If we take the FVIFs for \$1 in the 8% column and multiply them by \$100, we get figures (aside from some rounding) that correspond to our calculations for \$100 in the final column of Table 3.2. Notice, too, that in rows corresponding to two or more years, the proportional increase in future value becomes greater as the interest rate rises. A picture may help make this point a little clearer. Therefore, in Figure 3.1 we graph the growth in future value for a \$100 initial deposit with interest rates of 5, 10, and 15 percent. As can be seen from the graph, the greater the interest rate, the steeper the growth curve by which future value increases. Also, the greater the number of years during which compound interest can be earned, obviously the greater the future value.

On a number of business professional (certification) exams you will be provided with interest factor tables and be limited to using only basic, non-programmable, hand-held calculators. So, for some of you, it makes added sense to get familiar with interest factor tables now.

Compound Growth. Although our concern so far has been with interest rates, it is important to realize that the concept involved applies to compound growth of any sort - for example, in gas prices, tuition fees, corporate earnings, or dividends. Suppose that a corporation's most recent dividend was \$10 per share but tjhat we expect this dividend to grow at a 10 percent compound annual rate. For the next five years we would expect dividends to look as shown in the table.

 YEAR GROWTH FACTOR EXPECTED DIVIDEND/SHARE 1 (1.10)1 \$11.00 2 (1.10)2 12.10 3 (1.10)3 13.31 4 (1.10)4 14.64 5 (1.10)5 16.11

Similarly, we can determine the future levels of other variables that are subject to compound growth. This principle will prove especially important when we consider certain valuation models for common stock, which we do in the next chapter.

Present (or Discounted) Value. We all realize that a dollar today is worth more than a dollar to be received one, two, or three years from now. Calculating the present value of future cash flows allows us to place all cash flows on a current footing so that comparisons can be made in terms of today's dollars.