Cheapest GPU for max LoL

[lagmanx]

Now I know this question has been asked a dozen times before but I have never seen a good solid answer.

All I want is a graphics card that can play LoL on max settings at 60 fps while spending as little as possible. I just do not accept I have to spend $120 to do that.

If this at all helps I have:
Intel Pentium G3220 3.0GHz Dual-Core Processor
MSI H81M-P33 Micro ATX LGA1150 Motherboard
ViewSonic VA2037A-LED 20.0" 16:9 Monitor

 

[learningbitbybit]

lol this: http://pcpartpicker.com/part/sapphire-video-card-100292ddr3l