$2$ years ago, Caroline invested $$20,000.$ She has earned and will earn compound interest of $14\mathrm{.}7$ percent per year. In $1$ year from today, Mardy can make an investment and earn simple interest of $8\mathrm{.}8$ percent per year. If Mardy wants to have as much in $4$ years from today as Caroline will have in $4$ years from today, then how much should Mardy invest in $1$ year from today?