You need to have $$20,000$ for a down payment on a house in $4$ years. If you can earn an annual interest rate of $3\mathrm{.}8$ percent, how much will you have to deposit today? $($Assume annual compounding.$)$

Multiple Choice

$$16,707\mathrm{.}18$

$$16,900\mathrm{.}24$

$$15,404\mathrm{.}53$

$$17,228\mathrm{.}23$

$$16,597\mathrm{.}52$