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+1 Navy FCU.. You are also eligible for USAA as Active Military as well.
You really should join USAA and Navy FCU. I'd go the Navy FCU route for the auto. You won't regret it. Penfed is the alternative but they are usually the same APR's but the win goes to Navy for ease of approvals.. You are eligible for USA and Navy because you are active now. Penfed can be joined anytime but those two can be difficult if you do not stay enlisted.
With an actual 700 score and ur income without any mates or anything on credit card or any other loan.. U shouldn't have a problem getting any loan even with zero down.. U should try credit union or depending what kind of vehicle ur getting.. Some brand as special in house rates like Toyota and Honda. I wouldn't put anything down finance the whole 32000 get gap insurance through the dealership(cost more) or thru ur insurance company. Gap is for ur loan being 32000. Let's say u drive ur car for 3 months and some moron hits u ur car totaled. Insurance payout only 25000 but u still owe 30500 on loan with gap gap will pay the remaining on it so u pay nothing out of pocket. Chanc rod it happening is slim but better safe than sorry don't wanna be stuck with paying the remaining cuz vehicle upside down