Bank interest — Emmef / Economie / Geld

Can interest be payed without first taking on more, new debt?

In general, the person that lends out Money will ask interest for that service. In the modern economy, bank credit creates money in the form of debt, while repaying debt destroys it. The interest money is not created with the loan. Some propose that it is therefore impossible to pay that interest without someone (else) taking on more debt first. It turns out taking the extra debt is necessary, however, not because of the interest. Fun!

The used money system

The “money system”1 used to explore the scenario, is necessary and sufficient. Necessary, because we need at least a proper concept of a bank with balance accounts for each participant. To keep the number of involved elements small, the bank and its participant, that include the owner, are situated on an island. The system is also sufficient, as all interactions that take place, including those in the critique that follows, can be perfectly described with the available elements and concepts.

If we accept the proposition that all interest must be borrowed into existence, this roughly means that (in average) for each period of time (principal due period), we need to borrow an extra amount of money (the interest) into existence. As the interest is roughly proportional to the principal and thus the amount of money in circulation (that is the amount of not yet paid back principal), this leads to a roughly exponential growth. It will be shown, however, that this proposition is false.

Scenario without necessity for additional debt

This is a free adaptation of the story on Positive Money2 that debunks the fact that it is “mathematically impossible” to pay back interest.

The story of Alice

On day 1, Alice wants to borrow 100 credits for one year. George agrees and demands 10% interest for the whole year. The 100 credits are called the principal of the loan, due in a year. The 100 credits are added to Alice's balance and in one year from now, Alice needs to repay George 100 credits and an extra 10 credits as interest: a total of 110 credits.

The total amount of legal tender in circulation is now 100 credits.

On day 2, Alice buys a machine from Pete (50 credits) that enables her to create stuff. She also buys bread from Bob (10 credits).

During the year, Bob, Alice and Pete exchange money on their balances for goods. Alice makes "stuff", Bob bread and Pete machines. Naturally, Alice makes sure she has the 100 credits back in time to repay her debt!

On day 361, just before the principal and interest are due, Alice pays George the interest in advance: her balance becomes 90 and George's 10 credits.

George now has 10 credits of legal tender to buy breads from Bob on day 363 and Bob uses that to buy 10 credits of "stuff" from Alice on day 364. So Alice, again, has 100 credits! Then she repays her debt to George on day 265, who dutifully resets her balance to zero, thereby also reducing the total amount of legal tender in circulation to zero.1

The story of Alice in numbers
Action Day Balances
    George Alice Bob Pete Grand-total
Day 0 0 - - - - 0
Alice gets loan with principal of 100,
George increases her balance with principal
1 - 100 - - 100
Alice buys machine from Pete 2 - 50 - 50 100
Alice buys bread from Bob 2 - 40 10 50 100
Arbitrary situation during year 42 - 15 35 50 100
Alice ensured she has money back 361 - 100 - - 100
Alice pays interest to George 362 10 90 - - 100
George buys bread from Bob 363 - 90 10 - 100
Bob buys stuff from Alice 364 - 100 - - 100
Alice pays principal of 100,
George decreases her balance with prinicpal
365 - - - - 0


Even though the story proves that it is possible that Alice pays her debt without anyone else taking out a loan: it is a rather contrived scenario where all inhabitants must make certain types of decisions and at the right time. Only then the flow of money that starts at the loan and ends at the payback, is fully circular. This scenario also plays in complete isolation of all other scenarios, a fact that is hardly realistic. This scenario will be referred to as scenario A (from “Alice”).

Imagine that in a scenario A', Bob decides to keep the 10 credits on day 364, instead paying them to Alice. He is allowed to do that and it is pretty realistic, considering all the great movies coming out next month. However: Bob's decisions disrupts the flow of money back to Alice, so Alice cannot pay back her loan on time. Because of Bob's decision, the flow of credits is not fully circular in the considered time interval.

Several things can happen. Alice and George (the bank) might agree on a new, temporary loan for Alice, so that the flow can be restored, later: let's call this scenario A''. It can also be that George extends the length of the loan, so that the flow can be restored: let's call this scenario A'''. It can also be that George (the bank) sees that after any of A', A'' or A''', the flow back to Alice will still not be restored and never will be. In that case, George (the bank) can allow Alice to default on the loan ad write it off. This can do interesting things to the grand-total of balances and unwinding things can be challenging, however, it is out of scope here.

Whatever decisions Alice and George make: Alice and George have a pretty sound overview of the situation. Scenarios A to A''' each happen in their own universe and in complete isolation of all other possible scenarios.

In a real world, more scenarios happen at the same time and there can be multiple banks. It is pretty realistic to assume that Bob uses another bank than Alice and that legal tender can easily transfer from Bob's bank to Alice's and vice versa.3 Assume that another scenario B overlaps (in time) with A' and one of the participants in B, Handyman, pays 10 credits to Alice on day 364. Handyman effectively “fixed” scenario A' as Alice now is able to pay back her principal in time! However, all scenarios should eventually end in paying back the principal, resetting the grand-total to what it was on day zero of the scenario. Handyman fixed A' but broke B with an amount of 10 credits! It can be shown that a decision like Bob's in A' cannot be fixed without either a default. In all other cases it will propagate through all scenarios that overlap in time (recursively). It can also be shown that there is no way to reorder scenarios in such a way that all of them are fixed.

So, the bank just needs to allow a default, right?

Even with just one bank, it is complex to track all IOUs on the island if different scenarios happen and overlap in time, let alone if there are multiple banks. In reality, as a result of Handyman;s decision, George will assume the problem is fixed. However, as mentioned before, the “problem” of 10 credits propagates to other scenarios (B). And the flow of credits in scenario A' cannot be considered fully circular, because of the “alien” money. Because new scenarios happen all the time, it is highly likely that no bank will recognise when a default should happen. The result is that scenarios that happen later will cover up the defect in circular money flow, by taking on new debt. This is recursive.

If the – acknowledged: crude – assumptions are made that on average the the money flow is only circular for less than 100%, and a certain number of transactions is made per period of time, we can make a crude prediction of what will happen. As the total amount of money in circulation is equal to the total of grand-totals for all scenarios, the defect in circular money flow is proportional to the total amount of money in circulation. Per period of time, this defect needs to be borrowed into existing by newer scenarios. And this is awfully familiar to a system with positive feedback, where the total amount of money in circulation MUST grow exponentially to prevent breakdown – awfully many breakdowns.


The proposition that money to pay back interest needs to be borrowed into existence, is false, as can be shown by analysing a simple, micro-economic system. However, expanding the analysis to a more realistic non-micro system also leads to a demand for money to be borrowed into existence, to prevent breakdown. This also leads to an exponential growth of the amount of money in circulation. This leads to the conclusion that the proposition is wrong, but the outcome is right.