Gaming PC for under $1500?

Hey everyone, I'm a 17 year old trying to enter the world of PC gaming. (I'm buying the computer with my own paycheck, so I don't think I'm spoiled in that sense) First of all, is $1500 too pricey for a gaming rig? I want a PC that can give me quite a few years before needing to be upgraded again, I hope to play Battlefield 3, Anno 2070, and other games in the future on the highest settings with good framerates.

Here are the specs of what I'm planning to buy.

  1. Case: Azza Hurrican 2000 Full Tower Gaming Case (with with 4 Hot Swappable HDD Cage & (4) 230MM Fans )
  2. CPU: Intel Core i5-3570K, 3.40 GHz 6MB Intel Smart Cache LGA1155
  3. SSD: 128 GB OCZ Vertex 4 SATA-III 6.0 GB/s - 535 MB/s Read & 200 MB/s Write
  4. HDD: 2 TB (2 TB x 1) SATA-III 6.0 GB/s 64MB Cache 7200RPM HDD
  5. Memory: 8GB (4GB x 2) DDR3 / 1600 MHz Dual Channel Memory (Corsair XMS w/ Heat Spreader)
  6. Mobo: (CrossFireX/SLI) ASRock Z77 Extreme 6 Intel Z77 Chipset DDR3 ATX Mainbord with IRST, Lucid Virtu MVP, XFast Technologies, 7.1 HD Audio, GbLAN, Display Port, 3x PCle x16 (2 Gen 3, 1 Gen 2), 1x PCle x 1 & 2 PCl
  7. Power Supply: 850 Watts - Corsair CMPSU-850TXV2 80 Plus Power Supply - Quad SLI Ready
  8. Video Card: AMD Radeon HD 7950 3GB 16X PCIe 3.0 Video Card
Which will be just over $1500 if bought together and shipped. Note: I'm a newbie at this, and so I've been going around for help.
Are there any cheaper builds? Is $1500 too high a budget?