Gary King invested $$8,400$ at $6\%$ annual interest, and left the money invested without withdrawing any of the interest for $9$ years. At the end of the $9$ years, Gary withdrew the accumulated amount of money.

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$($a$)$ What amount did Gary withdraw, assuming the investment earns simple interest?

The amount Gary withdrew

$

$($b$)$ What amount did Gary withdraw, assuming the investment earns interest compounded annually? $($For calculation purposes, use $5$ decimal places as displayed in the factor table provided, e$.$g$.5\mathrm{.}25471.$ Round answer to $2$ decimal places, e$.$g$.25\mathrm{.}25.)$

The amount Gary withdrew

$

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