The merchant pays a fee for it, and they do it to get a sale that they otherwise would have missed.

If you decide to save $25/mo for a $100 product, that is 4 months for you to change your mind, have an emergency suck up that money, or score a lower price by waiting for a sale. But for some segment of the population, they will close on a pay-in-4 right now instead of waiting, and that is guaranteed money.