HY Industries Ltd$.$ plans to replace a warehouse in eleveneleven years at an anticipated cost of $$$$50,000.$ To pay for the$$ replacement, a sinking fund has been established into which equal payments are made at the end of every $6$ months. Interest is $9\%$ semi annually.

$($a$)$ What is the size of the periodic$$ payment?

$($b$)$ What is the accumulated balance just after the $18$th $$payment$?$