You don't pay any tax. The person giving you the car would pay any gift tax that might be due.
In terms of how much gift tax your son would pay, he would pay tax on the excess over the annual gift tax exclusion amount of $13,000 so yes, he would pay gift tax on $2,000 if the car were worth $15,000.
A quick check on the Kelly Bluebook website suggests, however, that the trade-in value of the car would be only about $13,500 with that mileage (but without a lot of additional options on it). The private sale value ranges from about $13,000 to $15,000 (if the car is in pristine condition).
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I agree with the prior answer, but will add that the amount of the gift tax is ultimately reflected in a reduction of the unified credit available when the person that made the gift passes away, so unless NY has a gift tax that is payable, your son will not be out of pocket any monies for gift taxes.
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I agree with the first two answers.
Gift tax, if any, is the responsibility of the person making the gift. There is a $13,000 "tax free" limit, $26,000 if the "giftor" is married and the spouse joins in the gift. If the $13,000/$26,000 limit is exceeded, the person giving the gift is required to file a gift tax return, Form 709. However, no actual gift tax is due, unless the giftor's total gifts exceed $5,000,000 (with some other considerations). As you can see, the actual gift tax that might be due is not relevant to the great majority of people in the USA.
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