Five years ago, Diane secured a bank loan of $390,000 to help finance the purcha
ID: 3115405 • Letter: F
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 yr, and the interest rate was 9%/year compounded monthly on the unpaid balance. Because the interest rate for a conventional 30-yr home mortgage has now dropped to 7%/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-yr home mortgage loan in the amount of the current outstanding principal at the prevailing interest rate of 7%/year compounded monthly, what will be her monthly mortgage payment? $ (d) How much less would Diane's monthly mortgage payment be if she refinances? $
Explanation / Answer
The formula used to calculate the fixed monthly payment (P) required to fully amortize a mortgage loan of $ M, over a term of n months, at a monthly interest rate of r is P = M[r(1 + r)n]/[(1 + r)n - 1]
(a). Here, M = $390,000, r = 9%/12 = 9/1200 = 0.0075 and n = 30*12 = 360. Hence, P = 390000*0.0075* [ (1+0.0075)360]/ [ (1+0.0075)360 -1] = 2925*14.73057612/13.73057612 = $ 3138.03 = $ 3138 ( on rounding off to the nearest dollar ). Thus, Diane's current monthly mortgage payment is $ 3138.
(b). The formula is used to calculate the remaining loan balance (B) of a fixed payment mortgage loan after p months is B = M[(1 + r)n - (1 + r)p]/[(1 + r)n - 1]. Here, p = 5*12 = 60, so that B = 390000[(1.0075)360 –(1.0075)60]/[ (1.0075)360 -1] = 390000(14.73057612-1.56581027)/ 13.73057612 = 390000*13.16476585/13.73057612 = $ 373,928.86 = $ 373929 (on rounding off to the nearest dollar). Thus, Diane's current outstanding principal is $ 373,929.
(c ). If Diane decides to refinance her property by securing a 30-yr home mortgage loan of $ 373,928.86 at 7% per year ( 7%/12 = 7/1200), then her monthly mortgage payment will be 373,929*(7/1200)[(1+7/1200)360]/ [(1+7/1200)360-1] =373,929* 8.116497466/7.116497466 = $ 2487.76 = $ 2488(on rounding off to the nearest dollar). Thus, Diane's monthly mortgage payment will change to $ 2488.
(d). If Diane decides to refinance her property by securing another 30-yr home mortgage loan at 7 % per year, her monthly mortgage payment be lesser by $ 3138-$2488 = $ 650.
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