I am not aware of any Remington .22 rifle with a 672 designation. Unless there is a very late model from Remington with that model number, I believe you are referring to their model 572 rifle. The M/572 was a PUMP repeater that was initially produced in the 1950's, in various grades and is, or was until the last year or two, still being manufactured.
Serial numbers were not required on .22 rifles up until December of 1968, when the infamous "Gun Control Act of 1968" was passed.
If you do indeed actually have a model 572 PUMP rifle, and you can not find the serial number, you most likely have a unit manufactured prior to 12/68, since all M/572 rifles with serial numbers have them very plainly stamped on the side of the receiver.
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if the serial number is below 579600 it is considered a pre'64
300 to 500 depending on condition and accessories. The rifle can be replaced for under $500
.30 Remington is a caliber (now obsolete), not an identifier of the manufacturer of the rifle or its model number. Not many rifles were chambered for that round, and, if a Remington, it may be a Model 8 which was made in the time frame you reference. Take it to a reputable gun dealer to be examined and appraised, as it was made in various grades which can generate serious collector interest. It could also be a Model 14 or 14 1/2 slide action
1913 Remington MINT 750.00 U.S.
You could check out auctionarms.com to see what they are selling for. A recent copy of Gun Values will give you the present book value.