Arthur is planning for his son's college. He has estimated that the total cost of a $4-$year private college education will be $$300,000$ when his son enters college in $16$ years. Arthur currently has $$50,000$ to invest today and no more. What should the annual rate of interest be on this investment to be able to pay for the cost of his son's college education in $16$ years? Show your steps in solving this question.