If the barrel has not been replaced you look at the letter date code stamped on the left side of the barrel. The details are on the Manufactured Date page on the Remington Society of America.
OH and if you think the barrel might have been, post a serial I'll look it up.
The RemingtonModel 121 fieldmaster was introduce in 1936 and discontinued in 1954
remington 740 fieldmaster . 30-06 caliber rifle
Check date code, see related links
Check the barrel codes on the Remington Society of America. http://remingtonsociety.com/rsa/questions/barrelcodes
The Remington Model 572 Fieldmaster slide action .22 caliber rifle was made from 1955 until 1988. The receiver on your rifle was made in 1980 but may not have been assembled into a rifle until 1981 or 82.
It's date code stamped on the barrel, see related links for information on the Remington Society of America.
The link gives barrel code location and tables to look up date.
Get the date code stamped on the barrel and look on the Remington Society of America for manufacturing date page, also has diagram of location if you can't find them.
Request an owner's manual from Remington on their web site, it's free.
50-150 usd
You need to look up the barrel codes, the details are on the Remington Society of America here: http://remingtonsociety.com/rsa/questions/barrelcodes
1949 - there is a date code on the barrel for month/year details on the Remington Society of Amerca here: http://remingtonsociety.com/rsa/questions/barrelcodes