Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 23

Compound Interest Gone Berserk
The effect of compounding can be gigantic if a sufficiently long period is used. Here are three of your authors' favorite examples.
Manhattan Island
Legend has it that in 1623 Dutch settlers "purchased" Manhattan Island from Native Americans living there for trinkets worth about $24. The usual version of the story claims that the sellers were robbed in this transaction. But suppose they had invested the money? Real returns on stocks have averaged about 7 percent, so let's calculate how the $24 invested in stocks would have grown during the 390 years since the sale.
That is, the funds would have grown to be nearly $7 trillion-a value that is probably greater than the land on Manhattan Island is worth today.
Horse Manure in Philadelphia
In the 1840s the horse population of Philadelphia was growing at 10 percent per year. The city fathers, fearing excessive crowding, decided to restrict the number of horses in the city. It's a good thing! If the horse population of 50,000 in 1845 had continued to grow at 10 percent per year, there would have been quite a few of them in 2013.
Nearly 450 billion horses would have posed some problems for the city. Assuming each horse produces 0.25 cubic feet of manure per day, there would be about 3,000 feet of manure per year covering each square foot of Philadelphia today. Luckily, the City of Brotherly Love (author Nicholson's hometown) was spared this fate through timely government action.
Rabbits in Australia
Rabbits were first introduced into Australia in 1860. They found a country relatively free of natural predators and multiplied rapidly. If we assume that two rabbits started this process and that the population was growing at 100 percent per year, in only 20 years there were
If the growth continued for the next 133 years, by 2013 there would have been 2 154 rabbits, amounting to many trillions of rabbits per square foot of Australia. Clearly they built the "rabbit-proof fence" for a reason.
The preposterous numbers in these examples suggest there is something wrong with the calculations. Can you put your finger on precisely why each is pure nonsense?