If it is a 1996 then the prefix letter in the serial number on the receiver will most likely be "B" or possible "C" Please always keep in mind that if you bought your gun used or second hand it may have had the barrels swapped and this can cause much confusion......example is a 1996 barrel will fit just fine on a 1978 receiver or vice versa!!!!!
In addition to what Tu Jays said, the barrel date stamps usually take long enough to repeat that you can get a pretty solid idea of which potential date applies to your gun based on its features.
In any case, an "RS-" serial number points to a manufacture date of 2009/2010 (not sure exactly which) or later.
Best thing to do is use the serial number trick above (w/o serial # pre 67, w/serial # post 67). There have been several discussions in the Forum regarding date codes and serial numbers and is a good resource for more information on the subject.
I'm close, but I'm having trouble finding help with the last few details.
Remington of course just stonewalled me when I tried to email them directly about it.
Also note that sometimes you will find 3 or 4 letters on the barrel.
My understanding is that when sent back to the factory for repairs, they stamped another letter on it to indicate that is had been repaired.