Renting vs buying: the honest arithmetic
The question is one division: the modem's price divided by your ISP's monthly equipment fee is the number of months until an owned modem has paid for itself. After that, the fee you're no longer paying is the return. Most cable equipment fees put that break-even inside the first year or two.
What tips it toward buying
A fee on your bill every month, plans to stay with cable internet for more than a year or so, and an ISP whose approved list includes plain modems (so a mid-range purchase qualifies). The fee never stops; the purchase does.
What tips it toward renting
Some ISPs bundle the modem at no separate charge — then there is nothing to save. Some require their own equipment outright (we mark those pages "not allowed" — don't buy for them). Renting also moves swap-outs and support onto the ISP: when a rented unit dies, the truck roll is their problem. And a speed-tier upgrade can obsolete an owned modem before it has paid off.
Two mistakes that erase the savings
Buying a device that isn't on your ISP's list — it won't activate, and you're into return shipping. And buying far above your speed tier "for the future": if you pay for 300 Mbps, a top-tier multi-gig modem mostly buys headroom you can't use yet. Match the tier you actually pay for, from the list your ISP actually publishes — that's what this site is for.