Mathematics for Business and Personal Finance

Chapter 5: Saving Accounts

Business Math in Action

Compound Magic

Who wants to be a millionaire? You do not have to get on a game show and answer difficult trivia questions to achieve financial security. All you have to do is start investing a small amount of money every month when you are in your 20s, have patience, and you can become wealthy by retirement age. You do not have to be a stock-market whiz. Just pick a solid index fund (a large group of stocks), contribute a little money with every paycheck, and watch your investment grow through the magic of compounding interest.

Chapter 5 explains how compound interest works. Put simply, you invest a certain amount every interest period (usually one year), and collect interest on it. The next interest period, you collect interest on the original amount, plus the interest that it has already earned. If you invest $1,000 a year at 10 percent interest compounded annually, it will have a value of $1,100 at the end of the year. The following year, you will collect 10 percent interest on $1,100, so it will become $1,210. The idea is to keep investing every year, so that you keep adding to the amount that gets compounded. The younger you are when you begin, the greater the return on your investment.

Suppose you invest $2,000 a year, beginning when you are 19 and continuing for just eight years. That is a total investment of $16,000. If you invest that money in a fund that pays 10 percent interest compounded annually, by the time you are 65 your original $16,000 will have grown to $1,035,161. That is an amazing return on your investment. All you have to do is invest that much money and not touch it.

What happens if you wait until later to invest? The results are not as amazing. If you start investing $2,000 a year at age 27 and continue for 38 years, until you are 65, you will have invested a total of $78,000. Yet the value of your account will be only $805,185.

To repeat: An investment of $16,000 would earn you $1,019,161, and an investment of $78,000 would earn you $805,185. The only difference is the age you start investing. The lesson is clear: time is money when it comes to compound interest. It may be difficult for 19-year-olds to imagine retirement, but numbers like these ought to jump-start any imagination. Plus, if you get into the habit of investing at age 19 and keep doing it throughout your career instead of stopping at age 27, you will end up with an even larger pile of cash when you retire.

The magic of compound interest is sometimes explained by retelling the familiar story of the man who bought Manhattan. In 1626, a Dutch trader named Peter Minuit purchased the island of Manhattan from a Native American tribe for the equivalent of about $162. What would have happened if, instead of buying Manhattan, he had invested that money at 7 percent interest compounded annually? As of the year 2007, that original $162 would have been worth $53 trillion.

Start investing now, even if it's only $25 a month. Get in the habit. Do a bit of research and find a dependable fund, or contribute to your company's 401(k) plan. For the price of a few meals, you can pave the way to prosperity.

English Language Arts/Writing

Compound Interest

Write a short list of the ways you could cut back on expenses so you could invest $1,000 each year.

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