Rate per 100,000 persons for a quarter - divide annual population by 4?


How do I calculate the rate per 100,000 persons of something occurring for a quarter of a year?

If I have a count of 12 people bought cars in the September quarter and an annual population of 2000 how do I calculate the appropriate rate per 100000?

Fo a whole year I would do count / population * 100000. I've heard that you are to divide the population by 4 (quarters) as the count is for a quarter. Is that correct?

count / (population / 4) * 100000.

I've tried to find some information on the internet to no avail. Can someone provide a quick answer and reason so I will understand. Dividing by 4 doesn't intuitively gel with how I think of it.

Your time is very much appreciated,