Assume the annual interest rate on a $500,000 7-year balloon mortgage is 6 percent. Payments will be made monthly based on a 30-year amortization schedule.

a. What will be the monthly payment?

b. What will be the balance of the loan at the end of year 7?

c. What will be the balance of the loan at the end of year 3?

d. Assume that interest rates have fallen to 4.5% at the end of year 3. If the remaining mortgage balance at the end of year 3 is refinanced at the 4.5 percent annual rate, what would be the new monthly payment assuming a 27-year amortization schedule?

e. What is the difference in the old 6 percent monthly payment and the new 4.5 percent payment?

f. What will be the remaining mortgage balance on the new 4.5 percent loan at the end of year 7 (four years after refinancing)?

g. What will be the difference in the remaining mortgage balances at the end of year 7 (four years after refinancing)?

h. At the end of year 3 (beginning of year 4), what will be the present value of the difference in monthly payments in years 4-7, discounting at an annual rate of 4.5 percent?

i. At the end of year 3 (beginning of year 4), what will be the present value of the difference in loan balances at the end of year 7, discounting at an annual rate of 4.5 percent?

j. At the end of year 3 (beginning of year 4), what will be the total present value of lost payments in years 4-7 from the lender's perspective?

k. If the mortgage contains a yield maintenance agreement that requires the borrower to pay a lump sum prepayment penalty at the end of year 3 equal to the present value of the borrower's lost payments in years 4-7, what should that lump sum penalty be?