Mathematics with Business Applications
Business Math in Action
You, too, can be a millionaire! A late-night TV con job? Or a reasonable financial forecast? Its reasonable, and quite achievable. All you have to do is start investing a small amount of money every month when youre in your twenties, and you can become wealthy by retirement age. You dont 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% interest compounded annually, it will have a value of $1,100 at the end of the year. The following year, you will collect 10% 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 more spectacular the return on your investment.
Suppose you invest $2,000 a year, beginning when you are 19 and continuing for just eight years, until youre 26. Thats a total investment of $16,000. And say 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. Thats an extraordinary return on your investment. All you have to do is invest that much money and not touch it.
However, the real stunner is what happens if you dont invest until later. 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 themselves at 65, but numbers like these ought to jump-start any imagination. Obviously, if you get into the habit of investing at age 19 and keep doing it throughout your career instead of stopping at 26, 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 about $24. What would have happened if, instead of buying Manhattan, he had invested that $24 at 8% interest compounded annually? Would the amount he earned be equal to the amount Manhattan and all its real estate is worth today? As of the year 2000, that original $24 would have been worth $76 trillion, more than the estimated value of Manhattan real estate for that same year.
Start investing now, even if its only $25 a month. Get in the habit. Do a bit of research and find a dependable fund, or contribute to your companys 401K plan. For the price of a few meals, you can pave the way to prosperity. It doesnt take a genius to become a millionaire, it just takes starting early.