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Hmm, great requirement - tricky one to do.
In your Carry Over Fast Formula you have an Expiry Date. By default (meaning the seeded Fast Formulas) the expiry date is set to the end of the year into which it was carried forward. So, in your example, the Expiry Date of your 5 days from 2012 will expire on the 31st Dec 2013. That means when you run Carry Over from 2013 to 2014 it considers the 5 days from 2012. That's not what you want.
What about if you set the Expiry Date to one day earlier, ie the 30th Dec 2013? Add something like this towards the end of your carryover Fast Formula:
... Expiry_Date = add_days(Expiry_Date, -1) ... RETURN Max_Carryover, Effective_date, Expiry_Date, Process
Thank you so much, i will test it and feedback to you with the results.
Do you have another solution for such case.