I have 10 days per year. My policy is that each month, I have earned :-

# of personal days per year / # months in a year = 10 / 12 = 0.83 days each month.

If a client leaves when personal days have been earned but not taken, then their final bill includes the requirement to pay for these personal days. If a client leaves and I've taken more days than I've earned, too bad. This is laid out in my policies and see by clients when they join. I will add that I typically don't take my annual week until start August and so prior to August it's rare I've had more than one or two days for appointments.

Doing it this way means that if someone comes towards the end of the years, I've typically got a pot from the prior client's leaving and paying for annual days not taken which can be used as income for days off. This gives me the ability to waiver these fees on a case by case basis if I feel it's a bit unfair. i.e. If I decided to take all 10 days in the final two months of the year and someone was new into my care from September, then I likely would understand it is unfair to the new family to pay a full year's of leave. I would pro-rota the fees they would have to pay and take the other days from the fees charged to the family who left.