Question #5:

You have found your dream home in Bedford for $400,000. In order to avoid buying mortgage loan insurance from the Canadian Mortgage Housing Corporation, you have decided to go for a conventional mortgage by making a down payment of 20% and financing the balance with a mortgage loan. Your local bank has offered you a 25-year mortgage at their preferred client APR of 4.35% compounded semi-annually for 5 years. You have chosen a monthly amortization schedule. Unless otherwise stated, assume each of the questions below is independent. (40 marks)

1. a)Suppose your monthly payments are made at the end of each month, what will each payment be?
2. b)Suppose at the time that your mortgage is due for renewal after the first five years, you inherit a significant fortune from your grandmother and decide to just pay off the outstanding principal

Total value today

PV

$ 13,888.89

$ 17,146.78

$ 19,845.81

$ 22,050.90

$ 23,820.41

$ 96,752.78

balance by making a balloon payment. How much will be the balloon payment in order for you to be mortgage-free?

c) Suppose you are like most people and did not inherit a significant fortune but instead had to go back to your bank for a new mortgage quote after the first five years. If your bank quotes you a rate of 5.5% (compounded semi-annually) for a three-year term. What are your new monthly payments on the mortgage?

1. d)Even though you have chosen a 25-year mortgage, you plan to prepay the loan by making an additional payment each period along with your regular payment. How much extra must you pay each period if you wish to pay off the loan in 15 years? Hint: you would need to find the payment over the new time period and the difference between the new and your original payments would be the prepayment.
2. e)Your banker suggests that, rather than obtaining a 25-year mortgage and paying it off early, you should simply obtain a 15-year loan for the same amount. The rate on this loan is 4% compounded semi- annually. By how much will your monthly payment increase/decrease if you choose the 15-year loan option rather than the regular mortgage with prepayment option (i.e. your answer in Part C above)?
3. f)Supposeinsteadofmakingonepaymentamonth,youdecideto divide the same monthly payment (your answer in Part A above) into 2 and make two payments in a month (i.e. semi-monthly or bi- monthly), how many months or years would you be able to save in mortgage payments if your current mortgage terms remain the same over the 25-year life of the mortgage?