## Compound Interest Is Different

I know no one who is intuitive about compound interest.  Because there is no intuition, people get it very wrong.

I noticed a day ago that the Buffett partnership and Berkshire Hathaway from 1965 to the end of 2013 earned about 21% annually.  48 years of growth at a comparatively very high rate. Every \$1,000 of capital in the beginning became more than \$9.4 million.  Rather nice.

If they earned half as much yield would they have half as much money?  I think not, but how much less than half.  Think of a number.

Compare your answer to actual and get a sense of your margin of error.  Things where your intuitive answer is vastly wrong makes for a serious planning problem.  It is is hard to know when you are right and when you are wrong. People who think they are right when they are not, can get very far off track.  People can just as easily think they are wrong when they are not and thus stop doing smart things too soon.

Compound, sometimes called exponential growth,  is unlike anything we experience in everyday life.  You must actually think about it. The way you do it is to know about the rule of 72. It says the time to double money is roughly 72 divided by the interest rate.  In Buffett’s case 72 divided by 21 or roughly double every 3.5 year.  In 48 years he gets a bit more than 13 doubles.

At 10.5% there are just 7 doubles.  Thirteen+ doubles is 2 to the power 6+ more. About 78 times as much. Awesome!

For thinking purposes, investment yield is not the same as mowing the lawn.  When mowing the lawn, it is easy to tell when you are half done.  But with compound interest you are half done when you are one double from the end. In Buffett’s case, when you quit 3.5 years early, you get one half the money. You make \$4.7 million in 44.5 years and another \$4.7 million in the next three and half years.

There are interest formulas that you can build into a spreadsheet to help you with this sort of thinking.

The moral of the story is simple.

1. Time matters more than capital.
2. Yield is as important as time.
3. Taxes shrink your yield, so you must pay attention to taxes.  With a yield of 21%, a 50% tax rate for 48 years costs you 98.7% of the income.

There are not many investments like this. High yields help show the effects because they are dramatic.  The effects are less pronounced at lower rates, but the shape remains the same. You get much less if you keep less of the yield or keep it for a shorter time.

Forty-eight years looks like a long time, but if you are a couple 45 years old or less, there is a 50-50 probability that at least one of you will be around for 48 years.  Unless you plan to spend all of your money before you die, it is a reasonable time frame to consider.