Interest and stability (IV)

Text 25 August, 27–29 September and 1–


In part 12 and part 13, I discussed the document by Sergio Domínguez and Marc Gauvin called Analysis which I wrote about. “Formal Stability Analysis of Common Lending Practices and Consequences of Chronic Currency Devaluation”. This Analysis states that interest-bearing loans, and therefore a financial system using interest, is inherently unstable.

Where the loans themselves are concerned, I admit that they are inherently unstable in the sense that they are not mathematically guaranteed to be always stable, in 100% of cases. However, my evaluation of that fact is different from that by Marc Gauvin.

Where financial systems based on interest-bearing loans are concerned, I do not believe there is an inherent instability, not even in theory. That is what this article is about.

In articles 12 and 13 I focussed on mathematics and the validity of the model of the loan. Now in part 15, I will look at the wider model that the authors present, not of one loan, but of the economy as a whole and the role of banks in that.

Correct model?

I’m looking at pages 13 and 14 of the Analysis now, chapter 3, called “Broader implications and overall currency stability”.

The authors state “that the prevalent financial system’s design is inherently unstable as a whole because it has a bounded (finite) input in the form of pledged wealth but has an unbounded debt output.

I don’t agree with that conclusion and I think that is due to flaws in their model of the economy on page 14.

From this sentence on page 13:
Therefore, since money creation and lending at interest is at the heart of the system, interest bearing loans represent an instability that is not compensated for within the design of the system itself and therefore must be absorbed by the greater economy.
I get the impression the authors make a clear distinction between the financial system and the economy as a whole. But then it seems inconsistent that the notion of “Wealth” is included in figure 6 which is labelled “Financial System Model”. To me, wealth is part of the economy, but not of the financial system.

Myself, I don’t clearly make that distinction and in the following, I will often cross the borders between them. Perhaps that is again that fundamental difference between Marc Gauvin and me, which already became clear during the e-mail discussion I had with him. We are probably both right, each in our own way, but we look at the world in quite a different way.

In terms of the car analogy: do we consider just the car as the model, or do we look at the car including the driver? I make a clear choice for the latter, because that makes the conclusion more practically meaningful.

About the model in detail

Principal and wealth

The text “Production of W(k) is the result of a fixed spending of previously created P(k−1) [...]” suggests that wealth can only be obtained, can only be bought, with money from a principal. A principal is the total, original amount of a loan. So the suggestion is that people must always borrow money in order to buy anything.
(See note!)

That’s clearly not true: people can also buy things with money they saved up, money they earned by working for an employer, by providing services (example: teachers) or producing or improving goods (adding value).

Now my critics might argue that money you earn is paid by somebody else, and that any money is ultimately debt, because it was created by granting credits, either by a central bank, or, through a multiplication mechanism, by a non-central bank.

That in fact is true. Money is debt, which is almost literally the title of the well-known video I will write about later: Money as Debt. But one man’s debt is another man’s asset. A debit entry in one balance sheet is mirrored as a credit entry in another one. So we might as well say that money is claims! The suggestion of that statement is much more sympathetic: money gives you a claim to currency, a claim to goods, it gives you purchasing power. More on that in a follow-up article.

Perhaps I misunderstand, and the wealth in Figure 6 is meant to represent only wealth that actually serves as collateral for the loan, which in turn serves to pay for that same wealth.

For example: when buying a house or a car. But even then it is not always the case that the full purchasing amount is paid from the loan. Usually people also use some money of their own. This is especially true when someone moves to a new house from a house they bought long ago: the proceeds from selling the previous house, minus what remains of the mortgage loan, can be a considerable amount.

Wealth, collateral and principal

Quote from page 14 of the Analysis (item 3):

“[...] banking institutions are required to maintain a fixed ratio of P(k):C(k) sufficient to guaranty P(k+n), therefore the ratio is required to be constant and, [...]”.

