3. Your mother is buying a house for $500,000 and intends to pay $100,000 down, and borrow the remaining $400,000 (including all closing costs). She is evaluating two loan options: borrow $400,000 at 10 percent on a 30-year term loan (i.e., a mortgage, with monthly payments), or borrow the same amount at 9 percent, but with a loan fee equal to 3 percent of the loan amount. This fee is payable upon closing and cannot be financed. Her opportunity cost on her money is 9 percent, and she has asked your assistance. Please ignore any tax effects.

a. How much will her monthly payments be if she chooses the 10 per- cent loan? (Hint: the monthly interest rate equals the annual rate divided by 12.)

b. How much will her monthly payments be if she chooses the 9 per- cent loan?

c. Your mother expects to stay in this house for only 5 years, at which time she plans to sell her house. Ignoring any differences in the principal values of the loans in five years, which mortgage would you advise her to take? Why?