Mortgage analysis (10 points): A student got his RMC (Royal Military College) diploma last year and he has just been transferred to his first permanent position. He is interested in a home that has a sale price of $350,000. He plans to make a deposit to buy 5% of the house value. In addition, his broker offers him a mortgage with a fixed rate of 4% compounded semi-annually for a term of 5 years with an amortization period of 25 years.

(a) Calculate the monthly interest rate according to the information. (1 point)

(b) Calculate the monthly payment of the mortgage. (1 point)

(c) Calculate the non-paid value of the home at the end of the 5 th year of the mortgage and the interest paid during the first 5 years. (2 points)

(d) If he can get the same interest rate (i.e. 4 % compounded semi-annually) for the entire 25 years amortization period, how much total interest will he pay during the term of the mortgage? (2 points)

(e) For each monthly payment made during the 25 years amortization period, a portion of the payment is used to repay the loan while the other portion covers the interest expense incurred. Prepare a graph with the following lines: 1) portion of the monthly payment for repayment of the loan over time and 2) portion of the monthly payment for interest expense incurred with respect to time. (2 points)

(f) Rather than making the minimum monthly payment, he decided to accelerate his payments by paying a monthly $2,000. How many monthly payments will be required to pay for the house in this case? How much interest will be saved in this case compared to the minimum monthly payments? (2 points)