Anthony and Michelle Constantino just got married and received$$24,000$ in cash gifts for their wedding. How much will they have on their$25$th anniversary if they place half of this money in a fixed$-$rate investment earning $10$ percent compounded annually? Would the future value be larger or smaller if the compounding period was $6$ months? How much more or less would they have earned with this shorter compounding period? If they place half of this money $,$ PV$,$ in a fixed rate investment earning $10$ percent compounded annually, the amount they will have $,$ FV$,$ on their $25$th anniversary is $$\_\_\_\_\_\_\_\_\_\_\_\_$