Given: $(1)121-$day spot T$-$bill trading $98\mathrm{.}318$ to yield $5\mathrm{.}25\%$; $(2)30-$day risk$-$free rate of $5\mathrm{.}15\%$; $(3)$ a T$-$bill futures contract with an expiration of T $=30$ days.

a$.$ What is the equilibrium T$-$bill futures price?

b$.$ Explain the arbitrage a money market manager could execute if she were holding $121-$day T$-$bills and the T$-$bill futures were trading at $98.$