CPU: Intel Core i3-4130 3.4GHz Dual-Core ProcessorP ($109.99 @ Newegg)
Motherboard: Gigabyte GA-B85M-DS3H Micro ATX LGA1150 MotherboardP ($63.99 @ Newegg)
Memory: G.Skill Ripjaws X Series 4GB (2 x 2GB) DDR3-1600 MemoryP ($41.40 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard DriveP ($54.98 @ OutletPC)
Video Card: Sapphire Radeon R9 270 2GB Dual-X Video CardP ($147.98 @ Newegg)
Case: Enermax ECA3253-BL ATX Mid Tower CaseP ($29.99 @ Newegg)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power SupplyP ($34.99 @ NCIX US)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD WriterP ($14.99 @ Newegg)
Total: $498.31
Prices include shipping, taxes, and discounts when available
~530 After shipment~
http
/pcpartpicker.com/p/KHdXJx
This would run you BF4 on mid~low with constant FPS

! It's only 530 after shipment a bit over your budget but if you can squeeze those 30$ you'd be in a good spot!