Probably will. However when I built my computer about a year ago I created a public wish list and shared it at: https://community.newegg.com/eggxpert/computer_hardware/default.aspx
I got a lot of comments and re-reinforcements. Sounds like it may be your first build, so give yourself some confidence I would advise doing the same thing.
Sounds like you are spending a lot more than I did .
What is your motherboard?
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James Murphy
Trent Smith
I would go with a minimum of a 1000 based on the specs of the computer that you listed. I have always been fond of using Cooler Master power supplies. The Cooler Master V1000 will fit and should give you all the power you will need. It also has Modular system so you just connect the cables that you need to use. I haven't used Rosewill power supplies so I don't know how good they are. Both power supplies have a 5 year warranty.
dbrunton
There are a number of online power supply calculators you can use to calculate how much power you need. Examples below.
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Other things to bear in mind are whether it's a modular power supply - high-end units often have many different internal power cables, and you may want to have these to be detachable, to reduce the internal spaghetti inside the case. As well as looking nicer, this also helps airflow.
However the gold PSU suggested will have plenty of power:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817182325
Or the corsair ( the one I have) mentioned is a little and Bronze less and would probably work also:
http://www.newegg.com/Product/Product.aspx?Item=17-139-051
My two cents.