Question 2: Fixed Rate Mortgage

Carl would like to purchase a house in Toronto at a price/value of $675,000. He just turned 36 years old, lives alone, and has a gross annual income of $130,000 per year. He has managed to save $160,000 for a down-payment and will borrow the remainder via a mortgage. He did some research and thinks that he should apply for one of the following mortgages (note these are hypothetical offers):

1. Closed, 4-year term with a 15-year amortization period at a fixed interest rate of 5.2% APR with monthly payments.

2. Closed, 3-year term, 20-year amortization period with a fixed interest rate of 4.5% per year, compounded annually with monthly payments.

3. Closed, 1-year term, 25-year amortization period with a fixed interest rate of 3.95% per year, compounded semi-annually, with monthly payments.

Part A: Compare (compute) the monthly payment required by each offer. Based on industry standards, is there any offer he would not qualify for?

Part B: How much interest would he expect to pay over the life (amortization period) of each mortgage?

*For the next two parts (C and D) assume that he ends up choosing the 3-year term, 20-year amortization period with a fixed interest rate of 4.5% per year, compounded annually with monthly payments.

Part C: How long will it take you to pay off half of the initial principal?

Part D: At what point in time does the amount of each payment going towards principal exceed the amount going towards interest? Put differently, when does the proportion of your payment that goes towards principal exceed 50%? You can simply state the period (month), i.e. The proportion of the payment going towards principal will exceed 50% after x months...