so we round our APYs to 2 decimal places - e.g. 3.094% becomes 3.10%
We now have a customer who wants to know at maturity -" how come my interest didn't add up to 3.10%, your $1.95 short."
Anyone else ever had this issue

Couple of points to consider. First, Reg D requires that the APR be rounded to the nearest one-hundredth of one percentage point (.01%), In your example I think 3.094 would be disclosed as 3.09% APY (not 3.10%). That would have avoided the customer's perception of an interest shortage. However, if the calculated APY was 3.096 then the APY would be disclosed as 3.10% and the perception of a "shortage" could still arise. In that situation I would simply explain that federal law requires the APY to be rounded to the nearest .01%. Not sure if that will satisfy the customer, though!.

Reg. D 1030.3(f)
(f) Rounding and accuracy rules for rates and yields —
(1) Rounding. The annual percentage yield, the annual percentage yield earned, and the interest rate shall be rounded to the nearest one-hundredth of one percentage point (.01%) and expressed to two decimal places. For account disclosures, the interest rate may be expressed to more than two decimal places.