Bjt amp with 2 voltage sources bias point
There appears to be an issue with the circuit you have drawn. I recreated the circuit and I see 4V and 2.5mA across R3 which is what one should expect

If you want Vc to be .5V instead of 1V you need to decrease the value of your Emitter resistor to increase the current though the transistor. R4 of ~170R is about what you would need.







simulate this circuit &ndash; Schematic created using CircuitLab

One thing to note is that if you modify the beta of the transistor up/down from 100  it can have a significant effect on the Q point of the transistor has only small effect on the Q point. This allows part-to-part variation (within reason) to be accommodated without having to individually trim the circuit to each transistor.

EDIT: I renumbered my resistors to match yours.