The Martinezes are planning to refinance their home (assuming that there are no
ID: 3186162 • Letter: T
Question
The Martinezes are planning to refinance their home (assuming that there are no additional finance charges). The outstanding balance on their has offered them two options ) original loan is $100,000. Their finance company Option A: A fixed-rate mortgage at an interest rate of 6.S% per year compounded monthly, payable over a 3 0-year period in 360 equal monthly installments Option B: A fixed-rate mortgage at an interest rate of 6.25% per year compounded monthly, payable over a 12-year period in 144 equal monthly inetallr monthily payment required to amortize each of these loans over the life of the loan. (Round your answers to the nearest Option A: Option 8: (b) How much interest would the Martinezes save if they chose the 12-year mortgage instead of the 30-year mortgage? Use the rounded monthly payment values from part (a). (Round your answer to the nearest cent.)Explanation / Answer
The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is P = L[r(1 + r)n]/[(1 + r)n - 1]. Here, L = 100000.
(a).Option A: Here n=360 and r=6.5/1200=13/2400 so that P=100000(13/2400)[(1+13/2400)360]/ [(1+13/2400)360-1] = (1625/3)*6.991797982/5.991797982 = $ 632.07 (on rounding off to the nearest cent).
Option B: Here, n = 144, and r = 6.25/1200 = 1/192 so that P = 100000(1/192)[1+1/192)144]/ [(1+1/192)144-1] = (3125/6)*2.112883558/1.112883558= $ 988.84(on rounding off to the nearest cent).
(b). The total amount repaid as per option A is 360* $ 632.07 = $ 227545.20, of which, the amount of interest is $ 227545.20- $ 100000 = $ 127545.20.
The total amount repaid as per option B is 144* $ 988.84 = $142392.96, of which, the amount of interest is $ 142392.96- $ 100000 = $ 42392.96.
Hence, the amount saved by the Martinezes, if they chose option B, is $ 127545.20-$ 42392.96 = $ 85152.24.
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