Image: 401k © Don Farrall, Photodisc, Getty Images

When you were a kid, perhaps one of your friends asked you the following trick question: "Would you rather have $10,000 per day for 30 days or a penny that doubled in value every day for 30 days?" Today, we know to choose the doubling penny, because at the end of 30 days, we'd have about $5 million versus the $300,000 we'd have if we chose $10,000 per day.

Compound interest is often called the eighth wonder of the world, because it seems to possess magical powers, like turning a penny into $5 million. The great part about compound interest is that it applies to money, and it helps us to achieve our financial goals, such as becoming a millionaire, retiring comfortably or being financially independent.

The components of compound interest

A dollar invested at a 10% return will be worth $1.10 in a year. Invest that $1.10 and get 10% again, and you'll end up with $1.21 two years from your original investment. The first year earned you only $0.10, but the second generated $0.11. This is compounding at its most basic level: gains begetting more gains. Increase the amounts and the time involved, and the benefits of compounding become much more pronounced.

Compound interest can be calculated with the following formula:

FV = PV (1 + i)^N

FV = Future Value (the amount you will have in the future)

PV = Present Value (the amount you have today)

i = Interest (your rate of return or interest rate earned)

N = Number

 

Who wants to be a millionaire?

As a fun way to learn about compound interest, let's examine a few different ways to become a millionaire. First we'll look at a couple of investors and how they have chosen to accumulate $1 million:

  • Jack saves $25,000 per year for 40 years.
  • Jeff starts with $1 and doubles his money each year for 20 years.

While most would love to be able to save $25,000 every year like Jack, this is too difficult for most of us. If we earn an average of $50,000 per year, we would have to save 50% of our salary!

In the second example, Jeff uses compound interest, invests only $1, and earns 100% on his money for 20 consecutive years. The magic of compound interest has made it easy for Jeff to earn his $1 million and to do it in only half the time as Jack. However, Jeff's example is also a little unrealistic since very few investments can earn 100% in any given year, much less for 20 consecutive years.

Tip: A simple way to know the time it takes for money to double is to use the rule of 72. For example, if you wanted to know how many years it would take for an investment earning 12% to double, simply divide 72 by 12, and the answer would be approximately six years. The reverse is also true. If you wanted to know what interest rate you would have to earn to double your money in five years, then divide 72 by five, and the answer is about 15%.

Time is on your side

Between the two extremes of Jeff and Jack, there are realistic situations in which compound interest helps the average individual. One of the key concepts about compounding is this: The earlier you start, the better off you'll be. So what are you waiting for?

Let's consider the case of two other investors, Luke and Walt, who'd also like to become millionaires. Say Luke put $2,000 per year into the market between the ages of 24 and 30, that he earned a 12% after-tax return and that he continued to earn 12% per year until he retired at age 65. Walt also put in $2,000 per year, earned the same return, but waited until he was 30 to start and continued to invest $2,000 per year until he retired at age 65. In the end, both would end up with about $1 million. However, Luke had to invest only $12,000 (i.e., $2,000 for six years), while Walt had to invest $72,000 ($2,000 for 36 years), or six times the amount that Walt invested, just for waiting an additional six years to start investing.

Clearly, investing early can be at least as important as the actual amount invested over a lifetime. Therefore, to truly benefit from the magic of compounding, it's important to start investing early. We can't stress this fact enough! After all, it's not just how much money you start with that counts, it's also how much time you allow that money to work for you.

In our first example, Jack had to save $25,000 a year for 40 years to reach $1 million without the benefit of compound interest. Luke and Walt, however, were each able to become millionaires by saving only $12,000 and $72,000, respectively, in relatively modest $2,000 increments. Luke and Walt earned $988,000 and $928,000, respectively, thanks to compound interest. Gains beget gains, which beget even larger gains. This is again the magic of compound interest.

Why is compound interest important to stock investing?

In addition to the amount you invest and an early start, the rate of return you earn from investing is also crucial. The higher the rate, the more money you'll have later. Let's assume that Luke from our previous example had two sisters who, at age 24, also began saving $2,000 a year for six years. But unlike Luke, who earned 12%, sister Charlotte earned only 8%, while sister Rose did not make good investment decisions and earned only 4%. When they all retired at age 65, Luke would have $1,074,968, Charlotte would have $253,025, and Rose would have only $56,620. Even though Luke earned only 8 percentage points more per year on his investments, or $160 per year more on the initial $2,000 investment, he would end up with about 20 times more money than Rose.

Clearly, a few percentage points in investment returns or interest rates can mean a huge difference in your future wealth. Therefore, while stocks may be a riskier investment in the short run, in the long run the rewards can certainly outweigh the risks.

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The bottom line

Compound interest can help you attain your goals in life. In order to use it most effectively, you should start investing early, invest as much as possible and attempt to earn a reasonable rate of return.