When I was considering what to do with my $$10,000$ lottery winnings, my broker suggested that I invest half of it in gold, the value of which was growing by $11\%$ per year, and the other half in certificates of deposit $($CDs$),$ which were yielding $2\%$ per year, compounded every $6$ months. Assuming that these rates are sustained, how much will my investment be worth in $5$ years? $($Round your answer to the nearest cent.$)$

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