The mistake you are making is it looks like you think you can use the number on the HUD website as your rent amount. 

The amount your target tenant would want =) In other words, it depends.Are you expecting remote workers to rent your MTR?

You usually end up with the same amount of taxes over two years, you just get your Amazon package and your tax deduction one year sooner.Buy a new car.

Should I charge her a prorated amount of the original rent or the increased month-to-month rent for January?

It can affect estimated replacement cost and therefore the amount of coverage recommended/required.  

ON the more risk type product we do land speculation and Land entitlements but the returns blow most any cash flow at the the same dollar amount out of the water..

couple of bullet points to bring up:* she's on M2M* I told her on 12/7 of the new rent which would apply to a new Jan. 1 effective lease, this is when I got the "I'm moving out" message* Sent her the move-out letter on 12/11, with options for her to either be moved out by 12/31 (she's fully paid up for month of December) or by 1/11 (30 days from date of notice) and pay a pro-rated rent based on her CURRENT rent amount. her choice, either is fine with me.With all that said, I'd love to do as you mentioned and post a notice on her door. 

Can you post a property with an ADU and the recently appraised amount?  

Be ready for a huge amount of information at your finger tips.

The amount saved can dwarf $6k.