Question

# Suppose that five years ago you borrowed \$500,000 using a 30-year fixed-rate mortgage with an annual...

1. Suppose that five years ago you borrowed \$500,000 using a 30-year fixed-rate mortgage with an annual interest rate of 7.00% with monthly payments and compounding. The interest rate on 30-year fixed-rate mortgages has fallen to 6.25% and you are wondering whether you should refinance the loan. Refinancing costs are expected to be 4% of the new loan amount.
1. What is the net present value of refinancing if you make all of the scheduled payments on the new loan?
2. What is the net present value of refinancing if you pay off the new loan at the end of the 6th year?
3. How many payments do you need to make on the new loan in order for refinancing to have a positive net present value?

a. Existing EMI = \$3,313 (Rate if interest is 7%)

New EMI = \$3,079 (Rate of interest is 6.25%)

Difference = \$234

This our saving for one month. We need to find the PV of all the savings for the remaining months

The PV of monthly savings is \$38,000

The cost of refinancing loan is 4% of \$500,000 which is \$20,000

Therefore the net savings or the Net Present value of the refinancing option is \$18,000 (\$38,000-\$20,000)

b. Existing EMI = \$3,313

New EMI = \$2,408

Difference = \$905

This our saving for one month. We need to find the PV of all the savings for the remaining months

The PV of monthly savings at the end of 6th year is \$30,950

The cost of refinancing loan is 4% of \$500,000 which is \$20,000

Therefore the net savings or the Net Present value of the refinancing option is \$10,950 at the end of 6th year(\$38,000-\$20,000). We can also discount the same to todays date using the interest rate as 6.25% and the answer comes to \$7,221

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