Today is January $2,2008.$ The LIBOR curve is shown in the first column of Table $5\mathrm{.}13.$

You decide to enter into a $1-$year fixed$-$for$-$floating swap agreement with quarterly

payments and $$100$ million notional.

$($a$)$ What is the $1-$year swap rate for a quarterly fixed$-$for$-$floating swap?

$($b$)$ What is the value of the agreement at inception?

$($c$)$ Calculate the value of the swap for each one of the subsequent dates in Table

$5\mathrm{.}13.$

Table $5\mathrm{.}13$ The LIBOR Curve: January, $2008-$ October, $2008$

Source: Bloomberg.