TimeSolv uses both compound and simple interest.
In the case of Simple, interest will always be calculated against the principal balance amount.
Whereas in the case of Compound, interest will be calculated against the total balance amount. In short, if interest is unpaid, your clients will be charged interest on top of interest because it is calculated on the balance owed. For example, if your invoices give a 30 day grace period, then no interest is calculated within the first 30 days. On day 31, it would start to calculate interest on the unpaid balance owed at the percentage that you have assigned it.
Interest is calculated based on the percentage you assign (please see this article on how to turn interest on and how to assign that percentage). Interest is assigned at that percentage for anything that is due over their grace period time.