Jeff Keebler is choosing between a fixed-rate and an adjustable-rate mortgage (A

Question

Jeff Keebler is choosing between a fixed-rate and an adjustable-rate mortgage (ARM) for $30,000. Both are 30-year mortgages with monthly compounding and payments. The fixed rate is offered at 8%, while the initial rate on the ARM is 6%. Jeff is concerned that inflation may be a problem in 10 years and that reates may return to levels not seen since the mid-1980's, i.e., in the neighborhood of 12%. Compare the payment to the fixed-rate loan to what Jeff would have to pay on the ARM if it reset to 12% after 10 years. For simplicity, assume that just one reset occurs. Round all calculations to the nearest dollar.

Explanation / Answer

Jeff Keebler is choosing between a fixed-rate and an adjustable-rate mortgage (ARM) for $30,000. Both are 30-year mortgages with monthly compounding and payments. The fixed rate is offered at 8%, while the initial rate on the ARM is 6%. Jeff is concerned that inflation may be a problem in 10 years and that reates may return to levels not seen since the mid-1980's, i.e., in the neighborhood of 12%. Compare the payment to the fixed-rate loan to what Jeff would have to pay on the ARM if it reset to 12% after 10 years. For simplicity, assume that just one reset occurs. Round all calculations to the nearest dollar

initial ARM payment.

             k = 6 / 12 = .5 n = 30 x 12 = 360

             PVA = PMT [PVFAk,n]

            $300,000 = PMT [PVFA.5,360]=       $300,000 = PMT [166.792]=   

         PMT = $1,799

the projected unpaid ARM balance after ten years (20 years or 240 months remaining).

        PVA = PMT [PVFAk,n]

         = $1,799 [PVFA.5,240]    = $1,799 [139.581]       = $251,106

payment required to amortize $251,106 over the remaining 20 years at 12%.

                                    k = 12 / 12 = 1 n = 20 x 12 = 240

                                                PVA = PMT [PVFAk,n]    =        $251,106 = PMT [PVFA1,240]

                                       $251,106 = PMT [90.8194]=   

PMT = $2,765

fixed rate payment at 8% is

                                    k = 8 / 12 = .67            n = 30 x 12 = 360

PVA = PMT [PVFAk,n]=       $300,000 = PMT [PVFA.67,360]=      $300,000 = PMT [136.283]

                                                PMT = $2,201

the ARM would be $564 per month higher

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