As part of your retirement plan, you have decided to deposit $$6,000$ at the beginning of each year into an account paying $5\%$ interest compounded annually. $($Round your answers to the nearest cent.$)($a$)$ How much $($in $$)$ 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 $$500$ at the beginning of each month instead of $$6,000$ at the beginning of each year. $