4.)7,616

5.) 5,240

Answer 1

Loan = 500000,, Period of Loan = 30years = 30 x 12 = 360 months

Calculating monthly payment under alternative 1

Interest rate = 3% per year. , Monthly rate = Yearly rate / 12 = 3%/12

For calculating the monthly payment we will use pmt function in excel

Formula to be used: =pmt(rate,nper,pv)

                             =pmt(3%/12,360,-500000)

Calculating monthly payment
Loan (pv)	500000
monthly rate (rate)	3%/12
No of months (nper)	360
Monthly payment (pmt)	2108.02

Using pmt function in excel, we get monthly payment = 2108.02

Calculating monthly payment under alternative 2

Interest rate = 2.75% per year. , Monthly rate = Yearly rate / 12 = 2.75%/12, Points = 2

For calculating the monthly payment we will use pmt function in excel

Formula to be used: =pmt(rate,nper,pv)

                             =pmt(2.75/12,360,-500000)

Calculating monthly payment
Loan (pv)	500000
monthly rate (rate)	2.75%/12
No of months (nper)	360
Monthly payment (pmt)	2041.21

Using pmt function in excel we get pv we get monthly payment = 2041.21

cash flow benefit per month = Monthly payment when interest rate is 2.75% - Monthly payment when interest rate is 3%

= 2108.02 - 2041.21 = 66.81

We know that Net present value of paying points = Present value of benefits - Present value of costs

Present value of benefits = Sum of present value of cash flow benefits per month discounted at current mortgage rate of 2.75%/12

We will use pv function in excel to calculate present value of benefits

Formula to be used in excel : =pvrate,nper,-pmt)

                                           pv(2.75%/12,360,-66.81)

Calculating present value of benefits
Monthly benefit (pmt)	66.81
Discount rate (rate)	2.75%/12
No of Months (nper)	360
Present value of benefits (pv)	16365.33

We get present value of benefit = 16365.33

Present value of costs = Present value of 2 points on Alternative 2

2 points on Alternative 2 = 2% of Loan = 2% x 500000 = 10000

Since 2 points are paid initially at beginning of the loan

therefore present value of costs = Present value of 2 points on Alternative 2 = 10000

Net present value of paying points = Present value of benefits - Present value of costs = 16365.33 - 10000 = 6365.33

which is approximately equal to 6366

Therefore Answer is option 3)6366