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 8%/year compounded monthly on the unpaid balance. Because the interest rate for a conventional 30-year home mortgage has now dropped to 6.5%/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 principal?
$ _____________

(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 6.5%/year compounded monthly, what will be her monthly mortgage payment?
$ ______________

(d) How much less will Diane's monthly mortgage payment be if she refinances?
$ ________________

Answer 1

Answer; Part (A)

Current Monthly Installment Amount =

No of Year = 30 Years

No of period = 30 X 12 = 360 monthly payments

Rate = 8% per annum monthly compounded

Effective annual Rate = (1+ 8%/12)¹² -1 = 8.3%

Monthly rate = 8.3 % / 12 = .69167%

Principal Amount = $ 390,000

Formula ; Monthly Installment =  = P × r × (1 + r)n/((1 + r)^n - 1)

   = 390,000 x .69167% [ (1.0069167)^360/ (1.0069167)^360 -1]

= 2600 x[11.95832889/(11.95832889-1)]

   = 2697.50 x 1.09125479

   = $2943.66 Per Month

Answer Part B

Ramaining Amount = Formula

Ramaining Amount =

= 390000*(1.0069167)^60 - 2943.66*[(1.006917)^60 - 1]/.006917

= $371769.69

Answer Part (C)

New Monthly Installment Amount =

No of Year = 30 Years

No of period = 30 X 12 = 360 monthly payments

Rate = 6.5% per annum monthly compounded

Effective annual Rate = (1+ 6.5%/12)¹² -1 = 6.70%

Monthly rate = 6.7 % / 12 = .558333%

Principal Amount = $ 371769.69

Formula ; Monthly Installment =  = P × r × (1 + r)n/((1 + r)^n - 1)

   = 371769.69 x .558333% [ (1.00558333)^360/ (1.00558333)^360 -1]

= 2075.71 x[7.421701592/(7.421701592-1)]

   = 2075.71 x 1.155721966

= $2398.95

Answer Part D

Monthly mortgage Payment less by =

   = $2943.66 - $2398.95

= $544.71