As Jewelerguy stated in the other discussion of your find, the clutch-pins (with plain iron/steel disc in the back of the brass front) mean it is from the World War Two era. To see a time-dated example of your disc's back, from an authoritative info-source, go to the following link, and scroll about 2/3rds down the webpage to "Posterior WWII Type V Disk with Ballou Clutches": Dating Metallic Insignia: Collar Disks
The Sergeant's insignia, having clutch-pins for attachment to the uniform, can date from World War Two to 1970... but in view of your finding of it near the definitely WW2-only collar-disc insignia indicates that both are from the same time period.