# Building Intuition About Compound Growth

Most people miss essential things about yield and time taken together.

Here is a simple way to help you understand how a one-year yield is not the same as that growth over a long time.

There are hundreds of clips of the Antiques Road Show on the internet. This one will help you understand compound growth. A Federalist Card Table

If you watch it, you will find a table bought at a garage sale in the late 60s for \$25 was worth \$200,000 by 1997.

### Finding an approximate growth rate

The \$200,000 value, divided by the \$25 price, is 8,000 times the original price. 8,000 is approximately 13 doubles. 2 to the power 13 is 8,192. If something doubles 13 times in 30 years, that is one double every 2.3 years, the rate of return is about 72/2.3, a bit more than 31%. The actual number is closer to 35%.

### The rule of 72.

The rule supplies approximations of yield using the formula The time to double is 72 divided by the growth rate. So if your yield is 9%, the time to double is 72/9 or 8 years. 1.09 to the power 8 is 1.99256, so very close to 2. As the yield moves away from that space, it gradually becomes less accurate. For example, at 18%, it should double in 4 years. 1.18 to the power 4 is actually 1.9387. Not so exact, but certainly close enough for intuitive decisions.

By reorganizing the equation, 72 divided by the number of doubles will produce a rate of return. Like we did above.

### What we can learn.

Very high rates of return are improbable. I would be surprised if there are more than five examples of 8,000 times your money purchases in the history of garage sales. Probabilistically – zero to many decimals. The very high yields are outside reasonable expectations. The fundamental is luck, not management.

Try this out for an idea. Warren Buffet is 92 this year. His net worth after many donations is \$125 billion. Suppose he earns 14% with his money. How much would he have had at age 65? It is like this. 14% doubles in 72/14 years or 5.14 years. There are then 27/5.14 doubles = 5.25 doubles. 2 to the power 5.25 is 38. His net worth at 65 would have been 125/38 in 1965. That is \$3.3 billion. Nice, but in 2021 Forbes listed the wealthiest people in the world. B. Wayne Hughes had a net worth of \$3.3 Billion and was tied with others ranking 925th in the world.

14% is a huge rate of return over a long time. “Over a long time” is what matters.

### Do you know why?

Think about doubles. The last of the doubles will double everything. So one double earlier, you would have had half as much money. The last double adds as much as all the money you had before it.

### The bits to take away

12% is twice as much as 6% in a single year. But over 25 years, it is four times more. Two more doubles. You could work it out using the rule of 72. calculate the doubles.

Don’t you think it would be a good idea to organize your life to get one more double?