As part of your retirement plan, you have decided to deposit $$9,000$ at the beginning of each year into an account paying $5\%$ interest compounded annually. $($Round your answers to the nearest cent.$)$

$($a$)$

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

$

$($b$)$

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

$

$($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 $5\%,$ 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.