A trust fund is set up to make payments of $$$ $1500\mathrm{.}00$ at the end of each quater for fifteen years. Interest on the fund is $3\%$ compounded quaterly.

$($a$)$ How much money must be deposited into the$$ fund?

$($b$)$ How much will be paid out of the$$ fund?

$($c$)$ How much interest is earned by the$$ fund?