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?$($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 $4\%,$ 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.