An infinitely recurring payment shouldn't be thought of as costing infinite money, even though that's what you'll pay over time. The later payments aren't worth

An infinitely recurring payment shouldn't be thought of as costing infinite money, even though that's what you'll pay over time. The later payments aren't worth as much as the payments today because the money today can be invested. It turns out that the value of money decays exponentially over time, and the total value of the money paid is an infinite series that converges to P/r, where P is the payment and r is the applicable interest rate. So a never-ending subscription of $100/yr is worth about 100/0.03 = $3333 total today (assuming you would have invested the money in something like a 5-year treasury bond instead). Still a lot, but not infinite.