What do you call the amount of money that is added to your bill if you don't pay on time?

In Russia we have a system where if you don't pay your bills on time, the service providers will keep adding on 1/130th (or something like that) of your debt every day, as a form of punishment.

In Russian, the formal term for that money (that is added on top of your debt) is "pennies" (if you translate it literally).

What is the term for that in English? Or do you guys not have this system?

Is it just called a late fee? https://en.wikipedia.org/wiki/Late_fee

If the penalty is some fixed fraction of the amount owed, and will continue to grow over time, it would be called interest on the debt. More generally, an added monetary penalty could be called a surcharge or fee, but that would usually be a one-time amount added to your bill. Here, your debt is accruing interest, as the amount owed gets larger every day you don't pay.