Question $3$ Consider the following information in Table $2,$ on three default$-$risk free bonds with annual coupon payments and face value of $$1,000.$ Table $2$ Bond Coupon rate $(\%)4$ A Time to maturity $($years$)$ Yield to maturity $(\%)1526386\mathrm{.}58($a$)$ Determine the prices of bonds A$,$ B and C$.(3$ marks$)($b$)$ Determine the current term structure of spot interest rates and briefly comment on the shape of the term structure. $(5$ marks$)($c$)$ Demonstrate how you can use bonds A$,$ B and C to replicate a $3-$year zero coupon bond with a face value of $$1,000.(6$ marks$)($d$)$ If the $3-$year zero coupon bond in $($c$)$ has a market price of $$780,$ show how you can earn an arbitrage profit. Make sure to clearly detail the arbitrage strategy. $(6$ marks$)($e$)$ Assume you can buy and sell zero coupon bonds $($face value $$1,000)$ of any maturity and that all bonds are trading at their no$-$arbitrage price implied by the term structure calculated in $($b$).$ An investor expects to receive a cash inflow of $$5$ million in one year's time, which she then plans to lend out immediately. The term of the loan will be two years, with fixed coupon interest paid to the investor at the end of each year, along with the repayment of the entire principal amount at the maturity of the loan. Explain how the investor could arrange this loan today and "lock in the interest rate on the loan, stating exactly how many units of the required bonds need to be long$/$short and the resultant cash flows. What should the interest rate on this loan be$?(8$ marks$)$