"Christopher recently inherited $$1,290,000,$ which she immediately invested in an equity index mutual fund. If she plans to withdraw $$6,000$ per month from her account, what annual interest rate must she earn in order to have $$284,000$ left after $47$ years? $($Enter your answer as a whole number with two decimal places. For example, if your answer is $14\mathrm{.}1025\%,$ enter $14\mathrm{.}10$ as your answer$)"$