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Leon Fillmore's lifelong dream is to own his own fishing boat to use in his retirement. Leon has recently come into an inheritance of $$420,900.$ He estimates that the boat he wants will cost $$339,800$ when he retires in $4$ years.

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Assuming quarterly compounding of amounts invested at $12\%,$ how much of Leon Fillmore's inheritance must be invested to have enough at retirement to buy the boat? $($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