A sinking fund is established to discharge a debt of $$50,000$ in $20$ years. If deposits are made at the end of each $6-$month period and interest is paid at the rate of $8\%,$ compounded semiannually, what is the amount of each deposit? $($Round your answer to the nearest cent.$)$

$($a$)$ Are you looking for the present or future value?

$($b$)$ Solve the problem.

A family wants to have a $$160,000$ college fund for their children at the end of $15$ years. What contribution must be made at the end of each quarter if their investment pays $7\mathrm{.}3\%,$ compounded quarterly?

$($a$)$ Are you looking for the present or future value?

$($b$)$ Solve the problem.