What periodic payment corresponds with a future value of $$10,786\mathrm{.}17$ when a $2\%$ interest rate is compounded semi$-$annually for eight years? Express the answer in dollars and cents, rounding off as necessary. Select the best response.

$$525\mathrm{.}00$

$$550\mathrm{.}00$

$$575\mathrm{.}00$

$$600\mathrm{.}00$

$$625\mathrm{.}00$

$$650\mathrm{.}00$

none of these answers