You neglected the input impedance Zin of the base to Re, as Zin = hFE*Re =~ 47k which is lowering the base bias. That's all.
Don't worry about hFE =100 unless you expect a 5% tolerance of Vc=Vcc/2 .there are better ways with negative feedback.
So what should 15k be increased to ? So that the effect in parallel with 47k results is 15k , as you intended.
To get Ic=mA, you must have Vbe= 600 mV to start with then add Re=470 mV you get around Vb=1V not 1.17
consider re is 26/Ic so for 1mA and subtract from Re. It would use 420 in this circuit and reduce 15k to 14k to get 1.0V on Vb.
But an NFB circuit is better.