Sunday, January 26, 2014

"£40,000 accumulating at 3¼ per cent compound interest approximately corresponds to the actual volume of England's foreign investments at various dates"

From Economic Possibilities for our Grandchildren, in Essays in Persuasion (1931) by John Maynard Keynes:
The modern age opened, I think, with the accumulation of capital which began in the sixteenth century. I believe—for reasons with which I must not encumber the present argument—that this was initially due to the rise of prices, and the profits to which that led, which resulted from the treasure of gold and silver which Spain brought from the New World into the Old. From that time until to-day the power of accumulation by compound interest, which seems to have been sleeping for many generations, was re-born and renewed its strength. And the power of compound interest over two hundred years is such as to stagger the imagination.

Let me give in illustration of this a sum which I have worked out. The value of Great Britain's foreign investments to-day is estimated at about £4,000,000,000. This yields us an income at the rate of about 6½ per cent. Half of this we bring home and enjoy; the other half, namely, 3¼ per cent, we leave to accumulate abroad at compound interest. Something of this sort has now been going on for about 250 years.

For I trace the beginnings of British foreign investment to the treasure which Drake stole from Spain in 1580. In that year he returned to England bringing with him the prodigious spoils of the Golden Hind. Queen Elizabeth was a considerable shareholder in the syndicate which had financed the expedition. Out of her share she paid off the whole of England's foreign debt, balanced her Budget, and found herself with about £40,000 in hand. This she invested in the Levant Company—which prospered. Out of the profits of the Levant Company, the East India Company was founded; and the profits of this great enterprise were the foundation of England's subsequent foreign investment. Now it happens that £40,000 accumulating at 3¼ per cent compound interest approximately corresponds to the actual volume of England's foreign investments at various dates, and would actually amount to-day to the total of £4,000,000,000 which I have already quoted as being what our foreign investments now are. Thus, every £1 which Drake brought home in 1580 has now become £100,000.


The Arthurian said...

Is it a typo? Or do I misunderstand?

Looks to me like Keynes says the power of compound interest reawakened "in the sixteenth century" -- 1580 specifically -- and "has now been going on for about 250 years."

1580 + 250 = 1830

1580 + 350 = 1930

Keynes wrote this around 1930. Is "250" a typo?

The Arthurian said...

Dunno about the typo yet. But in a long and slow-loading PDF, William J. Baumol writes:

"Keynes’s argument can be extended. According to Angus Maddison’s (2003) rather conservative estimate, during the twentieth century, British real per capita GDP rose by a multiple of approximately 4.5 (that of the United States rose nearly sevenfold). We may note that the British figure is right in the range in Keynes’s forecast. In the same period British total real GDP rose by a multiple of 6.5."

Link to PDF:

The Arthurian said...

In a post titled Original Sin Plus Compound Interest Equals Wealthy Nation?, Nikos Askitas quotes Keynes -- "the treasure which Drake stole from Spain in 1580" -- and says

So you take an original sin, you put it through compound interest and you have a wealthy nation! Is this more general than the case of UK and Spain?

Probably far more general. I read someting the other day where the guy said all wealth started with theft. I quit reading that post because it seemed an extreme exaggeration. But the guy could have made good use of this "original sin" idea.

As for myself, I have become quite fascinated by history. But I don't think we need to hold grudges against historical acts.

The Arthurian said...

And regarding the gold that England stole from Spain, 2ndlook reminds us that we all know where the Spaniards got their gold from!

Jazzbumpa said...

I can't make those numbers work. To get 1 to become 100,000 over 350 years, the rate is 4.0262%.

To get there in 250 years, you need 5.6818%

Of course, Keynes didn't have Excel.

The quote I saw follows; and to give it it's due, you need the entire quote.

"the thing that most fascinates me about this type of person is that he is entirely oblivious to the fact that in the world of adam smith – the world in which this clown believes he is living – you can’t get that wealthy.

free markets do not produce wealth: oligopoly produces wealth.

which is to say, cheating produces wealth (or, alternatively, behind every great fortune lies a crime).

i suspect that perkins has given this reality approximately 3 nanoseconds of thought in his life – and then dismissed it as irrelevant. he’s a maker, after all!"

The point is, with capitalism, you can get rich, but you can't legitimately become top fraction of 1% rich, because of free market competition. Getting there takes some kind of crime against man or nature. I've believed this since I was a kid.


Jazzbumpa said...

And the Spanish got their wealth by enslaving native Americans.

There was at least one native group in the islands that they completely annihilated.

Then came the African slave trade.

Every bit of the spoils of empire is ill-gotten gains.


The Arthurian said...

At this moment... 9:51 AM ... I've been looking for an answer to my question "Is '250' a typo?" since quarter after five this morning ... four and a half hours.

Finally found somebody besides myself who actually evaluated the statement instead of just copying and pasting and posting it.

I used Google Translate, Japanese to English, and turned up this paragraph:

Although not shown before and after this part is so long, for two reasons, that the 250 years of the original text is a mistake or misprint is clear. First, Keynes is discussed foreign investment in the UK Here, it is said that when operating in compound interest of 3.25% to 40,000 pounds of the original, to become the 4 billion pounds almost 250 years later. I can know right away if calculations, 250 square of 1.0325, so about three thousand, 40 thousand pounds is not only about £ 120 million. Second, because argues that it is 1580 is the starting point for overseas investment in the UK, it stood 350 years to 1930 which this essay was written.


The Arthurian said...

Yes Jazz, that is exactly the piece that I read. Thanks! Where'd you find it?

I didn't check the numbers yet, myself. Gotta go...

The Arthurian said...

In an Open Office spreadsheet
I put the value 1 in cell A1.
I put the value 1.0325 in cell B1.
I put the formula =A1*$B$1 in cell A2.
I copied cell A2 to the range of cells starting with A3 and ending with A350.

I know, it's only 349 years...

I had to increase the growth rate value in cell B1.

For a growth rate multiplier of 1.0335 I get 98,709.25 in cell A350, just a bit under the 100,000 target value.

For a growth rate multiplier of 1.0336 I get 102,099.29 in cell A350, just a bit over the target value.

I get a growth rate between 3.35% and 3.36%, close enough to the given number 3¼.

Keynes rolls over and asks, "What were you thinking, Jazz?"

Jazzbumpa said...

I found the quote in the comment stream at LGM and made it my QOTD.

I slipped a digit and calculated 1 expanding to a million rather then to 100,000.


To reach 100,000 in 350 years, I get 3.344105%.

I used this formula

(1+[cell reference])^350.

And played with the number in the reference cell until it came out to 100,000, arriving at .0344105.

I think your rate is at 3.35% + because you are only at 349 years.

At 349 Yrs I get 3.353847%.

Mysteries solved, I think.


Capcha is reasonings

The Arthurian said...

"my QOTD."

Ah!. Well at least you know I read it...

So at 3.25%, Keynes was even closer than I thought.

Jazzbumpa said...

At 3.25% it only goes to 70,409.

Over long time spans, tiny differences in interest make big differences in the final value.