Lindsay is $25$ years old and has a new job in web development. She wants to make sure that she is financially sound by the age of $55,$ so she plans to invest the same amount into a retirement account at the end of every year for the next $30$ years.

$($a$)$ Construct a data table in Excel that will show Lindsay the balance of her retirement account for various levels of annual investment and return. If Lindsay invests $$10,000$ at return of $6\%,$ what would be the balance at the end of the ${30}^{th}$ year? Note that because Lindsay invests at the end of the year, there is no interest earned on the contribution for the year in which she contributes. Round your answer to a whole dollar amount.

$($b$)$ Develop a two$-$way table for annual investment amounts of $$5,000$ to $$20,000$ in increments of $$1,000$ and for returns of $0\%$ to $12\%$ in increments of $1\%.$ From the $2-$way table, what are the minimum annual investments Lindsay must contribute for annual rates ranging from $6\%$ to $11\%,$ if she wants to accrue a final payout of at least $$1$ million? Note that because Lindsay invests at the end of the year, there is no interest earned on the contribution for the year in which she contributes.

$\backslash$table$[[\backslash$table$[[$Annual$],[$Return$]],\backslash$table$[[$Minimum Annual$],[$Investment$]],],[6\%,$$$,],[7\%,$$$,],[8\%,$$$,],[9\%,$$$,],[10\%,$$$,],[11\%,$$$,]]$