Change product price - changes existing rebills?

I thought I knew how this worked, but I wanted to ping the forum to make sure.

In Pro v.4 - if I change the monthly rebill price of a product, then next month everybody will be billed at the new amount? Or, will only new clients be billed at the new amount?

I have a significant number of clients and I DON'T want them to pay the new price, and to make my life easier, I don't want to make a new product.

I was hoping somebody in the forum knew for sure how this worked on Pro v.4.

Thanks