Well, but the "common" compound interest calcs aren't how compound interest is actually calculated. You use floating point to calculate the amount due, but once you do, you round to a fixed point (e.g. whole cents) and that's it, that's the final truth. The interest accrued, interest due and interest paid out is a fixed point value by definition. And then for the next interest period you start with that rounded off value as the basis for calculating the next interest which compounds.
So yes, if you use fixed point you obviously get different results, but you won't get correct results according to what's required by accounting standards unless you truncate to fixed point when needed. It's not that this difference is large - after all, it's about rounding off fractions of a cent - but accounting does need to be exact.
> aren't how compound interest is actually calculated.
Completely depends - package them in tranches to sell to secondary markets by the thousands - then you do exactly as I pointed out. Or if you're doing Monte Carlo futures projections modeled as compound interest and only need the value at a future time.... Or any of thousands of financial modeling needs....
If you're printing monthly bills for consumers then you round, but only at output, and only for viewable parts.
So you cannot claim things are not computed this way - it depends on the financial application you're working on,
>So yes, if you use fixed point you obviously get different results, but you won't get correct results according to what's required by accounting standards
Ha - which standard are these? Care to cite them? I've been through this space a long time, and every time someone tells me there is a standard and I ask them for it they soon realize there is no gold, single standard. There are zillions of acceptable choices. There are ones for consumers, ones for intrabank, interbank, fed to bank, loans, mortgagaes, taxes, and on and on. There is no "correct results according to what's required by accounting standards ".
Please cite your standards that apply to all these cases.
Have you worked in finance on numerical financial software?
>you round to a fixed point (e.g. whole cents) and that's it, that's the final truth
Having done numerical stuff, including finance for decades, you simply write the entire codebase in floating point, being sure to do proper analysis that things handle ranges correctly.
Then, and only for output, do you snap to desired observable precision. Never ever even once do you round something to make it look pretty, then jam it back into calculations.
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.
So yes, if you use fixed point you obviously get different results, but you won't get correct results according to what's required by accounting standards unless you truncate to fixed point when needed. It's not that this difference is large - after all, it's about rounding off fractions of a cent - but accounting does need to be exact.