An invoice for $$2,675\mathrm{.}99$ is dated June $23$ with terms $3/10,1/15,$ N$/30.($Note: June has $30$ days.$)$

$($a$)$ What is the last date the invoice can be paid to receive any sort of discount?

$($b$)$ Calculate the amount due to the nearest cent if the invoice is paid on July $6.$