It looks like you got yourself a Singer 20-2 from the 1920s or 1930s. I don’t think that there were any designated as a “K”, but there might have been. The early ones don’t have a serial number on them, which makes it hard to date them. You have to go by features. The model 20 started out having a 4-spoke handwheel, then changed briefly to an 8-spoke wheel, and then went to a 7-spoke wheel. Different wheel finishes help date the 7-spoke (polished, painted, etc). They were black until later models and designs of the model 20 came out in other colors like beige.
I have a 1914 model with the 8-spoke. The 4 and 8-spoke models didn’t have the numbered thread guides. The numbers started sometime with the 7-spoke. They added the felt base to the 7-spoke too. Your machine probably came out originally with the motor on it, so that’s why I’m thinking it may be 1920-30. Electrification must have been fairly common in cities for Singer to send them out with motors on them.
Nice little example of a somewhat unusual Singer Model 20. If I saw the correct auction, you got your money’s worth.
Note: Some of my information was provided by Needlebar.org and the rest by me.
CD in Oklahoma