Hailey and Sarah are considering purchasing a house together. They have identified a beautiful home in Raleigh, North Carolina that is listed at a price of $473,000. Aside from living in the house, Hailey and Sarah are considering this home as an investment, as they only plan to live in the house for 10 years before selling the house. They expect the house to sell of $680,000 in 10 years. As their brilliant friend who is taking Engineering Economy, they have asked for your help in selecting the best mortgage option for their needs.

Option A: A 15-year fixed rate mortgage, with bi-weekly payments (i.e., 26 payments per year). The loans interest rate is 3.94% compounded monthly. The bank will require a 25% down payment. The couple would owe an additional $3,200 in closing costs and fees, however the lender will allow them to include this $3,200 in the loan finance amount (i.e., the amount borrowed).

Option B: A conventional 30-year fixed rate mortgage with an interest rate of 4.375% compounded monthly, and requiring monthly payments. If they choose this option, they would need to make a 20% down payment and would owe an additional $5,250 in closing costs and fees. They are able to make the down payment, but the closing costs and fees would need to be included in the loan finance amount.

1. 1. [7 points] Determine the payments that they would make for each period of each loan (i.e., what is the bi-weekly payment for Option A, and the monthly payment for Option B?).
   2. [8 points] Which of these options should they choose, if their objective is to maximize profit after selling the house in 10 years? For this question, lets define profit as: = .
2. Hailey and Sarah have received one more offer for a home mortgage. The purchase cost of the house ($473,000) remains the same and the time they expect to remain in the house (10 years) remains the same. Details of this new loan option are described below.

Option C: A 30-year adjustable rate mortgage (ARM) in which the initial interest rate is 4.25% for the first three years of the loan. After this initial three-year period, the interest rate will change as described below (the first 10 years of the ARM schedule are shown, given that Hailey and Sarah will sell the house after 10 years). This option will require a 22% down payment, which will be paid from their savings. The $5,500 in closing costs and fees will be included in the loan finance amount. Payments will be made on a monthly basis, and interest is compounded monthly.

n	1	2	3	4	5	6	7	8	9	10
i	4.25%	4.25%	4.25%	4.75%	4.75%	4.89%	4.89%	5.10%	5.10%	5.10%

1. Find the monthly payment for each of the 10 years of this adjustable rate mortgage.
2. Is this a better choice for them, relative to Options A and B outlined in Question 2? This time, support your choice by calculating the total interest paid over the first ten years in these scenarios.