In January 1963, Warren Buffett included the following impish observation in his letter to his investment partners. “I have it from unreliable sources that the cost of the voyage Isabella underwrote for Columbus was approximately $30,000.”

Unreliable indeed; there was no dollar in 1492. But we get the gist. Buffett goes on to observe that while the voyage could be considered “at least a moderately successful utilisation of venture capital”, if Queen Isabella had instead invested the $30,000 in something yielding 4 per cent compound interest, the invested sum would have risen to $2tn by 1962. For her inheritors’ sake, perhaps Isabella should have said no to Columbus and simply found the 15th-century equivalent of a passive index fund instead.

Buffett’s thought experiment returned to me as I browsed through the latest list of billionaires from Forbes. None of the leading players had achieved their position by the simple accumulation of family wealth over generations. The top five — Bill Gates, Amancio Ortega, Buffett, Carlos Slim and Jeff Bezos — are all entrepreneurs of one form or another. According to economists Caroline Freund and Sarah Oliver, the proportion of billionaires who inherited their fortunes has fallen from 55 per cent two decades ago to 30 per cent today.

Is this absence of old-money trillionaires because Buffett’s 4 per cent compound interest was unavailable to the wealthy and powerful of pre-industrial Europe? Hardly. If anything, 4 per cent is conservative. According to Thomas Piketty’s bestselling book Capital in the Twenty-First Century (2013), the real rate of return on capital, after taxes and capital losses, was 4.5 per cent in the 16th and 17th centuries, then 5 per cent until 1913. Although it fell sharply between the wars, the effective average rate of return was very nearly 4.3 per cent across the five centuries. At that rate, $30,000 invested in 1492 would be worth $110tn today.

Not to get too technical, but $110tn is a lot of money. It’s more than 1,000 times the wealth of the richest man in the world, Bill Gates. It’s 17 times the total wealth of the 1,810 billionaires on the Forbes list — or, alternatively, nearly half the household wealth of every citizen on the planet. (According to Credit Suisse’s Global Wealth Report, total global household wealth is $250tn.) Queen Isabella’s investment advisers apparently let her down. Patient, conservative investments would have left her heir today with a fortune to tower over every modern plutocrat.

All this brought to mind Piketty’s “r>g”, a mathematical expression so celebrated that people started putting it on T-shirts. It describes a situation where “r” (the rate of return on capital) exceeds “g” (the growth rate of the economy as a whole). That is a situation that described most of human history, but notably not the 20th century, when growth rates soared while capital had a tendency to be nationalised, confiscated or reduced to rubble.

“r>g” is significant because if capital is reinvested and grows faster than the economy, it will tend to loom larger in economic activity. And since capital is more unequally distributed than labour income, “r>g” may describe a society of increasingly entrenched privilege, where wealth and power steadily accrue in the hands of heirs.

This is a fascinating, and worrying, possibility. But it is a poor description of the modern world. For one thing, when billionaires divide their inheritance, mere procreation can be a social equaliser. Historically, the great houses of Europe intermarried and concentrated wealth in the hands of a single heir. (No wonder: one of Queen Isabella’s grandsons, Ferdinand I, had 15 children.) But these days, disinheriting daughters and second sons is out of fashion. (That said, “assortative mating”, the tendency of educated people to marry each other, is back and may explain more about rising income inequality than we tend to realise.)

Another thing: the rich do not simply wallow in money vaults like Scrooge McDuck. They spend. According to Harvard economist Greg Mankiw: “A plausible estimate of the marginal propensity to consume out of wealth, based on both theory and empirical evidence, is about 3 per cent.” Instead of 4.3 per cent, then, wealth compounds at 1.3 per cent after allowing for this spending. Five centuries of compound interest at 1.3 per cent turns $30,000 into about $25m, a fine inheritance indeed but not the kind of money that will get you near the Forbes list.

Of course, inherited privilege shapes our societies not only among the plutocracy but down in the rolling foothills of English middle-class wealth. There, economic destiny is increasingly governed by whether your parents bought a house in the right place at the right time — and by the UK government’s astonishing abolition of inheritance tax on family homes.

But whether mega-wealth in the 21st century will be driven by the patient accumulation of rents on capital, rather than the disruptive entrepreneurship of the late 20th century, remains to be seen. After all, long-term real interest rates in advanced economies have fallen fairly steadily from 4 to 5 per cent three decades ago to nothing at all today. You don’t need to be Warren Buffett to figure out that if you want to get rich by accumulating compound interest of zero, you’ll be waiting a long time.