Do students for economics study theory about no-money-economies and about no-interest-economies (interest-free-economies), may these be ancient or futuristic?
Are these terms are even being introduced to the students in the bachelor's or even master's degree frame of study?
Edit: I clarify that in this question I seek to learn on a education standard / curriculum meta-review.
Are these terms are even being introduced to the students in the bachelor's or even master's degree frame of study?
Students do study moneyless economies, in fact that is the starting point of studying economics (e.g. see textbooks like MWG Microeconomic Theory). MWG is graduate level text but undergraduate texts such Microeconomics and Behavior by Frank follow similar path (e.g. start with models with no money).
Regarding problems without interest rates those are encountered typically only in static one period problems and are not very realistic.
no-money-economies and about no-interest-economies (interest-free-economies), may these be ancient or futuristic?
Economies without money are generally pre-historic, since civilizations that left any written record typically already had quite complex monetary arrangements (see Ferguson Ascent of Money). Furthermore, such economies are unlikely being futuristic (unless you predict some apocalypse) as barter is very inefficient due to the problem of double coincidences of wants. In addition, having complex economic systems without money is virtually impossible. As discussed by Edgeworth (2016):
Barter, as distinct from exchange, is defined by the absence of money both as a medium of exchange and a measure of value. In the absence of a measure of value, complicated transactions between several dealers are hardly possible; and accordingly barter is generally characterized by the absence of competition.
Mind you money in economics is just some unit of account, medium of exchange, and store of value. It does not matter if you change the name of money to 'tokens', 'social credits', 'stamps' etc it will still be money as long as it is generally accepted in exchange, you can use it to do accounting, or use it for exchange at a later date.
Regarding, the interest (which is not same as interest rate), is defined as (Ingersoll 2016):
Interest is payment for use of funds over a period of time, and the amount of interest paid per unit of time as a fraction of the balance is called the interest rate.
It is actually nearly impossible to have any working economy with some intertemporal long term decision making without interest, even ancient hunter gatherer societies had debt and likely some sort of interest (e.g. see this Wikipedia article about tally sticks), and we know for a fact that even ancient Egypt or Mesopotamia had not only transactions involving interest but wholly functioning capital markets where securities were traded (again see Ferguson Ascent of Money).
Given that capital markets can't really work properly without some sort of interest, and given the fact that capital markets have first order impact on material welfare of countries and its growth (Levine, 1997 or Levine 2005), again unless you predict some apocalyptic future, it will have some sort of interest no matter how it is named.
This being said there is a literature on Islamic banking which is supposed to be 'interest free' because charging interest is against sharia law. However, this sort of banking in essence just relabels interest as something else for religious reasons. For example, depending on different schools of Islamic jurisprudence just changing terms of loan from stating you borrow \$100 that has to be repaid with 10% interest to you borrow \$100 and repay \$110, may already not count as paying interest. Or bank might instead 'share' loss with borrowers and 'profit' with depositors, which in essence again works just like charging interest rates on deposits and loans just does not qualify for the label of interest under religious law.
One could imagine future where instead of having standard interest rate as we know it now in the west, financial institutions would offer some loss/profit sharing contracts, but economically that is no different from having interest rates.
In mathematical models of economies (e.g., exchange economies), it is not necessary to include money. Prices do turn up as mathematical constructs ("shadow prices"). Modern economies have money to simplify trade - barter is difficult.
You can specify in these models that the interest rate has to be zero. The credit market will most likely not "clear" in this instance, there will be excess demand for goods in the present, and an excess supply of promise of future goods.
I guess students of economic history also study historical scenarios where the interest rate was zero, but I don't think they study the future because the History of Economic Thought Department's time machine grant keeps getting rejected.
