Two parties enter a $2-$year fixed$-$for floating interest rate swap with semi$-$annual payments and notional amount of USD $1$ million. Annualized LIBOR rate at initiation of the swap are as follows:

LIBOR

Rate

$180-$day

$5\mathrm{.}0\%$

$360-$day

$6\mathrm{.}0\%$

$540-$day

$6\mathrm{.}5\%$

$720-$day

$7\mathrm{.}0\%$

After $100$ days, the swap is marked to market when the $80-$day, $260-$day, $440-$day and $620-$day annualized LIBOR rates are $4\mathrm{.}5\%,5\%,6\%$ and $6\mathrm{.}5\%$ respectively.

Required

a$)$ Calculate the price of the swap at initiation

b$)$ Calculate the value of the swap to the floating rate payer, $100$ days into the swap.