I currently have the following for a formula:
=IF(AN9<7,AM16,IF(AN9<10,AM17,IF(AN9<13,AM18,IF(AN 9<15,AM19,IF(AN914,"Manager Appr")))))

I have seen and used a less intense one where all of the IFs are in the
first set of brackets and all of the results are in the second set. I cannot
find the same formula and cannot make it work on my own.

=IF(7,10,13,15,???) (results set)