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Graphs, Graphs, Graphs
Better isn't always the best at all times. There are times where the $100 a day deal (Blue Line) is actually more beneficial.
But Why? When?
If you invested for say, 10 days, the $100 a day deal is better. The other deal (Green Line) grows quickly after Day 10, but is barely worth anything before that. So, for an investment time 10 days or less, the Blue Line deal makes more.
Note:
The point where the two lines intersect represent a point where the amount of money is the same on the same day.