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Indeed. You will get the same amount of money. If you want to know how much your investment earned you I would suggest to do it right after tax, but that's the only reason to be picky about the date.
Or when control is Province. :p
Timing in relation to tax day or harvest day will not affect the total return on the investment. It will only affect the distribution of that return between the different tax days.Timing in relation to seasons will affect the return on food production if the investment overlaps a season change. This applies only to the two islands with seasons: FEI and Dwilight.
Best to invest in autumn, then summer, then spring, then winter. Gold won't change, and you'll get a larger absolute number of bushels in autumn (though the percentage increase will be the same regardless of season).