You want to buy a house in $10$ years and expect to need $$20000$ for a down payment. If you have $$16000$ to invest, how much interest do you have to earn $($compounded annually$)$ to reach your goal? $($Enter your answers as a decimal rounded to $4$ decimal places, not a percentage. For example, enter $0\mathrm{.}0843$ instead of $8\mathrm{.}43\%)$