The simplest way to get the age of your gun is to ask Remington; however I can show you a way to get a reasonably close "ball park" estimate of its age. Previous threads in this forum have given lots of information on where to get parts. Try the Search feature of this forum for that.
If its too much trouble or expense to obtain the age of your gun from Remington, here's an idea for how to determine its approximate age:
A previous poster to this forum mentioned that he owned a Remington Model 11 that he said was manufactured in 1910. It's 5 digit serial number was 85XXX. I have a Model 11 manufactured in 1938 with the six digit serial number 406XXX. If we assume that Remington used consecutive serial numbers for each Model 11 that they manufactured during this period, and assuming that they manufactured about same number of Model 11's every year between 1910 and 1938, then the approximately 321,000 that they manufactured during that period could be divided by the 28 years it took to manufacture them to find that approximately 11,464 Model 11's were made per year between 1910 and 1938. So you would simply add another 11, 464 guns per year to the approximately 85,000 guns that had already been made in 1910. Here's what the estimated serial numbers would look like each year until 1916 (based upon the approximations shown above):
1910 - SN 85000
1911 - SN 96464
1912 - SN 107928
1913 - SN 119392
1914 - SN 130856
1915 - SN 142320
1916 - SN 153784
Take all these numbers with a grain of salt. My math skills are shaky.