2. Three mortgage-based securities are up for auction today, in riskless, arbitrage-free markets, by bond traders in Toronto. The first is a single one-year $5000.00 mortgage coupon and the second a single $7000.00 two-year mortgage coupon payment, each sold off of interest-only Canadian residential mortgages of twenty years maturity. The third security consists of two coupon payments, with the first coupon paying in one year and the second in two years, each being taken from an interest-only Canadian residential mortgage. This mortgage is also of twenty years maturity and has an announced annual coupon rate of 8.00% and an initial balance Bo of $1, 000, 000.00. ^[1] Unfortunately, no one has yet bid for the second security, and consequently it does not yet have a market price, nor can corresponding market interest rate for two-year coupons be directly observed. Your supervisor, who is known as someone whose trading acuity cannot be underestimated, wishes however to bid on this second security and assigns you to estimate its market (no-arbitrage) price so he should know what to bid for it. Assuming the first security (the single one-year coupon) sells today for $98.80 per one hundred dollars of face value and the third security is selling today for $12, 824.5541, then based on these observed sales, infer the following:
   1. the respective market rates of interest and discount
   2. the current market (no-arbitrage) price of the second security
3. You've just been appointed senior mortgage loan officer at the Wawa (Ontario) brach of the Royal Bank. A Ms. K. Wynne, who is a potential mortgagor, comes to you seeking a $750, 000 fixed-rate mortgage loan, to be originated today, in order to purchase a local home currently listed for $1, 000, 000.00. Based on her credit record and this collateral, you offer her an announced annual mortgage rate of 5%, fixed over the life of the loan, with a renewable maturity of five years and an amortization period of twenty-five years. She would consider an interest-only mortgage or a constant coupon payment mortgage which has a zero balance at the end of twenty-five years. Prior to deciding, she asks you to show her a sample of the respective monthly interest and amortization portions of the coupon payment, as well as the total monthly coupon payment itself, for each of the two types of mortgage she would consider. She also wants to know the initial balance of each mortgage if she could renew it on the same terms after her sixtieth coupon payment (that is, her first coupon payment on the renewed mortgage would occur sixty-one months from today, once she has paid all required coupon payments at the end of the fifth year of their maturities.) Assuming the sample payments she wishes to see are those she would pay in the thirtieth month of her mortgage, calculate the interest, amortization and total coupon payments owed in the thirtieth and sixtieth months of the mortgage, for the two alternative types of amortization she wants to consider:
   1. the mortgage with renewable five year maturity periods and an interest-only amortization schedule over twenty-five years.
   2. the mortgage with renewable five year maturity periods and a constant payment amortization schedule over twenty-five years.