Consider a fixed$-$for$-$floating interest rate swap agreement that requires one party to pay a fixed rate of interest of $9\%$ a year on $$100$ million of principal in exchange for receiving from a counterparty interest equal to LIBOR plus $0\mathrm{.}5\%$ on $$100$ million. Assume that all settlements would be carried out by a financial intermediary such as an investment or commercial bank.

a$.$ If LIBOR is equal to $7\mathrm{.}5\%$ at the first settlement date, how much would the party paying a fixed rate owe the floating$-$rate counterparty? b$.$ If LIBOR had risen to $9\%$ at the next settlement date, what is the net cash payment that the fixed$-$rate party would receive from the floating rate counterparty?