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Money plus time equals interest

By ALAN MUSANTE

© St. Petersburg Times, published January 4, 2001


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[Times art: Teresanne Cossetta]
If I offered to give you $100 either now or five years from today, which would you prefer? Either would be nice, of course, but from the the economic perspective you should choose to take the money now. To explain why this is so, we must learn about the time value of money and a related concept: the Rule of 72.

The key to understanding why $100 now is preferable to $100 in five years is the idea that money can be invested (in lots of places, such as banks, stocks and bonds) to earn interest. Interest can be thought of as the rental fee for money, the payment made when money is used by someone else.

When you borrow, you pay interest to the lender. When you save and invest, or when you lend, your bank, for example, pays you interest for the use of your money. Interest is usually expressed as a yearly percentage. For example, 6 percent interest on $100 means $106 at the end of the year.

The time value of money refers to this idea that the earning of interest means that a dollar invested today will be worth more than a dollar in the future. If you choose to take the $100 now, you can turn it into more than $100 in five years. If you decide to wait five years for the $100, you would lose out on the interest that $100 could have earned for those five years.

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Click for larger chart

Just how much could that $100 invested today turn into in five years? We call that the future value of money. It depends upon the interest earned. You might be surprised to learn that the total at 6 percent yearly will be greater than $130. (You would come up with $130 if you multiplied the $6 profit we earlier determined for the first year by the five years and added it to the original $100.)

This is due to compounding, another important idea. This means that your previous interest earns interest, along with your original sum, which we call the principal. Thus, during the second year, you're earning interest on $106, not just on $100. This gives you $112.36 after the second year, and then you earn 6 percent on the $112.36 after the third year, and so on it goes. Your total for five years will be $133.82.

The $133.82 future value of $100 in five years at 6 percent interest may not seem like you are getting rich quick -- and you aren't. But what about bigger amounts of money and longer periods of time? You can turn every $1,000 invested at 6 percent yearly into $4,000, or quadruple your money, in 24 years. How did I know?

Money Stuff: Get it! Spend it! Keep It!

Introduction and previous chapters

That is where the Rule of 72 mentioned earlier comes in. If you know the yearly interest rate, dividing that percentage into 72 will give you the approximate number of years it takes an amount to double. So, because 72 divided by 6 is 12, it takes 12 years for your money to double at 6 percent. After twelve years, your $1,000 has turned into $2,000. Then your $2,000 doubles into $4,000 in the next twelve years.

The Rule of 72 is a short-cut for the multiplying and adding process we did earlier. It helps us see that the future value of our invested money is much bigger when we earn a little extra yearly interest. For example, the Rule of 72 tells us that $1,000 doubles every 9 years at 8 percent interest (72 divided by 8 equals 9), and it doubles every eight years at 9 percent interest (72 divided by 9 equals 8).

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The Rule of 72 also can help us understand inflation.

At 4 percent yearly inflation, prices on average rise 4 percent yearly. We barely notice. But the Rule of 72 helps us see that this means that average prices double in 18 years (72 divided by 4 equals 18). When older people talk about low prices in the "good old days" of the past, they are not kidding! Of course, incomes tended to be lower in the past, too.

What does all this have to do with your life? There will be lots of things you want to save for in the future. You'll be wanting to afford a car, college, a house and the expenses of the children you may have someday, for example. The money you save when you are young has a future value of many more dollars than you originally saved, which can be a big help in making your dreams become realities.

You have probably been told since you were very young that saving is a good thing. Knowing about money's time value and the Rule of 72 can help you see just how good it can be. As we saw with our examples, earning a higher yearly interest rate makes a big difference. The other big factor is the number of years you leave your invested money to grow, so it can double again and again. The younger you are, the more it is true that time is on your side. Now, go save some money and invest it for your own future.

Think about it

-- What do we mean by the time value of money?

-- Why is getting $100 now better than getting $100 in the future?

-- What is the future value of $100 in three years at 10 percent yearly?

-- What is compounding?

-- What does the Rule of 72 help us to figure out?

-- Use the Rule of 72 to determine how many years it will take $1,000 to become $2,000 at 3 percent, 4 percent, 6 percent and 12 percent yearly.

-- Explain how knowing about the time value of money and the Rule of 72 can help you make important decisions in your life.

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Alan Musante was named the Florida Economic Educator of the Year by the Florida Council on Economic Education in 1999. He also has won many national and state awards in economic education. Musante, a former attorney, has taught at Oviedo High School for nearly 20 years.

About the Florida Council on Economic Education

Money Stuff was developed by the Florida Council on Economic Education and project director Fonda Anderson. The council is a statewide non-profit organization founded in 1975 to educate K-12 teachers and students about the free enterprise system and to instill in them an appreciation for a market economy. For more information on the council's programs for teachers and students, please call (813) 289-8489.

About Newspaper in Education

The St. Petersburg Times devotes news space to NIE features throughout the year, including this classroom series. The Times' NIE department works with local businesses and individuals to enrich the classroom experience by providing newspapers, supplemental guides and educational services to schools in the Tampa Bay area. To find out how you can become involved in NIE, please call (727) 893-8969 or (800) 333-7505, ext. 8969. For past chapters check out http://www.sptimes.com/nie and click on Money Stuff.

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