Does it have a serial number? I know they weren't required on .22 rifles before 1968, and all of these Remington 512s were made from 1940-1967.
But if there was a way of establishing what year it was made, that might impact the value. Anything made before WWII would be worth quite a bit more than one made after, and if it was made in the 1960s it would probably be worth as much as a "shooter" as a "collector's item."
Remington's will have a date code (letters) on the barrel, left side, about half inch in front of where barrel joins reciever. Run Google serach for remington date of manufacture, will pull up the letter codes, and you can tell year and month your rifle was made.
most of the 5teen series remingtons (510, 511, 512, 513, 514, 521) are going for about $200 to $300 right now. There has been a big surge in the old Remington and Mossberg rifles. Some models will bring more money like the 513-T US will bring more than a 511-X. As more and more people figure out that for $300 they can get a great looking rifle that will out shoot many of the $500 22lr on the market today.
I have 2 a 511x and a 511/513 mashup. They are both tack drivers and will shoot right around 1/2" 5 shot 50 yard groups all day anyday. They are well ballanced rifles that offer so much to a shooter.
Check out Rimfirecenteral.com there are some hardcore Remmy 5teen fans over there. They have a sticky on the top of the remington forum with all the date codes.