Add 1 year to a date:
(adapted from Convert any date to the same date this year / month | formula)
dateAdd(prop("Original Billing Date"), year(now()) + 1 - year(prop("Original Billing Date")), "years")
Change the date format:
formatDate( dateAdd(prop("Original Billing Date"), year(now()) + 1 - year(prop("Original Billing Date")), "years") , "MM/DD/YYYY")
If condition to alter date if tick box is ticked (finished formula):
formatDate( if(prop("Paid Current Year?") == true, dateAdd(prop("Original Billing Date"), year(now()) + 1 - year(prop("Original Billing Date")), "years"), dateAdd(prop("Original Billing Date"), year(now()) - year(prop("Original Billing Date")), "years")) , "MM/DD/YYYY")
You could hide the Original Billing Date attribute.
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