3.2 Mr. Smith takes out a mortgage for $120,000. The agreed amortization time is twenty- five years and the negotiated initial interest rate is 7.5%, fixed for five years. During this time, Mr. Smith makes monthly payments based on this rate. Assume the interest is also compounded monthly. What are the size of these monthly payments? After five years, what is the remaining amount left to pay? At the end of the five years, the bank offers a reduced interest rate of 6%, fixed for another five years. Mr. Smith accepts these conditions and chooses to make payments on a weekly basis. How large are these subsequent payments assuming that the original amortization time is preserved? Assume in this renegotiated situation that the compounding is weekly as well as the payment schedule and that the number of weeks in a year is 52. Finally, plot P(t), the amount owing after t years, as a function of time for the entire 25 year period. Remark: Do your calculations using 7.5% and 6% as yearly nominal interest rates (ie, ignore the fact that Canadian mortgages are CSNA)