Ask HN: Financial data and rounding

I made a proposal to a client on how they should store and work with finaicnal data that has the potential to involve minute fractions of a dollar. (e.g. Pay contractor B 13.31% of the $55.53 billed)

I proposed that they keep financial values in as accurate a form as possible (to the ten-thousandths, because they use the T-SQL smallmoney type), use bankers' rounding and round at the last possible moment.

This proposal was rejected and I was told that they wanted to round to the hundredth, use "round half up" rounding and perform the rounding before any calculations were performed with the financial data.

I feel that their decisions are wrong, but they are adamant and this edict came from their financial department.

Am I worrying too much, or does it seem like this is a large potential problem?