An electric fireplace cost a retailer $$415\mathrm{.}00$ less $23\frac{3}{4}\%,20\%,5\%.$ Markup is $58\%$ of the regular selling price. During the end$-$of$-$season sale, the electric fireplace is marked down $22\%.$

$($a$)$ What is the end$-$of$-$season sale price?

$($b$)$ What rate of markup based on cost will be realized during the sale?