3. Serena Madison wishes to purchase a $820,000 house. She has accumulated a $180,000 down payment, but she wishes to borrow $640,000 on a 15-year mortgage. For simplicity, assume annual mortgage payments occur at the end of each year and there are no loan fees.

a. What are Madison's annual payments if her interest rate is (a) 4%, (b) 8%, and (c) 12%, compounded annually?

b. Repeat number 1 for a 10-year mortgage.

c. Suppose Madison had to choose between a 15-year and a 10-year mortgage, either one at a 8% interest rate. Compute the total payments and total interest paid on (a) a 15-year mortgage and (b) a 10-year mortgage.