Having the experience of seeing the precious metal market boom in the 2000's, from the lows when central banks were selling, to the high when accumulation increased due to systemic uncertainties, one has to ask whether something like that can happen again - and if it will, when will that be?
Given that these are markets with a very high degree of leverage and price manipulation, an accurate price prediction might be next to impossible without inside knowledge. Ultimately, one can crunch in all the factors on why things should go this or that way, but in the end they might not - due to market manipulation.
So, instead of focusing on what the price will do, I'll try to predict what the situation will be in the long term (2030-2060).
1. Fiat supply will continue to inflate
We know that fiat is going to continue its inflationary trend. It cannot happen any other way as all fiat money is issued in the form of debt. The debt has to be repaid with interest, which necessitates the creation of new money. If that doesn't happen, a liquidity crisis ensues and the economy goes down the drain. Now, the more debt and interest there is, the more money has to be created. In theory, this factor alone should allow gold prices to rise. But then again we know that this isn't always the case. Say between the 1980's and the 2000's there was no price rise.
2. Fiat will continue getting devalued
Due to both inflation and competitive devaluations, the price of fiat will continue declining. We are already seeing that low-denomination coins cannot use copper/bronze/brass anymore, as the face value is lower than the value of the metal content. When the value of the coin is not even worth the metal the coin is minted on, you know you are in trouble. Thus tricks are implemented to prevent the public from realizing this. Copper-plating and brass-plating on cheap metals like iron and zinc are now used in order to preserve the impression of "value" on money.
Devaluation affects citizens differently, depending where they live. Most developed countries have a comparatively lower degree of the problem compared to developing countries. This means that the demand for alternative money will also be different compared to how much the local population trust their national currency. In India, for example, it's pretty common to dump fiat for gold. In the USA, or Europe, it isn't. This reflects the difference in stability of the various currencies.
3. Fiat becoming digital
It is very possible that in the next 10 years or so, most fiat will be held in digital accounts, and most transactions will be digital as well. This means that dumping fiat for gold might be extremely traceable, or easily prevented by a state that doesn't want its citizens to accumulate gold (or something else).
4. Gold and Silver supply will continue to inflate - Gold at a faster pace
While precious metal supplies are not unlimited, what matters is the above ground quantities that we have mined - and these are a just fraction of what exists on Earth. We are currently producing ~3k tons per year of Gold and ~25k tons per year of Silver.
This is a major issue here. Note that since the 70's, we have doubled the above ground quantities that have been mined. In just 40 years, we have mined all the gold that humanity had mined up to the '70s. So there is a trend of increasing gold production, and this happened without even using AI, Robotics or cheap energy sources.
There are at least 4 factors that can accelerate these production rates:
a) Cheap energy: Mining costs are related to energy costs. Whether it is crushing rocks, excavating, moving soil from point A to point B, all these involve a lot of energy cost. The moment energy cost goes down, the easier it will be to increase output. There are various promising technologies that can reduce energy costs, and if these go online, it could be a game changer for mining costs and viability calculations. Cheap mineral extraction = soils that were considered non-viable, suddenly become viable for mining.
b) AI/Robotics and expanding the envelope of what can currently be mined: A lot of operations that require humans being in unfriendly environments can be solved by using AI/Robotics. Whether it involves the ocean floor (~70% of the Earth is water - and currently there is very little mining done there), or a tunnel 3km down from the surface, an AI/Robot will be able to do what humans can't. What this means is that gold deposits which were previously unapproachable, can now be extracted.
c) New mining techniques: A lot of the techniques used for Gold extraction are ancient - like weight separation. This could change with nanotechnology and AI. AI could recognize Gold in a water stream and then, combined with nanotechnology, use something like nano-gates to separate material efficiently, even at a microscopic level of concentration - something which is currently impossible. This could even allow extraction of Gold from the ocean water. But that's just one application - the applications of advanced technology could be many. For example, there are gold concentrations mixed with clay that are difficult to separate, which would be easier if there was something that solved this problem.
d) New prospecting techniques: Prospecting is currently based on a bit of geology and a lot of luck. However this could change with new technological advances. For example, precious metal formations follow certain patterns. These patterns are ideal candidates for pattern recognition software that can then extrapolate how the veins map out. Another example is that there is currently a lack of a hand-held analyzer, where you can take 1 gram of dust and it'll tell you right away what this 1 gram is and what it contains. Metal detectors also lack granularity to detect microscopic quantities of metals in the ground - and analyze them for what they are. Prospecting is still in primitive state compared to what it should be, and when this changes, the rate at which newfound deposits come online for production will be a lot.
5. Disposable income in the future
In an economy where automation starts to take over people's jobs, the system of worker=consumer breaks down because there is no worker (who gets money that he can then spend as a consumer). Systems like basic income could be channeled in a controlled way where people cannot dispose their income into "investing". With a digital transaction system it would be easy to check how these money are spent.
6. Attractiveness of Gold for major funds
For institutional investors I suspect that the accumulation of Gold will only be desirable if either the price is very cheap or the long-term inflationary trend of Gold is showing signs of slowing down. Personally, I expect that once new technologies come online that rapidly increase output (this might happen in 10-20 years) Gold might become unattractive due to the bursts of mining output. However as production ceilings start appearing 20-30-50 years later, even with newer tech, then it could be a game-changer in terms of price.
7. The Silver Market
Given the outlook of future Gold production, if I were the Elite, today, I think I'd follow their current strategy of perpetual Gold shorting and price suppression, basing this shorting on future outputs of several decades later when Gold production could be hitting over 10k or even 20k tons per year. However, for Silver, things might be different due to the way Silver is extracted right now.
Silver is generally mined as a secondary metal in several mines and thus I do not expect similar groundbreaking advances, except perhaps in the energy sector (lower energy costs = lower mining costs).
I think Gold inflation could lead to paradoxes where the mined output could reach up to 5:1 (gold/silver) from the current 9:1, since Silver production will not be able to scale upwards by 3-5-10x. Unlike Gold which can be selectively extracted from the ground in "targeted" operations, Silver is not generally a native metal and this means that you have to process enormous amounts of crushed ore in order to extract it - and even then as a secondary metal. The efficiency of these operations cannot be dramatically improved, unlike Gold mining operations.
8. Governments (not) monetizing Precious Metals
Except in the case where some kind of major crisis shakes the confidence in fiat, I do not expect governments to monetize Gold or Silver. This is because enormous debts would also be converted to Gold-debts, which would then make these debts un-serviceable. As a government, it's much easier to repay by issuing your own national currency.
Conclusion
While I don't expect anything serious in the short-term in terms of fundamentals affecting Gold and Silver, there are obviously many uncertainties when predicting the future, especially amidst a changing world in terms of money (digital economy transition) and technology (new technologies allowing new capabilities). For the long-term I expect that fiat will continue to be inflated and devalued - based on how the monetary system works. I also expect that technology will make Gold inflate faster than the current pace, while Silver will not benefit in the same way from technological advancements. I believe Silver will, in terms of fundamentals, prove to be a better investment.
In theory the rate of production (inflation) of Precious Metals will also determine their attractiveness compared to fiat money which will be inflated and devalued in parallel. It will probably be a case where fiat inflates and devalues faster. Not all countries have similar fiat characteristics, hence, the level of attractiveness of PMs will differ from one economy to another - but as the global economy unifies this divergence will decrease.
The long term price of PMs will also be affected by the disposable income of people which could be channeled in PM investments. Due to changes in how the workforce economy (the worker-consumer model might not be viable in the future), assumptions based on the current model might be broken.