Billy McMahon is interested in buying a waterfront vacation home and has saved $100,000 for the down payment. His plans call for making additional monthly deposits into an investment account over the next 12 months. Billy McMahon wants to make the purchase 18 months from today and wants to have $400,000 saved up for the down payment. 

a. What is the amount of each of the additional payments he must make for his plan to work out? Assume Billy can earn 4% annual return in his investment account. 

b. Prepare an amortization schedule proving the answer you computed in a. is correct. 

c. If Billy takes out a 30-year, $800,000 mortgage at 5%, what will his mortgage payments be? 

d. Prepare an amortization schedule to prove that your answer is right and his mortgage will be paid off in 30 years. 

e. Assume he pays an additional $500 towards his mortgage each month. How much sooner will he be able to pay off her mortgage? 

f. Prepare an amortization schedule proving your answer in e.