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I think I found the answer on my own....
I was just doing "too much" with my first calculation of:
The temporal year matches the issue year if
TemporalOn(MakeDate(ExtractYear(AddYears(the issue date, TemporalYearsSince(the issue date, AddDays(the maturity date, 1)))),ExtractMonth(the issue date), ExtractDay(the issue date)))
To figure out if I am on a year anniversary, all I had to do was:
We are on the year anniversary if
TemporalOn(AddYears(the issue date, TemporalYearsSince(the issue date, AddDays(the maturity date, 1))))
Of course, I am still figuring out the quarterly math, but I will probably get there in time...
For anyone interested, I found the quarterly dates by the formula:
(TemporalMonthsSince(the start date, the maturity date) \ 3) * 3
Basically, do integer division followed by a multiplication and I got my equivalent of TemporalOncePerQuarter.