John Johnson has $$2,600$ 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 John's brother to deliver on his promise? $($Round intermediate calculations to $4$ decimal places, e$.$g$.2\mathrm{.}5125$ and final answer to $2$ decimal places, e$.$g$.15\mathrm{.}25.)$

Expected rate of return

$\%$