Question 3: Floating Rate Mortgage

Steve is planning to buy a house worth $500,000, has $100,000 in savings that he will use as a down-payment and will borrow the remainder via a mortgage. He selects a floating rate, closed mortgage with a 3-year term and 25-year amortization period. He will make monthly payments and be charged an interest rate of 3.35% p.a., compounded semi-annually.

Part A: How much will Steve owe after 1 year has passed if interest rates do not change?

Part B: How much will Steve owe at the end of his term if, after 1 year, interest rates rise to 3.65% p.a., semi-annual compounding? What fraction of his payments went to principal and what fraction went to interest?