A corporate treasurer wishes to hedge against an increase in future borrowing costs due to possible rise in short$-$term interest rates. She proposes to hedge against this risk by entering a long FRA contract that expires in $180$ days and is based on $180-$Day LIBOR. The current term structure for LIBOR is as follows:

Term $($Days$)$ Interest Rate $(\%)$

$305\mathrm{.}1$

$905\mathrm{.}25$

$1805\mathrm{.}7$

$3605\mathrm{.}95$

Interest rates are measured with a compounding frequency reflecting the length of the period they apply to$.$

a$.$ Calculate the rate that the treasurer would receive on this FRA.

b$.$ Suppose the treasurer went long this FRA. Now, $45$ days later, interest rates have risen and the LIBOR term structure is as follows:

Term $($Days$)$ Interest Rate $(\%)$

$1355\mathrm{.}9$

$3156\mathrm{.}15$

Calculate the market value of this FRA based on a notional principal of $$10,000,000.$

c$.$ At expiration, the $180-$day LIBOR is $6\mathrm{.}25\%.$ Calculate the payoff on the FRA. Does the treasurer receive a payment or make a payment to the dealer?