$(1)$ Consider a $1-$year, $$50,000CD.$

$($a$)$ What is its value at maturity if it pays $5\mathrm{.}25$ percent annual interest?

$($b$)$ What would be the future value if the CD pays $4$ percent? What if it pays $6\mathrm{.}5$ percent?

$($c$)$ The Fourth National Bank of Oakland offers CDs with a $5\mathrm{.}25$ percent nominal Interest rate but compounds semiannually. What is the effective rate on such a CD$?$ What would its future value be$?$

$($d$)$ Golden Gate Trust offers $5\mathrm{.}20$ percent CDs with dally compounding. What is such a CD$\text{'}$s effective annual rate and its value at maturity?

$($e$)$ What nominal rate would the Fourth National Bank have to offer to make iss semiannual compounding CD competitive with Golden Gatels dallycompounding CD$?$