You are given with the following information of two proposal of financing programs for your home loan. Suppose the new house costs you $650,000 (sales taxes and others are included). One program is asking you to deposit a 20% down payment on the $650,000 and it provides you with 5.5% interest rate for 15-year monthly payments of the remaining balance, the other program is a 100% financing program which gives you a 2.5% for the first 5 year with the balloon payment as 600,000 plus the PMI (property mortgage insurance) as $200 per month and the rate increases to 6.75% afterward for a 30-year mortgage if no balloon payment for the remaining balance or refinancing is pursued. Let there be no prepayment penalty. That is, you may pay off the loan should you have some extra cash later on. The brokerage fees and commissions are already considered 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 is more favorable to you if your monthly income is $6,000 before tax? (Notice that most lenders will require the borrower to have ratio between mortgage payment and monthly income no greater than 33%).
b) Suppose 4 years later, the market price of your house is $800,000. The tax rate on gains/losses on house sales is 8%. Will you consider selling this house and buy a bigger one if your income has gained to $7000 per month? What is the annualized rate of return in your investment on housing? (Hint: you need to apply amortization of loan here first).
c) Which way of financing the house originally gives you more rate of return if you in fact, sell the house?