Compound Interest

**Q:** I am completely new to investing and don't quite understand the idea of compounding interest. Can you explain? (Math was never my strong suit.) -- V.L., via the Internet

**A:** Albert Einstein supposedly said that compound interest was the greatest wonder of the universe, or words to that effect. No one seems to know exactly when he said this, or to whom, so maybe the story is apocryphal (today's vocabulary word). On the other hand, if he didn't say it, he should have. And if you'd asked him to explain it, he might have described it like this:

Say there are two twins, each of whom has $1,000 to invest, just before one of them jumps onto a spaceship. The timid sister who stays home chooses an account yielding simple interest at 5 percent. This means that each year her money is increased by 5 percent of the original $1,000 ($50). After year one, she has $1,050; after year two, $1,100; after year three, $1,150; and so on.

The adventurous astronaut sister, on the other hand, puts her $1,000 in an account that returns 5 percent compound interest. This means that she gets interest not only on her original $1,000, but on the interest that is added to it as well. At the end of year one, she too has $1,050. In year two, she earns another 5 percent -- but now it's 5 percent of $1,050, not of $1,000. So instead of getting $50 added to her money, she gets $52.50, bringing her total to $1,102.50. The next year, $55.13 is added. The year after, $57.88.

This difference between compound interest and simple interest may at first seem minuscule. But it increases astronomically with two factors: time (see how it all leads back to relativity?) and rate of return. Let's now extend the interest comparison out 25 years. The simple-interest sister's money will grow 25 times $50, to $2,250. The astronaut sister's compound interest, though, nets her $3,481.29. In other words, at the end of 25 years, she'll have about 50 percent more than her earthbound, simple-interest sister. (No wonder the earthbound sister ages faster!)

In fact, when we're talking about investing, we always refer to compound interest. So now let's assume that we're talking about compound interest, and look at the second prong of Einstein's General Theory of Compound Interest: rate of return.

Say you start with the same thousand dollars, but instead of your money earning 5 percent per year, it earns 15 percent. That's only 10 percent different, so after 25 years we figure that would only be about 10 percent more than $3,481.29 -- around $3,800, right? (Ha! Trick question!) The money will grow to $41,544.12. And if you hang on another 10 years, your money has grown to $184,464.75. Because the total amount of your money grows each year, the amount that is added on each year grows right along with it.

Remember that this assumes an initial investment of only $1,000 -- with no money being added each month or even each year. The power of compound interest over time is simply staggering -- and the higher the rate of return, the faster your investment grows. And, of course, you'll keep younger and fresher, full of the insouciance and joie de vivre (vocabulary words two and three for today) of the filthy rich.

**WHAT NOW? **Think about where you want to put your long-term savings. In a savings account that may give you about 3 percent annually? In U.S. Treasury bills, which have yielded roughly 4.2 percent per year during this century? Or in the stock market, which has historically yielded more than 11 percent per year? You do the math, Fool!

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