Acme Corporation enters into a $$75$ million notional amount interest rate swap. The swap calls for Acme to pay a fixed rate and receive a floating rate of SOFR. The payments will be made every $91$ days for one year and will be based on the adjustment factor $\frac{91}{365}.$ The term structure of SOFR when the swap is initiated is as follows:

$\backslash$table$[[$Days$,$Rate $(\%)],[91,4\mathrm{.}50],[182,4\mathrm{.}75],[273,5\mathrm{.}00],[365,5\mathrm{.}20]]$

Determine the fixed rate of the swap

Calculate the first net payment on the swap

Assume that it is $91$ days into the life of the swap. Determine the value of the Swap after $91$ days. The new term structure of SOFR is as follows:

$\backslash$table$[[$Days$,$Rate $(\%)],[91,4\mathrm{.}25],[182,4\mathrm{.}50],[273,4\mathrm{.}80],[365,5\mathrm{.}00]]$