Offtopic: I had to laugh at my dentist's text reminder of my time and date, with a line saying that late attendance would incur a £1 per minute fee.
I know it's supposed to be a deterrent, but if the terms worked both ways and the patient charged the business £1 a minute late, they'd be bankrupt within the month!
I do understand that it's the minority that ruin it for the rest of folk though, especially in a model like the UK's NHS provision.
They will if it's more than 45 days late, when that starts is usually going to be 'from tax day', that can vary, but it's usually for reasons that would typically be your fault (filed late, etc). They even use the same rates they would charge you if you were late to pay them. This has never happened to me, but I'm told that the interest accrual is automatic, supposedly don't even have to ask.