BF4 - i7 930+, gtx660+, 8gb+ram
CPU - The i7 930 is tier 3, so try an i5 4690k - tier 1. But you won't build a PC around that for $500.
For $500 try -
CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($63.98 @ OutletPC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($26.75 @ OutletPC)
Motherboard: ASRock Z97 Anniversary ATX LGA1150 Motherboard ($86.42 @ Newegg)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1866 Memory ($77.98 @ OutletPC)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($50.88 @ OutletPC)
Video Card: Gigabyte Radeon R7 260X 1GB Video Card ($127.27 @ TigerDirect)
Case: Corsair Graphite Series 230T Black ATX Mid Tower Case ($59.99 @ Micro Center)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Total: $519.26
It should play BF4 at low to medium sttings