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 10% 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 of7% 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 = 320000 / ((1-(1+10%/12)^-360)/(10%/12))

Diane's current monthly mortgage payment = $ 2808.23

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 = 2808.23*((1-(1+10%/12)^-300)/(10%/12))

Diane's current outstanding balance = $ 309,037.93

c)

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

r = 7%/12

n = 30*12 = 360

Refinance Loan Amount = 309,037.93

Monthly mortgage payment = 309,037.93 / ((1-(1+7%/12)^-360)/(7%/12))

Monthly mortgage payment = $ 2056.04

d)

Difference in Diane's monthly mortgage payment = 2808.23 - 2056.04

Difference in Diane's monthly mortgage payment = $ 752.19

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