I am not in banking finance but I think the double entry accounting would be if you deposit a $20 bill that physical $20 bill shows up on the "physical stack o cash" as an asset and the other entry (double entry, get it?) shows up as a liability in accounts payable because they owe you $20.

I was in IT at a stock trading firm a long time ago and the limited free training they provided for accounting was probably the most interesting non-job related on the job training I ever attended.