Five years ago, Diane secured a bank loan of $320,000 to help finance the purcha

Question

Five years ago, Diane secured a bank loan of $320,000 to help finance the purchase of a loft in the San Francisco Bay area. The term of the mortgage was 30 years, and the interest rate was 8% per year compounded monthly on the unpaid balance. Because the interest rate for a conventional 30-year home mortgage has now dropped to 7% per year compounded monthly, Diane is thinking of refinancing her property. (Round your answers to the nearest cent.) (a) What is Diane's current monthly mortgage payment? (b) What is Diane's current outstanding balance? (c) If Diane decides to refinance her property by securing a 30-year home mortgage loan in the amount of the current outstanding principal at the prevailing interest rate of 7% per year compounded monthly, what will be her monthly mortgage payment? Use the rounded outstanding balance. (d) How much less would Diane's monthly mortgage payment be if she refinances? Use the rounded values from parts (a)-(c).

Explanation / Answer

By extracting the information:

Secured bank loan = $320,000

Term of mortgage loan = 30 years

Interest rate = 8%

Fall in interest rate is 7%

    a) Calculate D's current monthly mortgage payment:

For calculating the monthly mortagage payment the below spread sheet is drawn:

Thus the monthly mortgage payment is $2,348.05

     b) Calculate D's current outstanding balance:

For calculating the current outstanding balance the following formula is used:

A = R x 1-(1+i)-n

                 i

Substitute:

A = $2,348.05 x 1-(1.0067)-360

                                      0.0067

Thus, the current outstanding balance is $318,788.16

      c) Calculate D's current monthly mortgage payment , when D decides

For calculating the monthly mortgage paymentb the below spreadsheet is drawn:

          

Thus, the monthly mortgage payment is $2,120.91

d) Difference between the monthly mortgage payment if D refinances:

The formula is given as follows:

Difference = Payment before refinancing - Payment after refinancing

Substitute:

Difference = $2,348.05 - $2,120.91

Thus , the difference between the monthly mortgage payments is $227.14

Working Present value $320,000 N 360 (12*30) Interest Rate 0.67% (8%12) FV 0 PMT ($2,348.05)

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