Troy is saving for his retirement $22$ years from now by setting up a savings plan. He has set up a savings plan wherein he will deposit $$137\mathrm{.}00$ at the end of every

three months for the next $14$ years. Interest is $12\%$ compounded quarterly.

$($a$)$ How much money will be in his account on the date of his retirement?

$($b$)$ How much will Troy contribute?

$($c$)$ How much will be interest?