The difference seems to be that you are talking about modeling and analysis and I was talking about calculating actual interest, as in the interest that is actually owed for a particular loan or contract (i.e. every particular contract) and properly accounting for that.
It doesn't matter if the interest is calculated for consumers, intrabank, interbank, fed to bank, loans, mortgages, taxes - the interest rates and interest periods and interest day basis and all kinds of details may vary, and of course accounting standards vary between countries, but the core principles are the same that it all eventually comes up to some amount of money owed to the counterparty - measured in whole cents or perhaps whole dollars or roubles or whatever, but never an arbitrary-precision float. You can't get to a final compounded result "only for output" because when interest compounds (for example, monthly) then at every such point you do have actual "intermediate output" which materializes into a customer-visible change of balance from which the next period's interest is then calculated, and that intermediate output gets rounded because that (unlike estimates or models) is a specific balance owed and it is denominated in a currency with fixed, limited precision. And so after many such steps, the total actual compound interest - i.e. the actual dollars and cents paid by (or to) the counterparty - is slightly different from what the common modeling approach gets if e.g., as you state, it does rounding only for the final output. The difference is tiny, so there is no problem for modeling to ignore it, but actual financial systems (i.e. tracking facts of money owed, not doing estimates and models for decision support) do have to come down to a rounded fixed-precision number owed for every contract at the end of every day.
It doesn't matter if the interest is calculated for consumers, intrabank, interbank, fed to bank, loans, mortgages, taxes - the interest rates and interest periods and interest day basis and all kinds of details may vary, and of course accounting standards vary between countries, but the core principles are the same that it all eventually comes up to some amount of money owed to the counterparty - measured in whole cents or perhaps whole dollars or roubles or whatever, but never an arbitrary-precision float. You can't get to a final compounded result "only for output" because when interest compounds (for example, monthly) then at every such point you do have actual "intermediate output" which materializes into a customer-visible change of balance from which the next period's interest is then calculated, and that intermediate output gets rounded because that (unlike estimates or models) is a specific balance owed and it is denominated in a currency with fixed, limited precision. And so after many such steps, the total actual compound interest - i.e. the actual dollars and cents paid by (or to) the counterparty - is slightly different from what the common modeling approach gets if e.g., as you state, it does rounding only for the final output. The difference is tiny, so there is no problem for modeling to ignore it, but actual financial systems (i.e. tracking facts of money owed, not doing estimates and models for decision support) do have to come down to a rounded fixed-precision number owed for every contract at the end of every day.