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Compounding and Compound Interest Explained

© Kirk Lindstrom

Some believe it was Benjamin Franklin who said, "Compound interest is the eighth wonder of the world," while attributing "Compound interest is the world's greatest discovery," to Albert Einstein. Still others attribute the whole thing to John Maynard Keynes. Whoever said it first, all three of these great minds recognized the power of compounding. It doesn't take a "genius" to see why.

One of the basic premises of long term investing is your money compounds over time. I was asked recently, "What exactly do you mean by compounding? Can you explain it to a novice?" Challenge accepted!

Definition

The first order of business is to look up "compounding." Click on Kirk's Financial Links.

You can easily find that link at the top of the list of useful links we have on the site. Go to the upper right hand side of most pages in this topic and click on Links.

OK, you are now on my Financial Links Page. Now, under "Kirk's Most Useful Links:" click on "Investment Dictionary - Investorwords" and navigate that page to "compounding" where you will get:

compounding "A process whereby the value of an investment increases exponentially over time due to compound interest. see also Rule of 72."

and

compound interest "Interest which is calculated not only on the initial principal but also the accumulated interest of prior periods."

The KEY points to notice here are

• Once you earn some interest on an investment over a period, the next rate period your earned interest will also gain some more interest so your total interest payment gets larger.
• the size of the interest payment you get each period grows at an exponential rate with time. That is, the longer you hold, the larger the interest payment.

Let's do an example

Let's start with $1,000 in a money market fund earning 5% per year with quarterly interest payments. Quarterly payments means you get 5% divided by 4 or 1.25% per quarter.

Quarterly Interest New
Quarter Amount Rate Earned Total
1 $1,000 1.25% $12.50 $1,012.50
2 $1,012.50 1.25% $12.66 $1,025.16
3 $1,025.16 1.25% $12.81 $1,037.97
4 $1,037.97 1.25% $12.97 $1,050.95

So, after 1 year, our $1,000 has grown to $1,050.95. This means our "compound interest rate" was 5.095% not 5.00%! The 5% is what we call the "simple interest rate."

Lets do a few more years of interest compounding:

Quarterly Interest Interest New
Quarter Amount Rate Earned Change Total
1 $1,000 1.25% $12.50 $1,012.50
2 $1,012.50 1.25% $12.66 $0.16 $1,025.16

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