Anthony Walker has $$2,000$ to invest. His brother approached him with an investment opportunity that could double his money in $4$ years. What annual interest rate would the investment have to yield in order for Anthony$$s brother to deliver on his promise? $($If you solve this problem with algebra round intermediate calculations to $4$ decimal places, in all cases round your final answer to $2$ decimal places, e$.$g$.8\mathrm{.}72\%.)$

Expected rate of return