The Continental Bank made a loan of $$34,000\mathrm{.}00$ on March $15$ to Dr$.$ Hirsch to purchase equipment for her office. The loan was secured by a demand loan subject to a variable rate of interest that was $6\%$ on March $15.$ The rate of interest was raised to $6\mathrm{.}6\%$ effective July $1$ and to $7\mathrm{.}1\%$ effective September $1.$ Dr$.$ Hirsch made partial payments on the loan as follows: $$600$ on May $9$;$$700$ on June $28$; and $$300$ on October $4.$ Each payment is first applied to any accumulated interest. Any remainder is then used to reduce the outstanding principal. The terms of the note require payment on October $31$ of any interest not paid off by partial payments. How much must Dr$.$ Hirsch pay on October $31?$

Dr$.$ Hirsch must pay $ $$ on Ociober $31.$

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$