Why doesn't my iMac totally shut down when it goes through shut down

Sorry. I do believe it happens every time. I normally don't shut off the computer at the end of the day, but did when I was going to be away, etc., and although now it goes through shut down and the screen goes totally black giving the appearance it is shut off, when I touch my keyboard in the morning it immediately starts up from as though it was just put to sleep. I have to unplug it now to be sure it is shut down.

This is an iMac Late 2015, 27" model with a 3.2 GHz Quad-Core Intel Core i5.

I have the free version of Malware Bytes on the system which an Apple tech installed. I run scans on occasion but have not found anything.

There are no apps in my User Login items for start up.

I am also having a continual grinding type noise which goes away for a bit after shut down but is now coming back. I don't think it is the fan, as that is a different sound.

Dan, Thanks for your reply. I did the SMC thing and actually in speaking to my sister today I took a look at my energy saver settings and actually under Schedule, which I never set, must be a system setting, it was set to restart at 7 am. I think that's the culprit. All other items you mentioned were unchecked.