I remember something similar from high school. "Would you rather have a million dollars today, or...
$1 doubled every day for a month?"
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Even without compounding or accumulating, (so just like the chessboard analogy) it starts to take off pretty soon:
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End of week 1: $64
End of week 2: $16,192
End of week 3: $2,072,576
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Now you're doubling in the millions...
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End of week 4: $265,289,728!
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So really, the 2nd 2/3 of the chessboard is pretty intense.
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Any gambler knows that doubling up can get real scary real quick!!
