Eighteen years from now, Mrs$.$ Smithson will need to have $$120,000$ to pay for her child's post$-$secondary education. She anticipates being able to earn $14\%$ compounded annually for the first $10$ years, and $11\%$ compounded annually for years #$11$ through #$20.$ To the nearest dollar, what amount of money should she invest today in order to meet her goal? $$30,790$ $$14,046$ $$21,750$ $$29,600$