Justin is saving for his retirement $23$ years from now by setting up a savings plan. He has set up a savings plan wherein he will deposit $$87\mathrm{.}00$ at the end of every six months for the next $14$ years.Interest is $12\%$ compounded semi$-$annually.$($a$)$ How much money will be in his account on the date of his retirement?$($b$)$ How much will Justin contribute?$($c$)$ How much will be interest?