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Default Problem using IF statement with dates as part of the formula

Hello, I'm trying to figure out why my current formula is not coming up with the correct result. I have a list of dates in column A:
02/15/2013
01/05/2013
03/01/2013
etc.

I would like column B to reference the corresponding cells in column A and populate the correct Quarter for which the date falls into (Qtr1, Qtr2,etc).

My current formula looks like this:
=IF(A1<4/1/2013,"Qtr1",IF(A1<7/1/2013,"Qtr2",IF(A1<10/1/2013,"Qtr3","Qtr4")))

The value that it gives me, regardless of the date in column A is Qtr4.
I'm sure there is something obvious that I am doing incorrectly.
Thanks in advance to anyone that can help!
 
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