You decide to buy a house that costs $350,000. You are required to provide a 10% down payment up front and you would like to pay off the remaining mortgage balance with equal annual payments over the course of 20 years, starting next year (i.e. payments from t=1 to 20).
Assume now that it is 10 years later (t=10)
1. Suppose a competing bank offers to refinance the mortgage at a new annual rate of 4%. That is, you would now owe this bank the amount left outstanding, which you would pay off over the next 10 years at the 4% rate. If you were to refinance, how much would your new annual payment be?
2. What is the fixed amount you would save per year due to refinancing?
3. Assume that the offer made by the competing bank is one time thing and applicable only to the specific mortgage. Also, assume that the rate at which you can invest or borrow outside this mortgage contract is 6%, and that the competing bank actually charges a fixed fee of $20,000 to refinance. Is it worth it to refinance? Hint: the amount saved earns you 6% per year for the next 10 years, but you have to pay $20,000 to refinance. It is equivalent to an investment project requiring $20,000 initial outflow, and $X (from question (4)) per year cash flow with a discount rate of 6%.