How to use Ebers-Moll equation to calculate collector current?
You are supplying 5V on the 1k resistor will give a base current of about 4.273mA. However you say you should get 3mA as the collector current. However this would violate the idea that the current gain is 100. 

If beta is truly 100 then the base current should be 30uA to give a collector current of 3mA when Vbe is 727mV. I suggest changing either the base resistor or voltage at end of base resistor to give a base current of 30uA and see if things improve.