Assuming your payment date is in cell A1, I came up with this. This
formula adds 28 days to the A1 date and determines if that day is a
weekday. If the date is a Saturday or Sunday it adds days
appropriately so the result date is a Monday.
=IF(WEEKDAY(A1+28)=1,A1+28+1,IF(WEEKDAY(A1+28)=7,A 1+28+2,A1+28))
.... where Sunday is day 1 and Saturday is day 7.

Also consider the WORKDAY() function, which disregards holidays (in a
list you specify) and weekends in its calculations; I tried assuming
that in 4 weeks there are 8 weekend days and tried =WORKDAY(A1,28-8)
but did not always come up with the same answers as the WEEKDAY
solution. Will either of these fit your situation?