$(8$ points$)$ You are entering into a $20-$day repo to repo out a $90-$day $T-$bill, face

value $$100$ million, currently trading at a discount rate of $3\%,$ at a repo rate of

$1\%$ p$.$a$.$ Assume that there is no haircut.

$($a$)$ How much will you have to pay your counter$-$party $20$ days from now in

order to get back the T$-$bill?

$($b$)$ You will break$-$even if the price of the T$-$bill $20$ days from now is equal

to the amount you pay your counter$-$party $($in order to get back the T$-$

bill$).$ At what rate the T$-$bill has to trade $20$ days from now for you to

break$-$even?