When I have need to make a large cash deposit in the ATM, I have
done this in the past:
If it's a weekend, I will go to a store or post office and buy
multiple money orders instead. It might cost a bit (less than $1 for
each $500) but it's worth it considering what you could lose. This is
only when I know I can't get to the bank on Monday.
When I was in college, another student friend of mine cashed her
student loan check at one bank and put cash into another bank. Part
of her deposit was missing, when she complained, the bank
investigated and after the review the bank found the missing money
and I think also fired an employee over the incident. This is when I
started doing the money orders instead of cash deposits, since $4000
is an awful lot to most college students!