An open loan of $$13,000$ was taken out today where payments $($deposits$)$ and withdrawals can be made freely with a loan rate of $4\mathrm{.}7\%$ compounded semiannually. To reduce the balance of the loan, $$1530$ was paid $7$ months from today, and $$5090$ was paid $14$ months from today. What is the final outstanding balance of the loan $30$ months from today $(16$ months after the last payment$)?$ State your final answer in dollars $($$$)$ with two decimals.

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