Question

I am thinking about refinancing my mortgage. My present balance is $95,000. It is a fifteen year mortgage that I have had for three years and the interest rate is 4.5%. I can refinance my mortgage with a new 15 year mortgage with a 3.5% interest rate with $2500 in closing costs and 1 point or a 3.7% rate with no points and $2500 in closing costs. If I roll the points and closing costs into the new mortgage, should I refinance? Please submit as an Excel spreadsheet.

Answer 1

Current interest rate is 4.5%. This rate is used as proxy for evaluating the options available.

Present value of the existing debt is $95,000

Option 1:

Closing cost= $2,500 Amount of points= $95,000*1%= $950. Total expenses = $2,500 + $950 = $3,450

If this is rolled into new mortgage, loan amount= $95,000+$3,450 = $98,450

Monthly payments will be $703.80 as follows:

Present value of these payments, at 4.5% discount rate is $92,000.81 as follows:

Option 2:

Closing costs: $2,500. No points

If this is rolled to the new loan, amount of loan= $95,000 + $2,500= $97,500

Monthly payments of this loan will be $706.83 as follows:

Present value of these payments at the current interest rate of 4.5% is $92,370.74 as follows:

It is seen that Present values are as follows:

(i) Continuing with the existing loan: PV=$95,000

(ii) Option one- 3.5% loan: PV=$92,000.81

(iii) Option two- 3.7% loan: PV= $92,370.74

Since the option 1 of new 15 year loan at 3.7% interest rate has the lower present value and is lower than the existing loan, it is beneficial to refinance with it.