Xavier Trust is planning to invest $$10$ million for one year. As an alternative to a one$-$year fixed$-$rate note paying $2\mathrm{.}5\%,$ the Trust is considering a synthetic investment formed by investing in a $5/3$ Bank one$-$year floating$-$rate note $($FRN$)$ paying LIBOR plus $100$ basis points and taking a position in a Eurodollar futures strip. The $5/3$ FRN starts on $12/20$ at $2\mathrm{.}00\%($LIBOR $=1\mathrm{.}00\%)$ and is then reset the next three quarters on $3/20,6/20,$ and $9/20.$ On December $20,$ the Eurodollar futures contract expiring on $3/20$ is trading at $98($IMM index$),$ the contract expiring on $6/20$ is trading at $99,$ and the contract expiring on $9/20$ is trading at $99$; the time separating each contract is $0\mathrm{.}25/$year and the reset dates on the floating$-$rate note and the expiration dates on the futures expiration are the same.

a$.$ Explain how Xavier Trust could use a strip to lock in a fixed rate. Calculate the rate Xavier could lock in with a floating$-$rate note and Eurodollar futures strip.

b$.$ Calculate and show in a table Xavier's quarterly interest receipts, futures profits, hedged interest return $($interest plus futures profit$),$ and hedged rate for each period $(12/20,3/20,6/20,$ and $9/20)$ given the following rates: LIBOR $=1\mathrm{.}5\%$ on $3/20,$ LIBOR $=1\mathrm{.}00\%$ on $6/20$ and LIBOR $=1\mathrm{.}5\%$ on $6/20.$