a$)$ Suppose that a bank has issued a $$1,000,000$ five$-$year loan to a customer with

a floating rate of interest. The rate equals LIBOR $+5\%$ and is reset each year.

Also assume that a swap dealer is willing to exchange cash flows based on

$$1,000,000$ in which the dealer pays $4\%$ in exchange for LIBOR. Show with a

diagram how the bank can lock in a fixed rate of interest by entering into a swap

with the dealer.

b$)$ What rate of interest is the bank guaranteed to receive each year instead of

LIBOR $+5\%?$