On January $1,2024,$ Eagle Corp. issued $$6$ million of $5$ year bonds at a $7\%$ stated interest rate to be paid annually. Eagle Corp. issued the bonds for $$5,763,060$ since the market rate of interest was $8\%.$ What is the carrying value of the bond that Eagle Corp. would report on its December $31,2024$ balance sheet? $($round to the nearest dollar$)$

$$ $$5,779,646$

$$5,806,345$

$$5,810,448$

$$5,807,388$

$$5,804,105$