According to the Remington website, the Model 514 .22 single shot bolt action rifle was manufactured from 1948 until 1971. I paid $19.00 for mine, in 1960. When I finally traded it in, in the early 80's, it was listed in a book of gun values at $75. They made a 514A, with a full sized stock, and a 514BC, or boy's carbine. The latter had a shorter stock and barrel to fit younger shooters. If you're looking at one to buy, be sure to check the spot where the extractor on the front of the bolt fits into the notch on the chamber end of the barrel. The weakness was that the extractor would wear that spot out until it was sufficiently oversized to cause extraction problems. I would suggest looking it up in a current edition of one of the books on gun values that are published. I think Peterson Press, the publishers of Guns and Ammo magazine, put one of those out, or used to. Value of any old firearm depends on it's condition, it's relative rarity, and whether or not anyone wants to buy it. I wouldn't take less than $75, as that's what I got for mine, in excellent condition, in the early 80's. Good luck.
Current market prices for a Remington 514 in fair to good condition are in the $90-$130 range. If you want to to learn more about these fine rifles check out the Remington Forum on rimfirecentral.com
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