The face value of a nine$-$month, $6\mathrm{.}1\%$ note dated April $30,2006,$ is $$589\mathrm{.}09.$ Determine each of the items listed below. Ignore any grace period.

$($a$)$ the legal due date

$($b$)$ the interest period $($in days$)$

$($c$)$ the amount of interest

$($d$)$ the maturity value

$($a$)$ The legal due date is