Field Formula for Soonest Date After X Amount of Days

Question

I'm trying to create a couple of fields to calculate the eligibility date for employee benefits.

-The first one should return a date of either the 1st or the 15th of the month 60 days after Hire Date. It would need to determine which date is soonest after the 60 days. For example, a hire date of 12/7/2022 would return the result 2/15/2023 while a hire date of 12/15/2022 would return the result of 3/1/2022

-The second one would be the same concept except the return dates would be either the 15th or the last day of the month.

Is this even something that can be done with a formula field?

*Edited to add:

I have a temporary formula in as a placeholder while I build everything out. It's set to return the 1st of the month after 60 days and is working as expected. I just found out that we needed the 15th as well and I don't know where to go from here.

DATE(IF(MONTH(Employee_ID__r.Date_of_Hire__c +60) = 12,
YEAR(Employee_ID__r.Date_of_Hire__c +60)+1,
YEAR(Employee_ID__r.Date_of_Hire__c +60)),
IF(MONTH(Employee_ID__r.Date_of_Hire__c +60)=12, 1,
MONTH(Employee_ID__r.Date_of_Hire__c +60)+1), 1) 

Answer 1

Your formula for the first use case would be something like this:

IF (DAY(Employee_ID__r.Date_of_Hire__c) < 15,
    ..formula to calculate 60 days from same month, day 15,
    ..formula to calculate 60 days from same month, day 1)
  

The reference formulas to use based on the specifics of your use case can be found in this Help article. For your first use case, Variation 3 looks helpful; for your second use case, a combination of Variation 3 and 4