An Excerpt from Proudhon's Stock Exchange Speculator’s Manual

It will be without any doubt useful to end this chapter with a summary of the necessary rules of arithmetic for the solution of the problems used in speculation.

We certainly won't stop there: How much do 25 shares at 750 fr. cost? But more than one reader would perhaps fumble to solve this other, slightly less simple one: How much does 2,250 fr. of 4 ½ annuity cost at 90? - 90 is not the price of 1 fr. of annuity, but the price of 4 fr. 50. Therefore, we need to find out how many times 2,250 contains 4 fr. 50. - Answer: 500 times. - It is by 500 that we must multiply 90. - Product : 45,000 fr.

How much does 3,000 fr. of 3 0/0 annuity cost at 67?

Answer: 67 x 3,000/3 or 67 x 1,000 = 67,000 fr.

Almost all calculations you need to make on the stock exchange can be solved with the help of the rule of three. The most important thing is to know how to set the proportion. Here's a summary of the principles to be followed.

One of the terms is always: A capital C is to a capital c; the other: An interest I is to an interest i. - C must correspond to I, and c to i.

Examples:

C : c : : I : i

c : C : : i : I

I : i : : C : c

The custom is to place the unknown at the last term. Let C be the unknown: c will be the third term, I the second, and i the first:

i:I::c : x = C

Let's apply this theory to our calculation.

1. Let's return to the one from earlier: how much does 2,250 fr. of annuity cost at 4 ½ 0/0 to 90?

When 4 fr. 50 of annuity (i) costs 90 fr. (c), how much will 2,250 fr. of annuity (I) cost? - The unknown is C. Thus, for the following proportion:

Proportion : i : I :: c : C

In numbers : 4 50 : 2,250 : : 90 : x

Hence : x = 2,250 x 90/4 50 = 45, 500 fr.

2. What is the rate of a public loan at 5 0/0 negotiated at 80 fr.?

When 80 fr. of capital (c) yields 5 fr. of annuity (i), how much will 100 fr. (C) yield? - The unknown is I, and the proportion must be written as:

Proportion : c : C : : i : I In numbers : 80 : 100 : : 5 : x Hence : x = 100 x 5/80 = 6 fr. 25

The loan is contracted at 6 fr. 25 0/0.

3. The 3 0/0 is 67 and the 4 ½ is 90: which is more expensive?

There are two ways of solving this problem: the first consists in finding the rate of each of the prices and making the difference; but the following is more expeditious.

When 3 fr. of annuity (i) cost 67 fr. (c), how much does 4 fr. 50 (I) cost? - The unknown is C, and we write:

Proportion : i : I : : c : C Numbers : 3 : 4 50 : : 67 : x Hence : x = 4 50 x 67/3 = 100 50.

Since 100 50 is in 4 ½ the price corresponding to 67 in 3 0/0, and whereas the former is only at 90, 3 is the most expensive. - How much more expensive is it per franc of income?

From 100 50 - 90/4 50 that is 10 50/4 50 or 105/45 or 2 fr. 33.

This problem can be solved using the unit or denier method. When 3 fr. of annuity (I) cost 67 fr. (C), how much will 1 fr. of annuity (i) cost? - the unknown is c, and we pose:

Proportion : I : i : : C : c In numbers : 3 : 1 : : 67 : x

Hence : x = 67/3 = 22 fr. 33. Likewise : 4 50 : : 90 : x

Hence : x = 90/4 50 = 20 fr.

The 3 is 22 33 in denier; the 4 ½ is at 20 in denier. - Difference 2 fr. 33 c.

4. How much, with 60,000 fr., can we purchase from 3 0/0 to 66?

When with 66 fr. (c) you have 3 fr. of income (i), how much will you have with 60,000 fr. (C)? - The unknown is I and I pose:

Proportion : c : C : : i : I In numbers : 66 : 60, 000 : : 3 : x Hence : x = 60,000 x 3/66 = 180,000/66 = 2,727 fr. 27.

You can therefore acquire 2,727 fr. of annuity.

5. 92,500 fr. have produced for me, in a carry-over operation, 815 fr. in one month: what rate per 100 a year does this profit represent?

I say: 815 fr. in one month gives, over twelve months or one year, 9,780 fr.

The question is therefore this: if 92,500 fr. (C) produce 9,780 fr. (I) in a year, how much do 100 fr. (c) produce? - The unknown is i.

Proportion : C : c : : I : i In numbers : 92,500 : 100 : : 9,780 : x Hence : x = 9,750/925 = 10 fr. 57

The carryover in this case therefore represents a rate of 10 fr. 57 c. 0/0 per annum.

6. If it is about foreign funds, the mode of procedure is no different. When 5 ducats of Naples annuity are worth 105 in capital, how much will 500 ducats of annuity be worth? Proportion : 5 : 500 : : 105 : x D’où : x = 10,500 ducats.

But how much is that in francs, given that the ducat is valued at 4 fr. 40 c.? - It's enough to multiply 10,500 by 4 40, which gives 46,200 fr. - In fact, 1 ducat gives 4 40 just as 10,500 ducats give x fr. - 1, that's i; 4 40, I; 10,500, c, and x the unknown, C.

Proportion : i : I : : c : C In numbers : 1 : 4 40 : : 10, 500 : x

As 1 does not divide, it is sufficient to multiply by 4 40.

7. The Austrian florin is worth 2 fr. 60: how much are 10,000 florins worth in francs?

Since 1 doesn't divide, it's 2 60 x 1,000, or 2,000 fr.

8. The type of foreign currencies is generally higher than ours, so the calculation indicated in numbers 6 and 7 is applicable almost everywhere. However, if the type were lower, there would still be nothing to change, if not in the position of the terms: the unity of the first term, it is then the foreign type.

Example. When the Amsterdam gros denier is worth 54 centimes, how much is 248 deniers worth in francs?

1 denier gives 54 centimes as 248 deniers x fr.

Proportion : 1 : 54 : : 248 : x Hence : x = 248 x 0 54 = 133 fr. 92.

9. Conversely, we may have to convert francs into foreign values.

When the Spanish pistole is worth 15 fr., how much is 36,000 fr. worth in pistoles?

I say: 15 fr. gives 1 pistole as 36,000 fr. gives x.

Proportion : 15 : 1 : : 36,000 : x.

1 does not multiply; therefore : x = 36,000/15 = 2,000 pistoles

It would be superfluous to further multiply the examples.

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