Claire has borrowed $\$5,\!000$. She plans to pay off the loan in full after two payments. She will make one payment in 3 years, then another payment in 6 years. The second payment will be exactly double the amount of the first payment. How much is the first payment if the interest rate of the loan is $8.5\%$, compounded annually? Express your answer as a dollar value rounded to the nearest cent.
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