Anthony and Michelle Constantino just got married and received $$26,000$ 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 $7$ 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?

Click on the table icon to view the FVIF table:

If they place half of this money, PV$,$ in a fixed rate investment earning $7$ percent compounded annually, the amount they will have, FV$,$ on their $25$ th anniversary is $$70556\mathrm{.}62.($Round to the nearest cent.$)$

Would the future value be larger or smaller if the compounding period was $6$ months? $($Select the best choice below.$)$

$\text{'}$A$.$ Larger. The greater the number of compounding periods per year, the larger the impact of compound interest, all else equal.

B$.$ Smaller. The greater the number of compounding periods per year, the smaller the impact of compound interest, all else equal.

C$.$ Equal. The number of compounding periods per year does not influence the future value.

The additional amount they would have earned with this shorter compounding period is $ $($Round to the nearest cent.$)$