My Remington 81 ser#162xx was manufactured 07/1941
There should be a two letter code on the barrel. you can cross reference the two letter code to a production date on Remingtons website.
1500.00
$400.00
Impossible to answer without the sn or date codes.
$300 without a scope in 95% condition!!
Check the date code stamp on barrel (see related link) by serial only a call to Remington can give you that answer.
At store in Northwest Ct. I saw some ranging in price from $150-$250, depending on condition.
Check barrel code on Remington Society of America: http://remingtonsociety.com/rsa/questions/barrelcodes
If it's not marked it's a model 12 made in 1914.
Not marked, Model 9
Only if it is marked ".223 Remington" on the barrel.
The Model 81's are all date code stamped, go to the Remington Society of America there is a diagram (click it) and a table which explains the codes (month/year)
Assuming it is the Model 81 Woodsmaster, excellent condition examples in .35 Rem are bringing more than $400. sales@countrygunsmith.net