Sorry to be so long responding.
The issue of purchase vs. rental is another 'run the numbers' answer. The issue, as far as I can tell, is that if you buy, you have to have an account which is billed monthly whether you use it or not. I've rented 3 or more times (don't keep count), and I'd never choose to own a sat phone in my circumstance (needing one for a week maybe once a year).