BF4 will be optimized for 8-cores (CPU), more cores = better performance in this particular case. AMD FX CPUs which I wouldn't have recomended before suddenly becomes a viable and smart option. A FX 6300/6350 will be cheaper than the i3 and perform way better.
It is hard to tell how it will run, but by shifting the CPU I'm betting you will get medium/high-ish settings with an average framerate above 30 FPS.
fx8320 4.1ghz oc
gtx650 ti boost oc
8 gb ddr3 1866 mhz
im playing bf4 on ultra settings without AA frame is ave 40fps and the game play is really good only smtimes on explosion scenes at least 25 fps. %90 im playing with 45~50 fps. Btw resolution is 1920x1080