Problem 3: Mortgages (45 marks)

The Nguyen has a choice between two mortgages of $200,000 for a new home, both offered by the Nunavut Northern Bank.

Fixed: conventional 6.25% p.a., five year term, 25 year amortisation

Variable: five year term, 25 year amortisation, at a rate that is currently 5% and which the bank can change monthly based on its prime lending rate + a premium.If the rate changes, the monthly payment is changed to make the maturity date remain the same.No switch to fixed rate is allowed for five years.

All amounts saved by comparing the payments of the two mortgages are deposited or deducted from a TFSA invested in a money market fund that earns 3% less than the variable mortgage rate, but compounded monthly.That means if the variable rate is stated as 5%, the money market fund earns (5% - 3%)/12 per month.To make a consistent reference point, start with this account as positive for savings from the initial use of the variable rate mortgage and keep adding the savings or deducting if the mortgage payment using the variable rate rises above the payment with the fixed rate as it does in part c).

a)What is the first month's payment for each mortgage?

b)How much will The save in five years by taking the variable rate if the rates never change?

c)Now suppose this scenario occurs:The chooses the variable rate mortgage and after two years the rate rises to 8% for the next three years?How much will The have gained or lost after five years, by taking the variable rate instead of the fixed rate?