Bay Street Vending received an invoice dated August $30$ with terms $\frac{2}{15},\frac{n}{30}.$ The amount stated on the invoice was $$1829\mathrm{.}00.$

$($a$)$ What is the last day for taking the cash discount?

$($b$)$ What is the amount due if the invoice is paid on the last day for taking the discount?

$($a$)$ The last day to take the cash discount is

$($b$)$ The amount due is $

$($Round to the nearest cent as needed.$)$