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

$($a$)$

Construct a data table that will show Lindsay the balance of her retirement account for various levels of annual investment and return. If Lindsay invests $$13,000$ at a return of $8\%$ how much will she have $($in dollars$)$ in her retirement account at the end of $30$ years. $($Round your answer to the nearest dollar.$)$

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$($b$)$

Develop the two$-$way table for annual investment amounts of $$5,000$ to $$20,000$ in increments of $$1,000$ and for returns of $0\%$ to $12\%$ in increments of $1\%.$ Using the table, what are the minimum annual investments Lindsay must contribute $($in dollars$)$ for annual rates ranging from $7\%$ to $11\%$ to accrue a final value of $$1,400,000$ after $30$ years. $($Round your answers up to the nearest thousand dollars.$)$