It is true that in each individual case of a loan being granted, secured by a collateral, that ratio is fixed. But what that ratio actually is, can vary a lot, depending on country, economic climate in the era under consideration and legislation. For example, current figures for Germany are 60% and 80% (see the Beleihungsgrenze). For the Netherlands, I remember things like 70% or 90% of the value under foreclosure, or also sometimes 100% or 110% of the acquisition price.

As mentioned before, sometimes the collateral is only partially financed by a loan, so the value of the collateral may be much higher that the principal. Moreover, during the maturity period the value of the collateral may remain the same, rise slowly and sometimes fall sharply (a house with a mortgage loan) or fall quickly after the purchase and then gradually more slowly (in the case of a new car). This means the current value of the collateral may be very different from the remaining principal.

As long as there is no need or wish to sell the collateral, that is no problem. That’s because the collateral is never meant to be forcibly sold by the lender, but only as a last resort, in case the borrower remains in arrears for too long.

So: in this summary of Marc Gauvin’s explanations (note), A does not equal B, because the principal is not the collateral, the collateral is not the wealth, and the wealth is not the principal. Each of the three in individual cases could be almost anything, and they vary over time, each in different ways.

By the way: many loans are not secured by any collateral at all. Examples are overdrawn transaction accounts and credit cards.

Accounting method

I quote again from page 14, now at item 5:

The amount P is entered as positive entries into users’ accounts and as negative entries in liability accounts such that when P(k) is subtracted from the users’ accounts to completely cancel the negative entries in liability accounts, total P(k) = 0, i.e. effectively removed from circulation. Thus, P(k) represents the total available money in circulation.

I’m having difficulty interpreting those positive and negative amounts. I prefer debits and credits, following the double-entry bookkeeping system described by Luca Pacioli as early as 1494. Also, it is not clear which accounts are referred to exactly. In “liability account”, whose liability is meant? The bank’s or the borrower’s?

In my example in article 10, after the loan has been granted, I also have two accounts (in the bank’s books, not in the borrower’s), but both are in the name of the borrower, i.e., the bank customer. One account constitutes the loan itself, and the other represents the availability of the amount to the borrower.

It is true that making the loan amount available causes money creation and redeeming the loan means that money destruction takes place. However, in case the loan is used for buying a house, the loan amount is normally made available – at least that is how it works here in the Netherlands – to a notary’s escrow account. The notary then pays the seller’s bank to redeem the seller’s mortgage loan (if any), and pays any remaining amount to the seller, after first subtracting fees and taxes.

Later redemptions by the buyer of the house (the borrower of the new mortgage loan) are done from yet another account, in the name of the borrower.

The way the authors of the Analysis describe what’s going on, may indicate that they are not familiar with double-entry bookkeeping and do not fully understand how money creation works. But maybe they do and my worries are groundless.

However, what is at the top of page 21 strengthens my suspicion. It says: “And the bank will also maintain the following table:

I don’t think banks really need columns 1 and 3. How should the bank know the current value of the collateral? By having a valuation carried out each month? Why would they spend effort or money on that? There is no need to know the value of the collateral as long as the borrower is not in arrears.

All the bank needs to know is how much the borrower owes the bank: the original principal minus redemptions paid so far.

The bank will also monitor if periodic payments are made as agreed. OK, that’s more or less the same as what is in column 3.

Long term savings

The text on page 14 continues (end of item 4):

Note that S also temporarily removes portions of P from circulation.

This S represents long term savings. Whether they are really removed from circulation depends on definitions of ‘money’ and on the maturity period of the savings.

Money in savings accounts does not belong to M1.

If the period of notice is three months or less, or the maturity is two years or less, these amounts are still part of M2 and M3. (This is according to European definitions. In America, anything under 100,000 dollars is M2 and above that is M3, regardless of maturity or notice period.) So when considering those money aggregates, the money is still in circulation.

If the notice period or maturity period is longer, such an amount is no longer considered money in a monetary sense – though of course it still has value and constitutes an asset to the account holder of the savings account in question!

In all cases, banks can use savings deposited as M2/M3, and also ‘non-money’ in longer-term savings, to fund new loans, so effectively, this money returns into circulation in the economy. That is one of the things which make banks useful.

