Recently, a certain bank offered six$-$month CDs at $5\mathrm{.}0\%$ interest compounded monthly and one$-$year CDs at $5\mathrm{.}20\%$ interest compounded monthly. Maria Ruiz bought a six$-$month $$2,000$ CD$,$ even though she knew she would not need the money for at least a year, because it was predicted that interest rates would rise. $($Round your answers to the nearest cent.$)$

$($a$)$ Find the future value of Maria's CD$.$

$($b$)$ Six months later, Maria's $CD$ has come to term, and in the intervening time, interest rates have risen. She reinvests the principal and interest from her first CD in a second six$-$month CD that pays $5\mathrm{.}25\%$ interest compounded monthly. Find the future value of Maria's second CD$.$

$\{$

$($c$)$ Would Maria have been better off if she had bought a one$-$year CD instead of two six$-$months CDs$?$

Yes

No

$($d$)$ If Maria's second CD pays $5\mathrm{.}52\%$ interest compounded monthly, rather than $5\mathrm{.}25\%,$ would she be better off with the two six$-$month CDs or the one$-$year CD$?$

two six$-$month CDs

one$-$year CD