Five years ago, Diane secured a bank loan of $390,000 to help finance the purcha

Question

Five years ago, Diane secured a bank loan of $390,000 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 10% per year compounded monthly on the unpaid balance. Because the interest rate for a conventional 30-year home mortgage has now dropped to 6% 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 6% 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

a)

Diane's current monthly mortgage payment = Loan Amount / ((1-(1+r)^-n)/r)

r = 10%/12

n= 30*12 = 360

Diane's current monthly mortgage payment = 390000 / ((1-(1+10%/12)^-360)/(10%/12))

Diane's current monthly mortgage payment = $ 3422.529.

b)

Diane's current outstanding balance = Diane's current monthly mortgage payment * ((1-(1+r)^-n)/r)

r = 10%/12

n= (30-5)*12 = 300

Diane's current outstanding balance = 3422.529*((1-(1+10%/12)^-300)/(10%/12))

Diane's current outstanding balance = $ 376,639.80.

c)

Monthly mortgage payment =Refinance Loan Amount / ((1-(1+r)^-n)/r)

r = 7%/12

n = 30*12 = 360

Refinance Loan Amount = 376,639.80

Monthly mortgage payment = 376,639.80 / ((1-(1+7%/12)^-360)/(7%/12))

Monthly mortgage payment = $ 2505.794

d)

Difference in Diane's monthly mortgage payment = 3422.529 - 2505.794

Difference in Diane's monthly mortgage payment = $ 916.735

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