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.