The Martinezes are planning to refinance their home (assuming that there are no
ID: 2720930 • Letter: T
Question
The Martinezes are planning to refinance their home (assuming that there are no additional finance charges). The outstanding balance on their original loan is $200,000. Their finance company has offered them two options:
Option A: A fixed-rate mortgage at an interest rate of 6.5% per year compounded monthly, payable over a 25-year period in 300 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 installments.
(a) Find the monthly payment required to amortize each of these loans over the life of the loan. (Round your answers to the nearest cent.)
Option A:
Option B:
(b) How much interest would the Martinezes save if they chose the 12-year mortgage instead of the 25-year mortgage?
Use the rounded monthly payment values from part (a). (Round your answer to the nearest cent.)
Explanation / Answer
The formula to calculate Monthly Instalment = P * r * (1 + r )n / [ (1 + r )n - ]
P = Principal amount, = $ 200,000 ( Option A and B)
r = monthly Interest rate = 6.5/12/100 = 0.005416 ( Option A ), 6.25/12/100 = 0.005208 ( Option B)
n = Number of months = 300 months ( Option A), 144 months (Option B)
After Inserting the values in the above formula, we get,
Option A:
Monthly Instalment = 200000 *0.005416 *( 1 + 0.005416)300 / [ ( 1 + 0.005416)300 - 1 ]
200000 *0.005416 *( 1 .005416)300 / [ ( 1 .005416)300 - 1 ]
200000 *0.005416 * 5.0552 / 4.0552
$ 1,350. 31 or say $ 1,350
Option B:
Monthly Instalment = 200000 *0.005416 *( 1 + 0.005208)144 / [ ( 1 + 0.005208)144 - 1 ]
200000 *0.005208 *( 1 .005208)144 / [ ( 1 .005208)144 - 1 ]
200000 *0.005208 * 2.1127 / 1.1127
$ 1,977.70 or say $ 1,978
The Answers:
Option A = Monthly Payment = $ 1,350
Option B = Monthly Payment = $ 1,978
The Answer to Question ( b )
The Interest Payment under Option A = $ 1,350 * 300 - $ 200,000 = $ 405,000 - $ 200,000 = $ 205,000
The Interest Payment under Option B = $ 1,978 * 144 - $ 200,000 = $ 284.832 - $ 200,000 = $ 84,832
The Interest saved in Option B compare to Option A = $ 120,168 ( 205,000 - 84,832)
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