As part of your retirement plan, you have decided to deposit $$9,000$ at the beginning of each year into an account paying $4\%$ interest compounded annually. $($Round your answers to the nearest cent.$)$

$($a$)$ How much $($in $$)$ would the account be worth after $10$ years?

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$($b$)$ How much $($in $ $)$ would the account be worth after $20$ years?

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$($c$)$ When you retire in $30$ years, what will be the total worth $($in $ $)$ of the account?

$($d$)$ If you found a bank that paid $6\%$ interest compounded annually rather than $4\%,$ how much $($in $$)$ would you have in the account after $30$ years?

$($e$)$ Use the future value of an annuity due formula to calculate how much $($in $$)$ you would have in the account after $30$ years if the bank in part $($d$)$ switched from annual compounding to monthly compounding and you deposited $$750$ at the beginning of each month instead of $$9,000$ at the beginning of each year.