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If you can afford to pay the $5k upfront you are much better off because that is $5k built in equity to the vehicle and you are avoiding the interest over the life of the loan.
If the money is an issue...I would call NFCU and ask them if they can reconsider the approval for the $40k using your existing application and HP.
+1000. Speaking as someone who is underwater on their car loan, I envy you the opportunity to have built-in equity from day one. Go for it if you are able to come up with the 5k.
If the VIN number is available, go ahead and hand over the check... Otherwise you can call NFCU and ask them to extend your deadline or your pre-approval
I got my pre-approval literally the day before I ordered the car. By the time the VIN number was available, there were about 10 days left until the NFCU check expired.