he Martinezes are planning to refinance their home (assuming that there are no a

Question

he Martinezes are planning to refinance their home (assuming that there are no additional finance charges). The outstanding balance on their original loan is $175,000. 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.)

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

Answer (a)

Option A

Monthly Payment = r(PV)/(1-(1+r)^-n where r is effective monthly interest rate= 6.5%/12 and PV is present value of loan = 175000 and n is number of installment =300

Monthly Payment = (6.5%/12(175000))/(1-(1+(6.5%/12))^-300 = 1181.61

Option B

Monthly Payment = r(PV)/(1-(1+r)^-n where r is effective monthly interest rate= 6.25%/12 and PV is present value of loan = 175000 and n is number of installment =144

Monthly Payment = ((6.25%/12)(175000))/(1-(1+(6.25%/12))^-144 = 1730.46

Answer (b)

Martinezes can interest in option B equal to total payments in each option reduced by principal loan amount.

(1181.61*300 -175000) - (1730.46*144-175000)

= 179483 - 74186.24 = 105296.76

So savings in interest under option B = 105296.76

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