I just typed a long reply and accidentally deleted it. Basically you are going to get 10 different answers from 10 different people. You can't compare apples and oranges. I have a 9k sq ft lawn that pays $400 a month. I also have a 9k sq ft lawn that pays $125 a month. Without knowing anything else, all you know is they are both have the same size lawn and one pays three times as much as the other. Hardly useful. I've got a friend on Lawnsite that lives on the west coast. We were comparing prices and came to the conclusion that I was making more per lawn, but he could do more lawns than I could. Mine were more detailed. His were more flat out mowing.
You know how this works. Time x the $ per hour you need to make. Some people will say they need to make $40 an hour solo with a tight route, others might say $60. Some might be able to get by with $30 an hour when things are bad, and others might go broke at that rate. And of course, someone will jump in and say if you are charging less than $80 an hour you are cutting your own throat.
For year round, billed monthly...How many hours a year is it going to take you? Multiply that by what you need to make an hour. Divide by 12. Pad it a little. If you think it will take you 35 minutes a week, figure 45.
I don't do by-the-cuts anymore. But when I did, I would give a price that made monthly billing seem like a much better value. On a lawn that I would charge $125 a month for, I would not have told them I would do it for any less than $40 a cut. But like I said, I don't ever give the option. Things may change, but for now I'll pass on waiting for the phone call to tell me to cut.