You are given with the following information of two proposals of financing programs for your home loan. Suppose the new house costs you $692,400 (sales taxes and others are included). One program is asking you to deposit a 20% down payment on the $692,400 and it provides you with 2.6% interest rate for 15-year monthly payments of the remaining balance, the other program is a 100% financing program which gives a 1.2% for the first 5 year plus the PMI (property mortgage insurance) as $160 per month with a balloon payment as $650,000, (that is, a lump-sum payment at the end of 5th year). The mortgage rate increases to 5.4% afterward for a 30-year mortgage if the balloon payment is not paid and refinancing is applied (That is, the extended program for refinancing is for 30 years and it's not for the 25 years leftover only). Let there be no prepayment penalty. That is, you may pay off the loan should you have some extra cash later. The brokerage fees and commissions are already included in all the numbers given. Answer the following questions:
a) What is the monthly payment for each program in the first 5 years? Which one more favorable to you if your monthly income is $6,000 before tax? (Notice that most lenders will require the borrower to have the ratio between mortgage payment and monthly gross income no greater than 33%).
b) Suppose 4 years later, the market price of your house is $868,000. The tax rate on gains/losses on house sales is 12%. Will you consider selling this house and buy a bigger one if your income has gained to $8500 per month? What is the annualized rate of return net of your financing cost in your housing investment for each financing program?
c) Suppose there is a 15% income tax on your gain in selling your house, how much is the after-tax return now for each financing program?