It’s not painless. E.g. dividing $100.00 by 12 month in integer cents requires 11 $8.33 and one $8.37 (or better 4x(2x8.33+8.34), depending on definition of ‘better’). You can forget this $0.04, but it will jump around in reports until you get rid of it – it requires someone’s attention anyway, no matter how small it is. Otoh, in unrounded floating point that will lead to a mismatch between (integer) payments and calculations. In rounded fp it’s the same problem, except when you’re trying very hard for error bits to accumulate (like cross-multiplying dataset sums with no intermediate rounding, which is nonsense in financial calc and where regular fixpoint integers will overflow anyway).
What I’m trying to show here is that both integers and floating point are not suitable for doing ‘simple’ financial math. But we get used to this Bresenhamming in integers and do not perceive it as solving an error correction problem.