Posted on 11/24/2010 11:58:51 AM PST by doug from upland
Compound Interest, Manhattan & the Indians
* Posted by Jeffrey Strain * January 15, 2006
I’ve always enjoyed a story that I have often told about the power of compound interest and the Indians who sold Manhattan.
I even wrote an article about the power of compound interest a couple of years back using the example I had found in an old shoe manual:
Inspiration is often found in the most unlikely places. I received my first lesson in the importance of compound interest and long term savings from a pair of training shoes I bought in high school. To emphasize the point that training a little bit every day could create vast improvements over time, the training manual used an example of the Native American Indians and pilgrims in the US.
In the early 1600s, the American Indians sold an island, now called Manhattan in New York, for various beads and trinkets worth about $16. Since Manhattan real estate is now some of the most expensive in the world, it would seem at first glance that the American Indians made a terrible deal. Had the American Indians, however, sold their beads and trinkets, invested their $16 and received 8% compounded annual interest, not only would they have enough money to buy back all of Manhattan, they would still have several hundred million dollars left over. That is the power of compound interest over time.
Manhattan Manhattan
A couple of days ago I received an email from a man who said that he didn’t believe this compound interest story could be true and was sure that the numbers must be incorrect. So I decided to try and calculate them myself from what I could find — and here are the results. I hope some of you will check my math as it’s definitely not one of my strong suits.
The most recent information I could find about the worth of Manhattan was from December 26, 2005 stating that the land in Central Park (843 acres) was worth $528,783,552,000. Manhattan is approximately 20 square miles in size. 1 square mile = 640 acres, so 20 square miles = 12,800 acres. Central Park therefore makes up approximately 6.586% of all Manhattan. This means 93.414% of the value of Manhattan is unaccounted for. We therefore take the $528,783,552,000 and multiply it by 15.184 to get a $8,029,049,453,000 for the total land value of Manhattan (that’s approximately $8 trillion)
Central Park Central Park
While my shoe manual said that the real estate transaction took place in the early 1600s, the exact date of the purchase was 1626, or 380 years ago. If I use the $16 that the shoe manual said the beads and trinkets were worth at 8% (assuming monthly compounding), the result comes to $230,599,491,667,000 which is a whopping $222 trillion more than the current value of Manhattan. If we use a more conservative 5% compounded interest, however, the result comes to only $2,745,186,908 or some $8 trillion less than the current worth of Manhattan (which goes to show that a few percentage points over 380 years is a big deal).
While my shoe manual used $16 as the price paid for the beads and trinkets, some research shows that $24 seems to be a more accepted number for their worth. Doing the calculations with $24 instead of $16 at 8% brings a compounded result of $345,899,237,500,501. Again, hundreds of trillions of dollars ahead of the current value of Manhattan. At 5% the result comes to $4,117,780,362, still well over $7 trillion less than the current price of Manhattan.
While commonly quoted, the $24 estimate was made in the 19th century according to The Straight Dope, so a more accurate value for the beads and trinkets would be $72 :
According to my Encyclopedia Britannica, 60 guilders in 1626 would buy you 1-1/2 pounds of silver. Naturally we assume this is troy weight, 12 ounces to the pound. Silver lately has been selling for a little more than a $4 per troy ounce.
10 ounce silver bar Appropriate Silver bar
Using the $72 figure at 8% gives us a result of $1,037,697,712,501,503 or over a quadrillion more than Manhattan is worth. At 5% to result comes to $12,353,341,088 which is still more than $7 trillion less than the current worth of Manhattan.
The Straight Dope used $4 an ounce for silver in their calculations which seemed a bit on the low side. A quick check of current silver prices puts them at about $9 an ounce which means the price for the beads and trinkets using their formula would be $162.
Here are the results using $162 as the value which I see as he most accurate with the following compound percentages:
1% – $7,230 2% – $321,666 3% – $14,265,720 4% – $630,686,305 5% – $27,795,017,449 6% – $1,221,115,163,451 7% – $53,479,172,822,455 8% – $2,334,819,853,128,382
The results are that the Indians would have had to earn an average of close to 7% a year compounded to have gotten a better deal out of the trade. If they had left it in a savings account in the bank the whole time, they would have faired quite poorly. If they had invested it in the stock market, however, they would own a lot more than just Manhattan. Since the stock market didn’t exist back then, the assumption would be that the Indians would have earned far less than 7% those crucial first centuries of compounding and thus they did not come out ahead.
