You are assuming that the cotton taken in the South by Union agents was paid for. The majority of the cotton taken in Mississippi by Union forces was never paid for. All that had to be done to confiscate cotton was to stamp the bails with "CSA" and it was taken as war prizes, never mind if the planter or owner was pro-Union or not. Then sold by Union officers to Northern agents, who then received a cut of the profit. SOME cotton was sold to the North by Southern planters, not as much that was stolen by the North, not even close. Confederate forces spent more time burning the cotton than selling it, to keep it out of the hands of the Union forces who were stealing it. When the market for Southern cotton dried up from the lack of cotton to steal, Grant had the contribands put on farms to plant and grow the cotton. So did other Union officers, they put the ex-slaves back on the plantations to grow more cotton for the North.
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David Upton