Assume you wish to borrow $500,000 and you are evaluating two mortgage choices. The first option is a 3.5% fully amortizing, monthly payment, fixed rate loan for 30 years with $9000 in origination fees and no points. Because you are unable to put 20% down, you will need to pay property mortgage insurance (PMI) on the loan. You are presented with two options for paying the PMI. You may pay it upfront for a one time fee of 3% of the initial principal balance of the loan (this fee is in addition to any other fees or costs). Alternatively, you may pay an additional .45% (quoted annually) of the initial principal balance of the loan every month with your monthly payment. For computational simplicity, assume you will need to pay this amount for the life of the loan. (In reality, you may remove the PMI whenever you reach a 20% equity position in the property, either through price appreciation or mortgage paydown). a. Compute the annual percentage rate for each loan if it is held for the entire 30 years. Assume there are no extra payments made. b. Compute the effective rate (not the EAR, just what you will actually pay over the time you hold the loan), assuming that you will pay the loan off after 4 years and that you never pay more than the required payment prior to that time. c. Which loan is better if you hold the loan to maturity and why? d. Which loan is better if you pay off the loan in 4 years and why?