A $$20,000$ bond loan was cleared in $4$ years by setting up a sinking fund that was

earning $6\mathrm{.}00\%$ compounded semi$-$annually. The deposits were made to the fund at the

end of every $6$ months.

a$.$ Calculate the size of the periodic payments deposited.

Round your answer up to the next cent

b$.$ What was the total interest earned by the fund?