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Consider the following scenario: John buys a house for $135,000 and takes out a

ID: 2674207 • Letter: C

Question

Consider the following scenario: John buys a house for $135,000 and takes out a five year adjustable rate mortgage with a beginning rate of 5%. He makes annual payments rather than monthly payments.

Unfortunately for John, interest rates go up by 1% for each of the five years of his loan (Year 1 is 5%, Year 2 is 6%, Year 3 is 7%, Year 4 is 8%, Year 5 is 9%).

Calculate the amount of John's payment over the life of his loan. Compare these findings if he would have taken out a fix rate loan for the same period at 6.5%. Which do you think is the better deal?

Explanation / Answer

For floating rate
payment in 1st year = 135000/5 + 135000*(0.05) = 33750
remaining principal of the loan = 135000 - 135000/5 = 108000
payment in 2nd year = 135000/5 + 108000*(0.06) = 33480
remaining principal of the loan = 108000 - 27000 = 81000
payment in 3rd year = 135000/5 + 81000*(0.07) = 32670
remaining principal of the loan = 81000 - 27000 = 54000
payment in 4th year = 135000/5 + 54000*(0.08) = 31320
remaining principal of the loan = 54000 - 27000 = 27000
payment in 5th year = 135000/5 + 27000*(0.09) = 29430
remaining principal of the loan = 27000 - 27000 = 0
Total payment = 33750+33480+32670+31320+29430 = 160650

For fixed rate
payment in 1st year = 135000/5 + 135000*(0.065) = 35775
remaining principal of the loan = 135000 - 135000/5 = 108000
payment in 2nd year = 135000/5 + 108000*(0.065) = 34020
remaining principal of the loan = 108000 - 27000 = 81000
payment in 3rd year = 135000/5 + 81000*(0.065) = 32265
remaining principal of the loan = 81000 - 27000 = 54000
payment in 4th year = 135000/5 + 54000*(0.065) = 30510
remaining principal of the loan = 54000 - 27000 = 27000
payment in 5th year = 135000/5 + 27000*(0.065) = 28755
remaining principal of the loan = 27000 - 27000 = 0
Total payment = 35775+34020+32265+30510+28755 = 161325

The floating rate is the better deal here