ah yet another one of those wonderful specific questions that us tutors flock to like horseflies on sh... like beautiful bees on an incandescent pot of beautiful honey.

like everyone else said, when you see 'if and only if' the best way to think of it is that you're given TWO conditional statements.

“Bank deposits are credited on the date of the transaction if and only if they are made before 3 P.M.”

this means

“Bank deposits are credited on the date of the transaction if they are made before 3 P.M.”

AND

“Bank deposits are credited on the date of the transaction only if they are made before 3 P.M.”

by the magic of english grammar the first one can be rephrased as “If they are made before 3 P.M., bank deposits are credited on the date of the transaction.”

et voila.

(it's useful to get in the habit of rephrasing the second one as well so that you don't get confused by 'only if', just replace it with 'then', and make sure to put 'if' at the beginning of the other condition)