Stacy Monroe wants to create a fund today that will enable her to withdraw $$31,600$ per year for $8$ years, with the first withdrawal to take place $5$ years from today.

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If the fund earns $15\%$ interest, how much must Stacy invest today? $($Round factor values to $5$ decimal places, e$.$g$.1\mathrm{.}25124$ and final answer to $0$ decimal places, e$.$g$.458,581.)$

Investment amount $