Likely close to that much, yes.
- We don't know the precise amounts of these trace precious metals in Psyche, merely that the main constituents are nickel and iron.
- Our understanding of the amounts of gold and platinum in asteroids derive largely from studying meteorites, which should be representative of asteroid compositions.
- Given those assumptions, Psyche likely does have several hundred quintillion dollars worth of nickel, iron, gold, platinum, and other metals.
- Verne's story could have been influenced by stories of meteorites, though not asteroids.
Psyche's composition was first investigated about 30 years ago through radar observations, which studied the properties of the surface and from there determined the asteroid's rough composition. Ostro 1985 and Magri et al. 1999 classified it as an M-type asteroid, the most metal-rich class, based on its high radar albedo. Nickel and iron are the most likely constituents, but as it's a metal-rich asteroid, we expect to see other (precious) metals inside it, too. From Ostro 1985:
Consider the case of asteroid 16 Psyche, whose radar albedo (0.29 ± 0.11) is the highest estimated for a main- belt asteroid. The VIS/IR data suggest an association of Psyche's surface mineralogy with either enstatite chondrites (w ^ 0.3) or iron meteorites (w > 0.9). To satisfy Psyche's radar albedo, the first possibility would require a nearly solid surface, whereas the latter is compatible with porosities typical of lunar soil. The case is not closed, but the radar results favor the hypothesis that Psyche is a nearly entirely metallic asteroid, presumably the collisionally stripped core of a differentiated object.
As we have yet to perform detailed studies of the internal structures of asteroids (heck, that's why Psyche is a target for future exploration), we're forced to turn to meteorites to provide clues as to their compositions. The amount of gold in meteorites is known to vary, from 0.0003 parts per million to 8.74 parts per million (Jones 1974). Psyche likely lies near that upper limit. Assuming the mass found by Kuzmanoski & Kovacevic 2002 (6.7 x 1019 kg) and a reasonable value for the price of gold ($45,670 per kilogram), I get a value of $26 quintillion from the gold alone.
Platinum's concentration in a metal-rich asteroid could be around 60 parts per million (Balir 2000). Assuming a price of about $26,733 per kilogram, this means that platinum should be worth about $110 quintillion. Let's add in the iron ($0.12 per kg) and nickel ($12.42 per kg). The value of Psyche then depends on the ratio of nickel to iron; a pure nickel asteroid would bring about $830 quintillion, while a pure iron asteroid would be worth $7.7 quintillion. Even the lower limit, with the gold and platinum factored in, should be worth over $140 quintillion.
This of course ignores several things:
- It's going to cost money - presumably much less than quintillions of dollars - to mine the materials.
- An influx of that much gold and platinum into any market would cause catastrophic financial effects, rapidly lowering the price of gold and thus the asteroid's value.
Mining Psyche would not necessarily be a good idea.
As for your question about Jules Verne - well, the scientific study of meteorites got going in the 1830s, well before the publication of The Chase of the Golden Meteor. Their composition was studied; at the same time, it became apparent that they came from space. Therefore, it is possible that Verne's story was influenced by tales of newly-discovered meteorites, especially as he constantly read about the latest scientific discoveries:
“Tut, tut,” cried M. Verne, deprecatingly, “that is a mere coincidence, and is doubtless owing to the fact that even when inventing scientific phenomena I always try and make everything seem as true and simple as possible. As to the accuracy of my descriptions, I owe that in a great measure to the fact that, even before I began writing stories, I always took numerous notes out of every book, newspaper, magazine, or scientific report that I came across. These notes were, and are, all classified according to the subject which they dealt, and I need hardly point out to you how invaluable much of this material has been to me.
“I subscribe to over twenty newspapers,” he continued, “and I am an assiduous reader of every scientific publication; even apart from my work I keenly enjoy reading or hearing about any new discovery or experiment in the worlds of science, astronomy, meteorology, or physiology.”