I found this information on VintageSingers group at Yahoo. You might want to join that.
Maybe it's a 15-86 or 15-96, if it's too early to be a 15-90. I don't think it matters that much, anyhow, at least not foe sewing with one, hehe.
Singer 15 class machines between the 15-30 and the 15-88/89/90/91
The four models in question are the 15-86/87/96/97. They kind of filled in the period between when the 15-30 was discontinued and the 15-88/89/90/91 came out. They were basically the same mechanism as the 15-30, and the series was short lived. The only way I can tell them apart is by going to my parts diagrams, because I have seen them so seldom.
In the parts page that covers all four models, I note that the BW on the 15-86/87 has the cam driven finger to guide the thread, while the 15-96/97 has the later type without the mechanical guide finger. Then I note that the 15-87/97 have the disk hand wheel, indicating that they were sold as electrics, while the 15-86/96 have spoke hand wheels, indicating that they were sold as treadles or hand cranks. In all of them, they had a lever action stitch length control, which would differentiate them from the 15-30.
Bill Holman