Robin and Teryll each have $$8{,}000$ to invest and they disagree about the best place to start a savings account. Teryll found a savings and loan company that will guarantee a rate of $3.9\%$ compounded monthly for the next $10$ years. Robin says her bank is much better because they will give her $4\%$ interest compounded semi-annually for the next ten years. In ten years, which account will end up with the greatest amount and how much difference is there?