At Griffin, we always accrue interest in whole pennies and pounds. When we need to round amounts (in case of fractions of a penny), we round off to the nearest whole penny.
For example, 12.434 would get rounded down to 12.43 while 12.436 would get rounded up to 12.44. In case of a tie, i.e exactly 0.5 pennies, we round off to the nearest "even penny." This is commonly called bankers' rounding. So, 12.435 would get rounded up to 12.44, but 12.425 would get rounded down to 12.42.
In all cases of rounding, we save the fractional penny amounts as a "carry" amount. We add the carried over amount to the accrual for the next day, and the same rounding process is applied.