Yes it will work. May i ask where you are buying from? I know you are trying to spend as little as possible but even in most countries you can get a much better Corsair CXM, SeaSonic S12-II or XFX TS Series supplies all for under $40 and they are much better quality. Hope this helps
It's not a very high quality psu, but there are loads worse. I'd say it's fine, but a brand like Seasonic or EVGA would be better, as the lower quality psus like the Corsair VP series that you have may not perform and give the right continuous wattage.
But since you're on a budget I say you will be fine.