I was just reading how \$1 from sometime in the mid-1800s is worth a little over $30 today.
This got me wondering, where does this go in the long term? In the year 2400, will a loaf of bread be $200? Will an average house be tens of millions? What about the year 2700?
My understanding is that inflation is a universal economic phenomenon. Has a currency ever lasted long enough to know where it leads in the very long term? If not, are there theories predicting what might happen?
Inflation is not a fixed number, so there is no way to predict the value that a loaf of bread or an average house will be in 2400 or 2700. Inflation is the result of a complex macroeconomic process rooted in the behaviour of individuals, and people's expectation of future inflation. The central bank is a key role player, so the integrity of that institution will determine how stable inflation is.
When there is high inflation, in the long run governments often just divide the numerical value of the currency by, for example, a million, in order to simplify the currency for the population. That doesn't change how much real wealth people hold, since it is done across the board. There is a common understanding that, for example, 1 million Zimbabwen Dollars yesterday is the same thing as 1 Zimbabwen Dollar today, so everyone catches on as to what happened.
The long term outcome of inflation is that Denomination eventually becomes excessive and must be re denominated
Inflation is not a "natural" phenomenon, but occurs whenever additional currency is issued.
Let's imagine a small island community, where the inhabitants specialize in making various goods and trade with each other using pearls (say, 100 of them) as currency; A swaps 2 fish for 10 of B's pearls. He later swaps 1 of those pearls to C for a coconut, etc. If no new pearls can be fished out of the ocean, the island will never experience inflation.
Under these conditions where no additional currency enters the system, prices (measured in pearls) will likely drop in the long run, as the islanders make better equipment for fishing, coconut picking etc. If a disaster breaks some of this equipment, prices will increase (fish become more scarce, so I want more pearls if I am to part with the few fish that I have!). Changes in prices can always occur for such "natural" reasons, but this should not be confused with "inflation" as explained in detail below:
Now let us suppose that D, the chief of the islanders, discovers a buried treasure chest crammed full of an astoundingly large number of pearls. He secretly takes 20 of them and goes back to the village. A has caught 2 new fish and is just about to sell them to B for the usual price of 10 pearls when D arrives. He is able to overbid B and buys the 2 fish for 10 pearls each. A is now able to overbid anyone attempting to buy C's coconuts, raising the price of coconuts in the process. The process repeats for each sale.
Notice that D's introduction of additional currency creates a kind of chain reaction, where the first people to get their hands on new money get to scoop up all the nice goods for themselves without having produced anything to exchange for them. Islanders who are late in this chain of "Cantillion effects" (such as ones that have retired to live off the pearls they have saved up) can suddenly buy less for their money. D's introduction of new money, which is referred to as "inflation", transfers purchasing power from late receivers to early receivers. It generates a lot of "economic activity" because people are encouraged to spend money and consume goods as quickly as possible. The bad thing is that fewer people save up resources that can be invested in better production equipment.
Note that if the first receivers keep buying huts for the steady stream of new money, a bubble will be created as housing prices on the island surge. The price of huts is high, but nobody (except the first receivers) is willing or able to pay for them. If the flow of pearls stops, the bubble will pop and the price of huts will plummet. If islanders have loaned the new money out to each other to finance hut purchases and sold the rights to collect these loans, they will basically experience a 2008-style financial crisis.
If D does not restrain his addition of extra pearls, the island may experience hyperinflation. If he adds just the right amount (so large that he can buy nice stuff with the new pearls, but so little that it takes a long time for people to notice the increase in prices) he can keep enjoying the benefits of inflation for a long time. Others will pay for his free lunch.
In real life, inflation occurs when state chartered central banks issue more currency. They can either print more physical notes or do it in more indirect ways (i.e. "Quantitative Easing"). Historically, central banks grew to prominence in the 20th century, because they allowed states to finance military spending and welfare/public works schemes to keep politically important special interest groups happy.
With all the technical details out of the way, the answer to your question depends on what politicians and their caretakers running central banks decide to do.
