A company received an invoice for $$2842\mathrm{.}26$ dated September $5$ with terms $\frac{4}{10},\frac{1}{30},$ n$/60.$

$($a$)$ If the invoice is paid on September $15,$ how much is to be paid?

$($b$)$ If the invoice is paid on October $1,$ how much is to be paid?

$($c$)$ If the invoice is paid on November $1,$ how much is to be paid?