This idea of payments plans/deferred payments seems very similar to how credit cards already operate. However, I could see this being viable if you offer low interest rates (I assume you'll have interest) and if your yearly membership fee is reasonable (I assume there is a fee).

Personally, I don't think I would use it. I prefer to spend within my means, and I have a credit card otherwise.

Good luck on your startup; it seems like this will be quite a large undertaking as you will be essentially acting as a credit company.