In his book "Money, Bank Credit and Economic Cycles' in chapter 4 subchapter 5 he writes on page 223 (second english edition, .pdf version - http://mises.org/books/desoto.pdf) that: "ds1 represents Bank A’s secondary deposits and equals 1,219,512 m.u", while (if I correctly understand the definition) I would argue that Bank A's secondary deposits equal 1 097 560 money units and 121 952 of primary deposits (pp 218-219). Do I err or he errs?

+ I have a second problem: on p. 239 author introduces the term 'gross deposits' without defining it, the same goes for 'net deposits', the term that he only gives formula for but again no definition.

I tried to derive those definitions inductively by simulating the credit expansion in bank's book entries in spreadsheet (akin to the table on p.230). I compared the sums in rows with result of numerical example [40] on p. 241, but they do not match, as they should given the formulas. Anyone, please?

I don't have an access to University Economics by Alchian&Allen, which Huerta de Soto cites.

. Of this amount,
1,000,000 m.u. correspond to physical monetary units; that is,
to primary deposits. The other 900,000 m.u. reflect fiduciary
media created from nothing; in other words, derivative or sec-
ondary deposits.

page 219:

Bank A

Balance Sheet
c=0.1 and k=0.2
Assets
Cash 121,952
Loans 1,097,560
Total Assets 1,219,512

Gross Deposits is what he used to call Deposits, meaning the sum of the amounts appearing as "Deposits" in the Credits Column [and the Liabilities Column] of the bank's Balance sheets.

Net Deposits is defined by the formula. There is no better definition than a formula.

I tried to derive those definitions inductively...

I'm not sure if there is a language problem here. You cannot derive a definition by simulating the credit expansion of something. The definition is something the author makes up in his head, and it is a short way of saying a lot of words.

...(akin to the table on p.230). I compared the sums in rows with result of numerical example [40] on p. 241...

Numerical example [40] is talking about a single bank. The table on 230 is talking about a series of banks. Of course the results won't be the same with one bank and a series of banks.

I came to the solution myself after a lot of experimentation.

But first, I would stick to the table on p. 230 for the purpose of clarity, because regardless of the banking system we are talking about (one monopolistic bank or a system of small banks) the operations are the same, even Huerta de Soto writes:

"This formula [[27] - for total deposits in the system of small banks with c=0,1,k=f=0] is identical to the deposit multiplier in the case of a single, monopolistic bank [14]."

So the reason why my calculations deviated from Soto's results is the confusion I had with his [40] example, since I mistakenly took numbers from his first numerical example in this subchapter on p. 239:

"f = 0.15, then when Bank A loans 900,000 m.u., the amount of money which would return to the banking system would be equal to (1 – f) 900,000 = (1 – 0.15) 900,000 = 0.85 x 900,000 = 765,000 m.u."

However in the [40] example there is no loan of 900 000 if my simulation is to be consistent with his calculations, because the first deposit in the bank is not of 1 000 000 m.u. but 150 000 less: of 850 000 m.u. The reserve, then, is 85 000 and the first loan is 765 000, the filtered out m.u. equals 765 000 x 0,15 = 114 750 and so on. Only with this procedure his [40] numerical results are consistent with my simulation results.

So if the first (primary) deposit in the bank is of din quantity, then the formula [36] has to look like Dn=(d/(1-f))/(c+(f/(1-f)))

...because the first deposit in the bank is not of 1 000 000 m.u. but 150 000 less: of 850 000 m.u.

I totally agree. He's assuming 150K is going to be taken out of the bank, so those 150K cannot be a "reserve" for fractional reserve banking, leaving only 850K.

Are there any situations where fiduciary media does not equal a secondary deposit or a derivative deposit? Do these terms all mean the exact same thing in all cases or are they applied differently?