The average annual rate of a private room in nursing homes in Florida now costs $82,125 while a semi-private room is about $74,825 according to this website:
Florida Long Term Care Insurance Costs, Information, Partnership Policies and Quotes for Miami, West Palm Beach, Tampa, Jacksonville & More
That is much more than the $54,000 you are considering ($4,500 per month). And, it seems other COL expenses should be added in. What is scary is that there are little, if any, COL increases from social security or pensions to offset.