# How Compound Interest Works

I watched a clip from the Antiques Roadshow recently. It included an odd, even ugly, piece created by Tiffany and Co for the 1893 Chicago World’s Fair. The piece was evaluated as an auction estimate at between 50 and 100 thousand dollars in 2009 and updated to 100 to 150 thousand in 2021. Let’s guess it went from \$75,000 to \$125,000 in 12 years. That’s a compound rate of return of 4.35%.

Not so special as an investment, but 4.35% for a long time is very powerful.

### Most people underestimate the value of time.

We know it was first offered for sale in 1893, and we have chosen 4.35% as a reasonable compounding factor. Here’s the test. What would it have sold for in 1893 to make all this work? That’s 128 years of compounding.

The price tag would have been \$537. That may not be impossible. In 1893, \$537 was a substantial sum. As Charlie Munger and many others have  opined, “The money is not in the buying; the money is in the waiting.”

That being true and easily proven, why won’t people wait?

The owner of the vase said it was ugly. That tends to harm the likelihood of being patient. Knowing this object this worth more than \$100,000, can you see its beauty? Me either.

The problem of patience extends to things that aren’t ugly. We think linearly in an exponential world.

At 4.35%, money doubles in 16 .2 years. The linear expectation of value would be the gain after 16.2 years should be 16.2 years/128 total years of the \$124,463 appreciation. That’s \$15,752. Easy enough to wait another 16.2 years to get to \$31,504 and so on until 128 years.

Reality doesn’t work like that. After 16.2 years, the object is worth \$1,074. If it appreciates 4.35% a year for another 16.2 years (one more double), it is worth \$2,148. Not exciting at all. Even after 111.8 years, it is worth just \$62,500.

The problem – when you think linearly, your expectation early on is immensely different from what compound growth will deliver. It looks like you made a foolish investment. That is not an observation of yourself that makes patience easier. People are not even slightly intuitive about compound growth and so make serious mistakes with long-term investing. Learn to think about it and find ways to simplify the calculations.

### One such simplification is the rule of 72.

The rule delivers an approximation of how many years it takes to double your money at a given interest rate. 72 divided by the rate equals the number of years needed. Or, if you know the number of years to double, the rate is 72 divided by the number of years. Remember, it is an approximation. Actually, a reasonably good one up to about 40%. In the example above, the rule would have produced 16.55 years to double at 4.35%. 16.55 years implies a real rate of 4.28%. In my experience, when you are projecting rates of return for a long time, the second number after the decimal is just pride. No one projects with that accuracy. Most of the time, the first number after doesn’t matter either.

The greatest enemy to an investment policy is a false expectation about what is possible or likely. Learn to do a little calculating before getting too involved.

Years ago, I did an article on the compounding growth question and how yield, time and taxes affect the result. You can see it here.

First We Sell Manhattan

The question it addressed was when the Dutch bought Manhattan Island for \$24, who got the better deal? The Dutch of the Canarsie?

The numbers show important things.

1. Longer time is your investing friend.
2. Taxes are destructive; avoid them or a least defer them if you can.
3. The original capital provides little information about what is possible in future.

Now, another 10 years have passed, so the accumulation is more than double what it was then.

The first thing you should notice is crucial. The last double adds more value than all the doubles before it.

### The bit to take away

Play with numbers until you get the idea that time matters at least as much as the rate of return. Seeking high returns increases the risk of loss, while taking longer doesn’t. Start sooner.

I build strategic, fact-based estate and income plans. The plans identify alternate ways to achieve spending and estate distribution goals. In the past, I have been a planner with a large insurance, employee benefits, and investment agency, a partner in a large international public accounting firm, CEO of a software startup, a partner in an energy management system importer, and briefly in the restaurant business. I have appeared on more than 100 television shows on financial planning. I have presented to organizations as varied as the Canadian Bar Association, The Ontario Institute of Chartered Accountants, The Ontario Ministry of Agriculture and Food, and Banks – from CIBC to the Federal Business Development Bank.

Be in touch at 705-927-4770 or by email at don.shaughnessy@gmail.com.

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