Question

# Tom has taken out a 9-year mortgage for \$450,000.00 that requires you to make a payment...

Tom has taken out a 9-year mortgage for \$450,000.00 that requires you to make a payment every month with the first payment being made exactly one month from now. The interest rate is fixed at 3.2 percent for the first three years if compounded monthly.

a. What is the initial monthly payment?

b. Immediately after the fixed-rate period expires, the loan interest rate increases to 4.65%. What is the new monthly payment (assume that the loan fully amortizes over the remaining term)?

 LOAN AMORTIZATION FORMULA PMT = L*r*(1+r)^n/((1+r)^n-1), where PMT = Periodic payment [installment] L = Loan amount r = interest rate per month n = number of months a] Initial monthly payment = 450000*(0.032/12)*(1+0.032/12)^108/((1+0.032/12)^108-1) = \$      4,800.94 b] Loan outstanding after 3 years = PV of the remaining 72 (6*12) monthly installments = 4800.94*((1+0.032/12)^72-1)/((0.032/12)*(1+0.032/12)^72) = \$ 314,129.47 New monthly payment = 314129.47*(0.0465/12)*(1+0.0465/12)^72/((1+0.0465/12)^72-1) = \$      5,008.19

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