Alan Fillmore's lifelong dream is to own his own fishing boat to use in his retirement. Alan has recently come into an inheritance of $$415,400.$ He estimates that the boat he wants will cost $$340,500$ when he retires in $6$ years.

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How much of his inheritance must he invest at an annual rate of $3\%($compounded annually$)$ to buy the boat at retirement? $($Round factor values to $5$ decimal places, e$.$g$.1\mathrm{.}25124$ and final answers to $0$ decimal places, e$.$g$.458,581.)$

Investment amount $