You are planning to purchase a new house or condominium to use as your primary residence. This assignment will analyze some of the financial aspects of doing so.

The final purchase price is $400,000 and, if you need a mortgage from the bank, your down payment will have to be 20% of the purchase price. The mortgage is a 30-year fixed rate loan with an Annual Percentage Rate (APR) of 4.20%. You will incur a one-time closing cost of $3,600 and you will add this closing cost to the loan borrowed. The mortgage will be amortized over the 30-year period with equal monthly payments. Exactly right after you pay the 60th monthly payment (5 years after the loan starts), you can sell the house for a net proceeds of $568,000 (this is the money you actually received after deducting all sale expenses but BEFORE you pay off your remaining loan principal). Ignore the capital gain tax or property tax in this case.

1. Compute both the annual and the monthly effective interest rates of this loan.

2. Compute the monthly payment amount of this loan.

3. Compute the remaining principal that will be due on the mortgage when you sell the house. Your last payment is made in month 60, so the remaining principal is the required payment immediately after that monthly payment.

4. Calculate the annual Internal Rate of Return (IRR) for this investment if the above mortgage is involved, assuming all 12 monthly payments paid together at the end of each year for this calculation.

5. Calculate the annual Internal Rate of Return (IRR) if an all-cash (no finance) investment is involved; i.e. you pay the full purchase price plus the closing cost at the beginning and collect all net sale proceeds at the end.

6. Assuming you can either finance the purchase as (4) or purchase with all-cash as (5) and there are no other differences between the two strategies, conduct an incremental IRR analysis to determine which strategy you should select and provide calculation and explanation for your decision. (Your cost of capital is at 5.50%)