$1.$ Recent sales of some real estate and record profits make it possible for a manufacturer to set aside $$900,000$ in a fund to be used for modernization and remodeling. How much can be withdrawn from this fund at the beginning of each half$-$year for the next $4$ years if the fund earns $7\mathrm{.}6\%,$ compounded semiannually?

$2.$A $$4\mathrm{.}8$ million state lottery pays $$20,000$ at the beginning of each month for $20$ years. How much money must the state actually have in hand to set up the payments for this prize if money is worth $7\mathrm{.}7\%,$ compounded monthly?

$3.$ Juanita Domingo's parents want to establish a college trust for her. They want to make $16$ quarterly withdrawals of $$1500,$ with the first withdrawal $3$ months from now. If money is worth $7\mathrm{.}3\%,$ compounded quarterly, how much must be deposited now to provide for this trust?