What do investment banking interns (and bankers) do which benefits from such long hours? Lots of manual data processing? Reading? I absolutely benefit from uninterrupted stretches of 12-24h working on problems sometimes, but only infrequently -- usually hit diminishing returns between 4-12h. The only times where I've been useful >24h was when the task was more "set up this thing which has lots of waiting on other peo…
You basically have two workdays: the client-facing workday, and the preparation-for-the-next-day workday. Client-facing workday goes roughly 9am-6pm. Preparation workday goes from 6pm to anything from midnight (on a good day) to 5am (on a bad day).
During the client-facing workday you're spending about 1-2 total hours having meetings with clients, usually on conference calls, occasionally in person; the more senior you are, the more personal interaction you have with clients. The remainder of the time is spent reviewing the materials you generated the previous night, talking about what needs to be done, etc -- basically a constant planning / execution workflow around multiple concurrent streams of deliverables.
In the evening, managing directors go home around 6pm and vice presidents go home around 8pm. That's when you become really "free" to hunker down and start jamming out work. It's a lot harder to be productive when your time is hacked into 30-minute chunks the way it is during the client-facing day.
It is quite common to have nothing to do for hours at a time, both during the day and evening, while you wait for people to get back to you with further instructions on what to prepare and/or instructions for changing what you've already made. So, a 16-hour workday isn't usually a full 16 hours straight. You usually have time to go to the very nice on-site gym, for example.
The deliverables you're making are usually PowerPoint presentations with a lot of model-driven Excel outputs in them. Occasionally the underlying models are intellectually interesting, but they usually are pretty monotonous to put together....you're building something to a clear spec, and the challenge is being 100.000% certain you did it without errors, not figuring out how to do it.
To answer the question about whether you're productive working such long hours: the time commitment and the stress certainly don't foster creativity, happiness, or high productivity, but they really don't need you to be doing inspired work. At a junior level they're looking for people who can follow defined processes at a high level of throughput with a low error rate, while contributing occasional flashes of original thought -- for example, when you have to build a new model based on a unique client situation. Those situations are actually really exciting (especially when you're working on a big problem for a big client) but the flipside of the excitement is the stress around the consequences of fucking it up -- e.g., if the client just got a "bear hug" letter from a competitor expressing interest in a merger and you have to model out whether it makes financial sense.
The downside is that it's a miserable and unhealthy way to spend a couple of years. The upside is that you ride an incredibly steep learning curve and gain a ton of knowledge on valuation models, the inner workings of various industries, corporate governance, and how to run merger / fundraising / hostile-defense processes.
Hope this was helpful.