Interest and Total System Debt

What is debt?

On page 14 of the Analysis, the authors also wrote (item 5):

Total outstanding D(k) is an unbounded sum of P(k) + I(k) so when the system refinances D(k−1), outstanding I(k−1) is compounded with I(k) and as shown above, growth of D becomes exponential.

I said it before and I say it again: it isn’t right to equate “debt” to outstanding principal plus interest. Debt is what you owe someone, in this case, what the borrower owes the bank. That is the remaining principal and any interest-terms that are due but still unpaid. Interest not yet due, and interest due but already paid as agreed, is not debt.

The economy is a meshwork of interconnected circuits

Figure 6 does show that the loan (principal) generates the need to pay interest (I), but it does not show that normally this interest is actually paid by the borrower, not where the borrower gets it from and not what the bank does with it after receiving that interest.

I wrote about that before. Banks spend the interest they receive from borrowers as credit interest for depositors, as operational costs (including possibly excessively high and undeserved salaries and bonuses for bank managers), dividends, loan-loss reserves.

All of that money returns to the economy and is either spent or put on a bank account, where it can be used as funding for new loans.

(Some money may be kept as cash outside of banks, in which case it is really out of circulation and no longer useful in the economy. It seems unlikely that this is a high percentage or that it is rising, especially because cash does not yield interest.)


We could compare the situation with a circuit consisting of many tubes carrying water flows. The water stands for money (in the wider sense of ‘value’, not the strictly technical sense). Water pumped into one of those tubes (interest paid to a bank) can eventually reach any other tube, including the one where a borrower must pay interest, because everything is connected.

Whether enough of it actually reaches that borrower depends on pressures, tube widths, flowing resistance, clogging. In economic terms: skills, talents, hard work, reasonable wages, cost of labour, progressive taxation, good or bad luck, health, efficiency, competition, trade barriers, etc. etc.

So there is no guarantee to success. But that is an economic and political problem, not the result of interest.

The point is that the interest a borrower pays to a bank isn’t lost anywhere, it is still in the economic circuitry, it doesn’t need to be replenished. Not by growth nor by anything else. That is why the (small but realistic!) toy economies in those spreadsheets I hyperlinked to before, are stable even in the absence of economic growth:

A scam?

From the above, it can be seen that one more of the equations in the web page, which I linked to before, is incorrect. The web page has the file name “The Scam short form.htm(note), and claims that C=A+D, in other words, that Debt = Principal + Interest.

That’s not true: debt is what you owe someone. If you pay the interest in time, you no longer owe it.

Marc Gauvin then draws this conclusion:

All current money contracts are centred on such flawed logic and according to several legal doctrines, they ALL are invalid.

That conclusion is invalid and the contracts are valid. There is no scam. Not checkmate, but wrong move.

In arrears

Even if for whatever reason the borrower does not pay the interest in time, that doesn’t cause instability for the economy as a whole. That’s because the money is still somewhere.

If for example the reason for getting into arrears is that the borrower works hard but is underpaid, or he loses his job, fewer money goes to the bank, but more money stays with his (current or former) employer.

There is a shortage of money for some individual companies or persons, but not a shortage (that money creation would need to replenish) for the economy as an interconnected meshwork full of financial interactions.

The same is true if the borrower gets into trouble as a result of an irresponsible spending pattern: the shops he pays money to, for things he cannot really afford, get more money, but the bank gets less. The net effect for the whole of the economy is zero.

Greedy bankers and shareholders

Some bank managers, and other managers, earn salaries that in my view are hardly justified by how hard they work or by the responsibility they bear.

Bonuses make that worse.

Shareholders may force managers to focus only on short term profits, instead of serving the interests of all the stakeholders, not least the clients of the bank. Hopefully, banks on a cooperative basis are better in this respect.

Although clearly I am not a fan of greedy bankers, the large amounts of money they receive eventually do return to the economy: they either spend the money, or save it or invest it; or they might even donate some to charity.

