Consider a one$-$year spot$-$starting quarterly swap, issued on $17$ February $2023.$ Suppose the NACC interest rate is $5\%$ for all terms.

$($a$)$ Determine the fair swap rate.

$($b$)$ Determine the value of the second payment, for a long contract with nominal of one million, assuming the reference rate resets at $5\mathrm{.}3\%.$