The spot rate term structure is flat at $5\mathrm{.}5\%$ per annum with continuous compounding.

Some time ago a financial institution entered into a $5-$year swap with a principal of $$100$ million in which every year it pays $12-$month LIBOR and receives $3\mathrm{.}2\%($both annual compounding$).$ The swap now has two and a half years to run. $6$ months ago $12-$month LIBOR was $5\mathrm{.}1\%($with annual compounding$).$

a$)$ What is the value of the swap to the financial institution today? $(8$ marks$)$