I used to play The Dark Eye (Das Schwarze Auge) myself and in my opinion it strongly resembles medieval Europe - apart from the obvious fantasy additions. It's rule books give information of the economy, trade and demography of nearly everything.
Therefore the dilemma is quite understandable; in medieval Europe a sword was worth a fortune and in the world of The Dark Eye it is the same. However, a hero needs a sword right?
Well, maybe not necessarily. In our group we don't have a rule to handle wealth but here are some thoughts on how we somehow deal with it usually (after writing it down I realised that our heroes are not that wealthy because of these guidelines so it may not suit your question that well):
Equipment has flaws. Nearly everything a (starting) character possesses is not a shiny new blade but rather a crude axe, and old dagger from the grandpa, a warm winter coat with some holes, the elven bow that was handed to the character in a ceremony and would not be considered for sale.
Producing goods has its cost. It is true that potions or magical items are worth a hell lot of money in The Dark Eye. But producing these is an investment and requires material and knowledge - both of which can be costly to find.
Valuable findings are rare. Again, nearly everything a character finds, loots or gets possession of has either flaws or is an unknown object that requires identification.
However, here you'll find yourself in a situation where player and character knowledge interferes. An adventurer may not have ever seen a telescope and finds no use in keeping it but the player knows it is worth a ton of money. We also have some problems with stealing because the players have knowledge about the worth of goods - also stealing creates a difficult situation by either letting it pass or punishing the character that may hinder adventure progress (but that's a different story).
Carrying gold or whatever currency is not very common. Carry a chest full of gold and silver and it will attract thieves. Taxes may be imposed upon crossing borders and cities. And the greedy tavern keeper will charge more if he spots the characters entering in bling bling.
Value comfortable but rule-speaking unnecessary goods. Create an environment where player not only value the next best weapon or armor because it will raise their damage and defence in battle. Good shoes can be expensive but keep from getting exhausted and have a minor impact on game balance. The same with regular feel-good massages, company during the night, the feast at the end of an adventure. The more characters act with each other and the more a personality they have the more readily the spend money on that. All these are sorts of money sinks.
But in the end the characters are heroes and it may be frustrating to not get a bit wealthy at some point. The reward for risking their life is loot, treasure and occasionally - a very special event - the acquisition of a new and shiny sword.
Best Answer
The conditions required to get the maximum possible wealth bonus are very artificial, but for the sake of argument let's assume the following:
Such a character can start with a wealth bonus of +20 at 1st level (8 from the 2d4 roll, +6 for Dilettante, and +3 x2 from taking Windfall twice).
At level-up, there are three ways the wealth bonus might increase:
So we can figure out what the maximum theoretical wealth increase is for each level by tracking the things that give bonuses to the Profession roll (Wisdom, Windfall feats, and ranks in Profession), and comparing that to the current wealth rating (which is the DC for Profession checks when leveling up). We can then calculate the maximum bonus from the Profession roll, from new Windfall feats, and from the flat bonus from having ranks in Profession. That's summarised in the following table.
Table key:
As you can see, the wealth bonus quickly becomes so large that it becomes impossible to beat the DC on the Profession check even when rolling perfect 20s. (And note that 20 is not an automatic success, see p. 44 Skill Checks.) After 4th level, only the Windfall feats and the flat bonus matter.
So, the maximum wealth bonus at 10th level is +70 (wealth bonus starts at +64, plus the total increase of 6), and the maximum wealth bonus at 20th level is +135 (wealth bonus starts at +127, plus the total increase of +8).
As for how much that is in real-world dollars, according to the system there is no way to translate it into dollars:
So a character with +70 Wealth is rich enough that credit is easy enough to come by that they almost never need to worry about money. For comparison, the table on p. 38 calls +31 and higher "Very rich". The only purchase that could even be noticed by such a character (i.e., which would drop their wealth by any amount) would have to have a Purchase DC of 85, which means they could have as many mansions (Purchase DC 36), Learjets (Purchase DC 40), or M1A1 Abrams tanks (Purchase DC 47) as they wanted to own. The only way money would ever be an object would be if the GM set an exorbitant custom DC for, say, buying a very large rival company.
A character with +135 Wealth is so exceedingly rich that they don't ever have to even think about money—their wealth is so great that everyone knows they're good for it, and their vast network of accountants pays for everything out of the complex financial empire they own. They probably don't even know exactly how much they're worth, and considering how the stock markets work, their exact wealth is probably impossible to know until they tried to use every last penny of it, at which point there would probably be world-wide financial panic. They can probably buy entire countries, unofficially.