Problem 1

You decide to buy a house with price of $250,000. You put 20% down payment and consider a 30-year fixed rate mortgage to pay the remaining balance. The lender offers you four choices of the mortgage with monthly payments:

Choice Mortgage Rate Points

a 7.00% 0.00

b 6.65% 0.30

c 6.50% 5.00

d 6.25% 7.00

Suppose that the origination cost is $5,500

Questions

1. If the loan will be outstanding for 30 years, what is the effective cost for each choice? Which choice would you like to make? Why?
2. Which mortgage choices are not properly priced? Why?

Problem 2

Two years ago, you purchase a house of $100,000. You borrow a mortgage with 80% of LTV (loan to value ratio). The interest rate on the mortgage is 6%. Payment terms are being made annually to amortize the loan over 30 years. You have found another lender who will refinance the current outstanding loan balance at 5.5% with annually payments for 30 years. The new lender will charge three discount points on the new loan. Other refinancing costs will equal $3,000.

1. If you hold the loan for 30 years, should you refinance?
2. If the new lender charges you 4.5% instead of 5.5% and you would like to refinance today, at least how many years should you stay in the house (do not prepay)? Why?