Which of the following investment options will maximize your future wealth at the end of $23$years$?$ Assume any funds that remain invested will earn a nominal rate of $13\%$ compounded monthly.

$($a$)$ Deposit $$$$4$ comma $400$ now.

$($b$)$ Deposit $$$$80$ at the end of each month for the first $9$ years.

$($c$)$ Deposit $$$$50$ at the end of each month for $23$ years.

$($d$)$ Deposit a lump sum in the amount of $$$$13$ comma $200$ at the end of year $9.$

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Part $1$

$($a$)$ If you deposit $$$$4$ comma $400$ now your future wealth at the end of $23$ years will be $$$

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enter your response here.$($Round to the nearest$$ dollar.$)$