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 and monthly payments. The third security consists of two monthly
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 Γ of 8.00% and an initial balance B0 of $1, 000, 000.00.2
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:

a. the respective market rates of interest and discount

b. the current market (no-arbitrage) price of the second security