Question

Assume that you are a homeowner, and are trying to determine if you should refinance your mortgage. The interest rate on your existing mortgage is 4.875%, and you have 22 years of payments remaining. Your unpaid mortgage balance is $285,000. If you refinance the mortgage, you must pay $7,000 in upfront fees to obtain a new 30 year mortgage. The interest rate on your new mortgage will be 4.3%.

A.What is the monthly mortgage payment on your existing mortgage?

B.What would be the monthly mortgage payment on the new (30 year) mortgage?

C.If you take out the new 30 year mortgage, how much interest will you pay across the entire 30 year period?

D.You are 99.9% certain that you will live in this house for exactly 7 more years, at which time you will pay off the remaining mortgage balance and move (regardless of whether you refinance the mortgage).

What is the present value of your expected net savings (or loss) if you refinance?

Would it be in your best financial interests to refinance the mortgage today?

Answer 1

Using the formula:

, where:

• r= periodic interest rate
• PV = PV of mortgage balance outstanding
• n = number of periods remaining.

A. For original mortgage:

• r = 4.875%/12= 0.4063%
• PV = 258,000
• n = 22*12=264

PMT =(0.4063%*285000)/(1-((1+0.4063%)^(-264))) = $1762.09 per month

B. For ner mortgage:

• r = 4.3%/12 = 0.3583%
• n=30*12 =360
• PV = 285000

PMT = =(0.3583%*285000)/(1-((1+0.3583%)^(-360))) = $1410.32 per month

C. Amount of interest paid = total payments made over the mortgage period - principal amount = (1410.32*360)-285000 = $222,715.20

D. I hav used financial calculator for this part:

Step 1: Calculate the balance outstanding for both the mortgages after next 7 years:

• original mortgage: N=7*12=84, I/Y=0.4063%, PV=285,000, PMT=-1762.09, CPT--->FV=224,649.24
• New mortgage: N=7*12=84, I/Y=0.3583%, PV=285,000, PMT=-1410.32, CPT--->FV=246,945.74

Step 2: Calculate present value of payments to be made over next 7 years in both the cases:

NOTE: I have used the current market interest rate i.e. 4.3% pa. for the PV calculations as this is the prevailing market interest rate at which the future payments should be discounted to get the PV:

• original mortgage: N=7*12=84, I/Y=0.3583%, PMT=-1762.09, FV=224,649.24, CPT--->PV=293,967.22
• New mortgage: N=7*12=84, I/Y=0.3583%, PMT=-1410.32, FV=246,945.74, CPT--->PV=285000 plus $7000 upfront fees = $292,000.00

Step 3: PV of Net savings on refinancing = 293,967.22-292,000 = $1967.22

Yes. Since the cost of refinancing is lower than original mortgage (refinancing results in savings).