Arnett College predicts that in $16$ years it will take $$350,000$ to attend the college for four years. Hailey has a substantial amount of cash and wishes to invest a lump sum of money for her childs college fund. How much should Hailey put aside in an account with an APR of $11\%$ compounded monthly in order to have $$350,000$ in the account in $16$ years? Round your answer to the nearest cent, if necessary.