## Table

Future Value Interest Factors

Fortunately, there are several easier ways to get future value factors. Most calculators have a key labeled "yx." You can usually just enter 1.1, press this key, enter 5, and press the "= " key to get the answer. This is an easy way to calculate future value factors because it's quick and accurate.

Alternatively, you can use a table that contains future value factors for some common interest rates and time periods. Table 5.2 contains some of these factors. Table A.1 in the appendix at the end of the book contains a much larger set. To use the table, find the column that corresponds to 10 percent. Then, look down the rows until you come to five periods. You should find the factor that we calculated, 1.6105.

Tables such as 5.2 are not as common as they once were because they predate inexpensive calculators and are only available for a relatively small number of rates. Interest rates are often quoted to three or four decimal places, so the tables needed to deal

Ross et al.: Fundamentals I III. Valuation of Future I 5. Introduction to I I © The McGraw-Hill of Corporate Finance, Sixth Cash Flows Valuation: The Time Value Companies, 2002

Edition, Alternate Edition of Money

134 PART THREE Valuation of Future Cash Flows with these accurately would be quite large. As a result, the real world has moved away from using them. We will emphasize the use of a calculator in this chapter.

These tables still serve a useful purpose. To make sure you are doing the calculations correctly, pick a factor from the table and then calculate it yourself to see that you get the same answer. There are plenty of numbers to choose from.

### Compound Interest

You've located an investment that pays 12 percent. That rate sounds good to you, so you invest $400. How much will you have in three years? How much will you have in seven years? At the end of seven years, how much interest will you have earned? How much of that interest results from compounding?

Based on our discussion, we can calculate the future value factor for 12 percent and three years as:

Your $400 thus grows to:

After seven years, you will have:

Thus, you will more than double your money over seven years.

Because you invested $400, the interest in the $884.27 future value is $884.27 - 400 = $484.27. At 12 percent, your $400 investment earns $400 X .12 = $48 in simple interest every year. Over seven years, the simple interest thus totals 7 X $48 = $336. The other $484.27 - 336 = $148.27 is from compounding.

The effect of compounding is not great over short time periods, but it really starts to add up as the horizon grows. To take an extreme case, suppose one of your more frugal ancestors had invested $5 for you at a 6 percent interest rate 200 years ago. How much would you have today? The future value factor is a substantial 1.06200 = 115,125.90 (you won't find this one in a table), so you would have $5 X 115,125.91 = $575,629.52 today. Notice that the simple interest is just $5 X .06 = $.30 per year. After 200 years, this amounts to $60. The rest is from reinvesting. Such is the power of compound interest!

How Much for That Island?

To further illustrate the effect of compounding for long horizons, consider the case of Peter Minuit and the American Indians. In 1626, Minuit bought all of Manhattan Island for about $24 in goods and trinkets. This sounds cheap, but the Indians may have gotten the better end of the deal. To see why, suppose the Indians had sold the goods and invested the $24 at 10 percent. How much would it be worth today?

Roughly 375 years have passed since the transaction. At 10 percent, $24 will grow by quite a bit over that time. How much? The future value factor is approximately:

That is, 3 followed by 15 zeroes. The future value is thus on the order of $24 X 3 quadrillion or about $72 quadrillion (give or take a few hundreds of trillions).

Well, $72 quadrillion is a lot of money. How much? If you had it, you could buy the United States. All of it. Cash. With money left over to buy Canada, Mexico, and the rest of the world, for that matter.

This example is something of an exaggeration, of course. In 1626, it would not have been easy to locate an investment that would pay 10 percent every year without fail for the next 375 years.

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