So even if there is no certainty that that money will also reach the borrower who has to pay interest, at least the money is circulating in the economy. When viewing the economy as a whole instead of individual players, there is no shortage of money.

What deficit?

Annuity loan

To end this article with, a last comment about the Analysis.

On page 20 there is a table showing an interest-bearing loan being redeemed under an annuity schedule. Every month, one twelfth of the annual percentage of 5 percent is paid as interest, the remainder of the term being used to redeem the principal.


The rightmost column is labelled “Deficit Loan 1”. It contains the amount of the principal, in the hypothetical situation that during that most recent period (but not all the previous ones!), the interest rate had been zero.

I don’t understand why that is a meaningful or interesting figure.

In an earlier article I commented on this same table saying:

But the calculated table on page 20, showing a typical annuity mortgage, nicely ends with «Balance Loan 1» at zero. So it has become stable after all.


In our e-mail discussion, on 26 Aug 2012 at 11:14:18B Marc Gauvin disagreed, stating that “it shows the Principal at zero but with an unpaid interest sum. Therefore it is not stable.

My first reaction (which so far I never sent yet) would be “OK, so simply pay that last interest term too, and it’s stable forever after that.”

But now that I look at it again, I notice that in fact, at the point when the principal becomes zero, the last interest term has already been paid. So there is no “unpaid interest sum”.


Here is why: after the first period, the interest due is: one month at an annual rate of 5% of the previous (and initial) principal of 500,000 dollars:

500,000 * (5 / 100 / 12) = 500,000 * 0.0146667 = 2083.33.

The monthly payment term is 42,803.74. What remains after paying the interest can be used for redeeming the principal: 42,803.74 − 2083.33 = 40,720.41 and 500,000 − 40,720.41 = 459,279.59. That is the new principal.

In the following periods the calculation is the same, each time using the previous amount of the principal to find the interest due.

For the last term that means:

42,626.13 * (0.05 / 12) = 42,449.26 * 0.0146667 = 177.61.
42,803.74 − 177.61 = 42,626.13, which is the remaining principal. After that, everything is zero and stable.

Note: summary origin

Addition 14 October 2012:

The “Scam short form” (mentioned in this article here and here) I thought was originally by Marc Gauvin.

But there is also a Dutch version on the web, which someone who sometimes calls himself Jac (is he the webmaster?) on 4 October 2012 claimed is his. Or theirs?

If that is so, maybe Marc Gauvin took his text from this almost identical English version, posted by someone called Jake. Same person as Jac?

The site holland4mpe may have been derived from australia4mpe, where the originator of MPE (Mathematically Perfected Economy) apparently is Mike Montagne, who in his many videos here, sounds like an American and not like an Australian. Mike Montagne says he developed his ideas already in 1977.

The few videos I watched took a long time before they came to the point (if there is any!), and what I heard didn’t seem very well prepared and coherent to me. But maybe that’s just me.

Links to more by Mike Montagne is here.


16 July 2013

In June and July 2013, mainly through Twitter, I came into contact with many adherents of MPE (Mathematically Perfected Economy), all over the world, including its founder Mike Montagne. Some kept discussing the issues, Mike and others soon backed out.

All this resulted in a long series of more specific articles, which can also be accessed from the same menu as the more generic ones.

This link takes you near that point in the menu.

Addition 7 October 2017

See also The Money PSYOP. The idea that is described as being in that book, is also in a newer site: Money Systems Transparency Alliance, more specifically 6 Facts to Change the World and The Misrepresentation of Money, by the same authors.

My opinion about these ideas: I don’t agree with them at all. I think the authors see problems where they aren’t any, as a result of an incorrect application of mathematics and formal logic to the practical realities of daily life.

Of course money can serve as a unit of account, as a medium of exchange, and as a store of value. There’s no reason why it couldn’t.

Addition 24 October 2017

See also Applying double-entry bookkeeping.

Copyright © 2012, 2017 R. Harmsen. All rights reserved.