Before we close the book on this, however, it should be noted that the Indians that sold Manhattan didn’t really live there (they just traded there). Also from The Straight Dope:
One popular history of Manhattan notes that the Canarsie Indians “dwelt on Long Island, merely trading on Manhattan, and their trickery [in selling what they didn't possess to the Dutch] made it necessary for the white man to buy part of the island over again from the tribes living near Washington Heights. Still more crafty were the Raritans of [Staten Island], for the records show that Staten Island was sold by these Indians no less than six times.”
This being the case, the Indians certainly did come out ahead since they sold something that wasn’t theirs in the first place.
Conclusions
1. Never base a personal finance article on information you find in a shoe manual. 2. The Indians should be credited with some of the earliest and biggest real estate scams in history. 3. Compound interest over time can do some amazing things.
Try it at 8% a YEAR
That's $627 million per acre. However a paper by the Federal Reserve Bank of New York lists one of the highest cost pieces of property in New York at about $100 million per acre (now the Time Warner Center, just off of Central Park), with prices dropping quickly as you get away from the Empire State Building. Many on the map were under $7.3 million / acre ($168/square foot) even on Manhattan.
***In the early 1600s, the American Indians sold an island, now called Manhattan in New York, for various beads and trinkets worth about $16****
Years ago Louis L’Amour was on the TODAY Show and said that we got took. The indians that sold the land didn’t own it, were from somewhere else, and just happened to be in the area fishing when the Europeans approached them about selling it.
He had the math right for that. 8% per year = 0.6667% per month. 1.006667 ^ (4560 months) is what he calculated.
8% per annum compounded monthly is equivalent to about 8.2999507% compounded annually.
1.006666667^4560 ~ 1.082999507^380
Of course, if the stupid Indians had rented it for $1.00/month, and placed the rents in an account bearing 8% annual interest compounded monthly, they would have more about 150 times more than the measely 1000 trillion they would haven’t gotten on the original $72 bucks placed in a savings account. Like all the money in the world. Even Obama might have trouble spending that much.
BTW, the original deed only covered the portion of Manhattan south of Wall Street, a tiny fraction of the whole island, so the Dutch really got ripped off. The Wall was there to keep the former tenants UIT.
The most relevant thing I see to this question is: What was the land “worth” at the time, and what were the beads and trinkets worth to the Indians?
Given that those trinkets were probably items that the Indians did not have and could not produce, that would’ve given them significant value as jewels.
From all I’ve heard, the value of diamonds has been very artificially manipulated for generations by the DeBeers corporation, who control most of the world’s supply.
After all, what is a diamond? It’s a trinket. It’s a hard rock that happens to also look pretty. The value is in its beauty, its prestige, and in its (artificially manipulated?) rarity.
Of course, the value of such trinkets would drop as they became more common.
At the time, the island was undeveloped, and the total population of North America (which probably includes Canada and Mexico as well) was around 1 million. So the population of the continent was probably around 1/400th of what it is today. There was PLENTY of land out there for the taking (whatever property you reside on, imagine that there is 400 times that amount freely available for you, and that your situation is the NORM for the entire continent.
When there’s that much land available, it can and WILL be bought and sold VERY cheaply.
Anyway, the following article makes the point that “there is no evidence either the Dutch or the Indians believed they had robbed or been robbed by the other party to the deal.”
the indians thought they were cheating the dutch. no concept of property.
If they’d just invested it in a growth fund instead of blowing it all on tobacco and peyote!
Just wait until the IRS hears this. Those Indians have a huge tax bill coming with penalties.
Yeah, I am sitting here laughing at the native Americans. Who would borrow 1,200 Billion dollars from a country, so we can afford to buy 265 Billion worth of trinkets from them?.....WAIT A MINUTE.....are we stupider den dem injuns?? me wunderz win dey wil giv us sum blanquets and put us on reservashuns?
What’s the annual rate of return on 8% compounded instaneously.
r* = limit[p => 0] (1+r*p)^(1/p) - 1
r* is the effective annual rate of return, p is the period, in years. For p = 1/12, r = 0.08, r* = 0.0829995...= 8.29995%. What happens to r* as p approaches zero?
r*(p=> 0) = (e^r)-1
If this does not prove that there is a God and Leonard Euler is his prophet, nothing does.
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