Troy is saving for his retirement $20$ years from now by setting up a savings plan. He has set up a savings plan wherein he will deposit $ $143\mathrm{.}00$ at the end of each month for the next $10$ years. Interest is $6\%$ compounded monthly.

$($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?