Consider a one$-$year interest rate swap with quarterly payments based on Actual$/360$ and a notional principal of $$1$ million. Assume that the current three$-$month LIBOR and the Eurodollar futures price for the next three quarters are as follows:

$\backslash$table$[[$Quarter$,\backslash$table$[[$# of Days in$],[$Quarter$]],\backslash$table$[[$Current$],[3-$Month$],[$LIBOR$]],\backslash$table$[[$Euro$-$dollar$],[$Futures$],[$Price$]]],[1,90,2\mathrm{.}0\%,],[2,91,,97\mathrm{.}4],[3,92,,97\mathrm{.}0],[4,92,,96\mathrm{.}8]]$

$($a$)$ What is the swap rate for this swap?

$(9$ marks$)$

$($b$)$ After six months, the three$-$month LIBOR is $4\mathrm{.}0\%$ and the Euro$-$dollar futures price for the next quarter is $95\mathrm{.}7.$ What is the value of this swap from the perspective of the floating$-$rate payer?

$(6$ marks$)$