A Little Quiz About Compound Interest

On October 18, 1867, American Secretary of State William Seward made one of the finest deals for undeveloped land in history.

He bought Alaska from Russia for one cent per acre. A total of $7.2 million. That was a lot of money at the time. Alaska cost around 0.09% of the year’s output for the whole country. Affordable enough. Today the same share of the economy would be around $20 billion. Of course Alaska is worth far, far more than $20 billion now. The oil reserves alone are worth at least ten times that. So a very fine deal.

Perhaps not as good a deal as the 1803 Louisiana Purchase where a quarter of the continental United States was purchased for 2.8 cents per acre. Triple the price per unit, but the three rules of real estate acquisition are very old.  Location! Location! And location!

The point for today, even spectacular deals can be analyzed in terms of rate of return. Let’s look at Alaska.

The quiz.

Suppose Alaska is worth $7.2 trillion now. A million times the investment. That’s little more than three times as much as the market cap of Apple.

What is the average rate of return on the investment? A million times your money in 153.5 years. Think for a moment. What would the yield have to be?

It works out to 9.4178%. Interesting isn’t it? You thought it would be far more. For perspective, that is a little less than the average rate of return for the S&P 500 total return index over the last 90 years or so. A million times the investment.

It’s a puzzle how wrong we can be when we guess exponential growth over long times.

For bonus marks

Bonus question #1. Suppose Alaska was worth not a million times more, but only 100,000 times as much.  Value of one tenth of the first example. Now what’s the rate of return. Way less, right?

The rate of return is 7.7887%. I know people who think they can make that trading corporate bonds, but they probably cannot do it year after year for 150 years.

Bonus question #2. How much would the land in the Louisiana purchase be worth now if the investment earned 9%. The total original price was $15,000,000. Ignore the improvements that have been made to the property. Just the land value as it was in 1803.

Answer: 144,203,748.9 times as much, or 2.16 quadrillion dollars. A hundred years worth of GDP. Compared to 0.03 years GDP when they bought it. Nice!

The lessons

  1. Time matters more than you think. Start investing a little money sooner, is a better choice than wait and invest more.
  2. Never trust your intuition when assessing rate of return over long periods. Do the arithmetic.
  3. Learn how to estimate using the Rule of 72.
  4. Over very long times average yield loses some of its meaning. Be cautious. Averages hide volatility.
  5. Warren Buffett might not want to buy Alaska, because the historic returns have been too low. He deals only in expectable future returns. BUT, what about climate change? Maybe Anchorage has the makings of a new Miami Beach.

I help people have more income and larger, more liquid estates.

Call or email don@moneyfyi.com in Canada 705-927-4770

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