$(5$ points$)$ Consider the borrowing rates for Parties A and B$.$ A wants to finance a $$100,000,000$

project at an annual fixed rate. B wants to finance a $$100,000,000$ project at an annual floating rate.

Both firms want the same maturity of five years.

Firm Fixed Rate Floating Rate

A $$10\mathrm{.}3\%$ Prime$+1\%$

B $$8\mathrm{.}9\%$ Prime$+0\mathrm{.}5\%$

a$.$ Is there any swap opportunity? Why?

b$.$ A swap bank quote an annual fixed rate of $8\mathrm{.}7\%-9\mathrm{.}0\%$ against the annual floating rate of

Prime $+1\%.$ Please draw the diagram to illustrate the swap.

c$.$ What are the savings or gains $($in $\%)$ for firm A$,$ firm B$,$ and the swap bank, respectively?