(I asked this question earlier today, but I did a poor job of explaining myself. Let me try again)

I have a client who is an industrial maintenance company. They sell service agreements that are prepaid 20 hour blocks of a technician's time. Some of their larger customers might burn through that agreement in two weeks while customers with fewer problems might go eight months on that same contract. I would like to use Python to help model projected sales revenue and determine how many billable hours per month that they'll be on the hook for.

If each customer only ever bought a single service contract (never renewed) it would be easy to figure sales as monthly_revenue = contract_value * qty_contracts_sold. Billable hours would also be easy: billable_hrs = hrs_per_contract * qty_contracts_sold. However, how do I account for renewals? Assuming that 90% (or some other arbitrary amount) of customers renew, then their monthly revenue ought to grow geometrically. Another important variable is how long the average customer burns through a contract. How do I determine what the revenue and billable hours will be 3, 6, or 12 months from now, based on various renewal and burn rates?

I assume that I'd use some type of recursive function but math was never one of my strong points. Any suggestions please?

Edit: I'm thinking that the best way to approach this is to think of it as a "time value of money" problem. I've retitled the question as such. The problem is probably a lot more common if you think of "monthly sales" as something similar to annuity payments.