Recently, a certain bank offered a $5-$year CD that earns $2\mathrm{.}52\%$ compounded continuously.

Use the given information to answer the questions.

$($a$)$ If $$20,000$ is invested in this $CD,$ how much will it be worth in $5$ years?

approximately $

$($Round to the nearest cent.$)$

$($b$)$ How long will it take for the account to be worth $$70,000?$

approximately years $($Round to two decimal places as needed.$)$