Suspicious face. "Any legible method of putting ink on the form will suffice."

Cam starts filling out fields without making use of table or quill. He will only be stumped if they want any really obscure information, like, uh, "address".

The teller looks vaguely disapproving but this is not against any actual rules. The form wants his name, address, date of birth, employment status, occupation and employer if any, and to know whether this is a personal account or for a business; if the latter it wants to know a great deal of other stuff. Also, does he want to let anyone else access his account, and would he prefer access to be controlled by a key or by providing a drop of blood every time he wants to make a deposit or withdrawal. 

"Can I add my own security measures in addition to the key or blood? Also, is 'Hogwarts' a sufficient address, and how quickly will you wish to be notified if that changes? Also, if my birthday appears on casual inspection to be a date which occurred five years ago, will there be any problems?"

"Any security measures you add yourself must be inside your vault and unable to affect patrons outside it. Hogwarts is an acceptable address; if it changes and you don't notify us any letters we send you may be delayed. Were you born five years ago? Falsifying information is subject to fines and, in certain cases, the seizure of your account."

"I am not five years old. However, my birth date is in 1987."

"Gone back in time, have you?"

"You could describe it that way."

Apparently the teller was being sarcastic, she raises an eyebrow and mutters something in an unfamiliar language*. "Hmm. Here, sign this affidavit." She hands him an affidavit asserting that as far as he knows, nobody thinks he is their dependent child and he is willing to be considered an adult for all banking purposes including criminal penalties.

*It translated to "Wizards and their weird wizard problems."

He signs the affidavit. "If I do the drop of blood thing does it have to come out of my actual body right then or can I conjure materially identical blood and have that work? Alternately, are the keys inherently magical?"

"A conjured drop of blood would fail to replicate your magical signature. The keys are enchanted so no-one can conjure a duplicate."

"Oh, interesting. May I test both of those features now?"

"Certainly. One moment." The teller disappears into a back office and comes back with a small metal bowl with a significant-looking pattern of grooves on the inner surface, and a small ordinary-looking brass key. "The key is already paired with your vault." She presses the handle end of the key into a matching divot on the bottom of the bowl, where it stays with a click. "Just bleed in here for an initial sample, and then you'll be able to access your vault by bleeding on the door."

Cam can with some ado get a drop of blood out of his thumb, and then try again with a conjured version. Also he can attempt to copy the key.

The bowl glows for a second when he puts the drop of blood in, then glows again when he adds the conjured drop, making the teller blink in surprise. Swapping out the key for a conjured key makes it unresponsive to any kind of blood.

"Okay, thanks. I don't want to have to keep track of a key, I'm out of the habit, so I'm going to go with the blood thing and supplement from there."

"Very well. I can have the key disconnected now that the blood method is set up. Would you like to go down to your vault now, to set up additional security or make a withdrawal?"

"Yes please!"

"Right this way, then." She comes out from behind the counter (descending several steps in the process; she comes up to Cam's ribcage) and leads him to a door at the far end from the exit, which opens into a torchlit cave. It's clearly at least partially an artificial cave system, the passages dug wider by magic or technology, but there are also still stalactites and stalagmites here and there where they haven't been cleared out to make room for a network of little carts on rails. The teller gets into one of the carts and gestures for Cam to join her.

He hops in. Is Lupin coming?

"I think I'll meet you back outside when you're done, actually; the carts are a bit . . . much."

The teller grins and taps the front of the cart with a long finger, and it takes off down the track like it's got something to prove.

Gosh, it's like flying but worse. Oh well, Cam is indestructible and is not going to lose his breakfast.

Down, up a bit, down some more, hard right, over a pit that probably isn't really bottomless, under some glowing blue stalactites, and shrieking-metal stop in a corridor lined on both sides with vault doors. The goblin hops out of the cart like that was a perfectly reasonable way to get from A to B and indicates the one on their left. "This one's yours. Just put some blood anywhere on the door." 

A dab of blood appears. "Is the idea that the minecart system will prevent a run on the bank?"

This gets a hint of a smile. "I expect it doesn't hurt, but mostly it's fast. Some vaults are much farther away than yours." Meanwhile, the vault door absorbs his blood and opens to reveal a pile of gold coins. It's not quite big enough to dive into Scrooge McDuck style, but it's big enough to suggest the idea.