Mortgage Mechanics $$ Floating Rate Mortgage

Question #$2-(5$ Points$)$

Imagine you purchase a house valued at $$500,000.$ You pay $$30,000$ of down$-$payment

and get a $$470,000$ closed floating rate mortgage, having a three$-$year term and

amortized over $25$ years. Although the interest rate on the mortgage would change, your

monthly payments would remain fixed for the term. Monthly payments would be

calculated based on APR of $\%4\mathrm{.}8$ compounded monthly and amortization period of $25$

years. The actual amount of the interest accrued will be deducted from your fixed monthly

payments and the rest would be used for principal repayment. Now, assume that the

floating rate itself is $4\mathrm{.}8\%$ for the first $6$ months, then suddenly jumps to $6\%$ for the next

$12$ months, then drops to $3\mathrm{.}6\%$ for the next $6$ months, and then declines to $2\mathrm{.}4\%$ for the

final $12$ months. Note that all rates are quoted as an APR and compounded monthly.

Remember that you need to buy a CMHC insurance for your mortgage.

Part A: How much money do you owe $($i$.$e$.$ what is the outstanding balance$)$ after $18$

months?

Part B: How much interest did you pay over the term of the mortgage? How much was

principal?