Rental billing looks simple: a rate per period, for as long as the equipment is out. In practice each rental starts mid-month, some bill in advance and some in arrears, rates change at renewal, and a return on the 17th means a partial final period. Multiply that by a few hundred units and the spreadsheet becomes the most important file in the company.
Advance or arrears is a whole period of revenue
Billing a month in advance versus at the end of the month moves an entire period of revenue. It should be stated once, per agreement, and applied the same way every time. It should never be inferred from the last invoice someone sent.
Partial periods need a rule
When a rental starts on the 12th, do you prorate by days or by calendar months? Either is fine. What matters is that the rule is written down and applied consistently, so the customer can check your arithmetic and get the same answer.
Rate changes are new terms from a date
A rate increase at renewal is a new rate from a date. The old rate still applies to the periods before it. Editing the rate in place makes past invoices impossible to explain.
Don't silently catch up
If billing falls behind, the worst outcome is a system that quietly generates six months of invoices at once. A schedule that is behind should say so and wait for a person.