The 1921-P Morgan has the single highest mintage in the entire series, and a huge number of them have survived into the present since they were not subject to Pittman Act melting; in fact, they were the result of the Pittman Act forcing the Mint to recreate all of the original coins melted. This is the reason for the massive mintages of 1921 Morgans and the Peace Dollar series. Your 1921 shows some circulation, and has a value on the low end for a Morgan. Similar can be found in a dealer's "junk bin" for $20 or a little over, and it's therefore not worth the cost of grading/slabbing. I see (potentially) the telltale hairlines of a brushing on the lower right quadrant of the obverse, which would further reduce the real-world value were it not already a minimal-value coin. Nothing in my words should be construed as advice to unload it. It's still history which you can hold in your hand.
Our friends across the water in China will counterfeit anything. 1921's, by virtue of their commonality, aren't too "dangerous" in that sense, but never say never. I see no reason to doubt your coin. Learn this reverse, particularly the difference in the arrow fletches by comparison to earlier Morgan issues. There are a number of Chinese fakes out there which mistakenly use this reverse and although it doesn't work every time, it's a "smoking gun" attribute for a fake not dated 1921. By 1921 the original Morgan Master Dies had long since been destroyed and they had to recreate the design from scratch, so there are differences on both faces from the "original."
Unfortunately, fakes are a part of life. Members that advocate buying slabbed examples (authenticated and graded by TPG's - Third Party Graders) are correct, but that 1) increases the price of the coin, both buying and selling and 2) locks your precious (golum...golum) away in a plastic tomb so you can't touch it. Quickest and simplest test for large silver coins...see if they are attracted to a magnet. Collect what you want but be careful of big money items until you find your footing.
