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I think CFA would definitely be a useful thing to add to your CV, and shows recruiters / potential hirers that you’re not just saying you want to get into the finance industry, i.e. it’s “proof” you’re taking it seriously.
However as to whether it would be ‘enough to open doors’, most definitely not. You’ll need to speak to people you know in the industry and see if you can get a foot in the door that way – that’s probably the most effective. It’s when they start to have a look at you (and your CV) that CFA starts to be useful.
An alternative that have worked for some forum members here (can’t remember who) is to also be active in your local CFA society, which again opens doors and makes the right introductions.
Good luck!