Don't discuss payment until price is determined. The dealerships count on a good bit of money from financing, you won't get as good of a deal if they know you won't be financing with through them.(in general) On the otherhand sometimes it's easier to just cut to the chase. It really varies and you just have to get a feel for it.
The majority of the "How to buy a car" articles I have read say that you should separate the parts of the deal (Purchase price - Trade in value - Financing) and treat them all as separate transactions. Get the best deal you can on each. And make sure you carefully review the final contract to assure they all reflect what you negotiate. I know when the salesperson pulls out their "Four square" I am about to go for a ride.
I would say that the offer you have for financing from NFCU is very fair. Unless the dealer has some special financing for the particular model you are looking at I probably would not let them shotgun my credit to various banks and load me with inquiries.
Car shopping is not my favorite thing and I always take along a friend to help with the negotiations (And SHE is a CPA / MBA so they don't get much past her). I may have a Y chromosome but that doesn't make me the best negotiator.
Starting Score: 500's
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