You are a mortgage banker at BB&T Bank in Miami. One customer, Peter, wants to borrow money from your bank to finance his new home. He just finds a new job and plans to buy the house at a price of $300,000. He wants to borrow a 80% loan to purchase the home. You tell Peter that a constant payment, 30 year amortization period, fully amortizing loan (FRM) is available. The interest rate for the loan is 4.5%, which is the same as the market interest rate. Moreover, you will charge a loan origination fee of 3% for the loan.
(a) What is the monthly payment for the loan?
(b) What is the effective interest rate, assuming the mortgage is paid off after 30 years?
(c) If Peter plans to repay the loan after three years, what is the effective interest rate?
(d) If Peter wants to borrow a 90% loan, the loan rate will be 5.5%. Everything else being equal (i.e., he prepays the loan after 3 years, with the 3% loan fee), would you recommend him to borrow the 90% loan? [hint: calculate incremental cost of borrowing]
(e) Suppose Peter can get a loan with a below-market interest rate from the homebuilder. This fully amortizing FRM loan will have a 80% LTV, 4% interest rate, 30 years amortization period, and with no loan fees. At what price should the homebuilder sell the home to Peter in order to earn the market rate of interest (4.5%) on the loan? Assume that Peter would have the loan for the entire term of 30 years and the home would normally sell for $300,000 without any special financing.