The Investment Advisor Body of Knowledge + Test Bank. IMCA

      After five years, the balance is

      After 10 years, the balance is

You can see the accumulation of interest from interest on the principal and interest on interest over time in Figure 4.2.

FIGURE 4.2 The Accumulation of Interest and Interest on Interest of a $1,000 Deposit with 6 Percent Compound Annual Interest

      If you invest $1,000 today and receive $1,790.85 at the end of 10 years, we say that you have a return of 6 percent on your investment. This return is an average annual return, considering compounding.

      Try It! 4.1: Savings

      Suppose you deposit $1,000 in an account that earns 5 percent interest per year. If you do not make any withdrawals, how much will you have in the account at the end of 20 years?

      What if interest was not compounded interest, but rather simple interest? Then we would have a somewhat lower balance in the account after the first year. At the end of one year, with simple interest, you will have:

      After two years:

      Financial Math in Action

      Analysts often come up with estimates of growth in revenues and earnings for publicly traded companies. We can use these estimates to make projections.

      Consider the Walt Disney Company. At the end of fiscal year 2008, analysts expected Disney's earnings to grow at a rate of 12.19 percent per year, in the long-term.* If Disney's earnings for fiscal year 2008 were $2.2788 per share and if we concur with the analysts, we can estimate the earnings per share for fiscal years into the future. For example, the estimate for the earnings per share for 2009 is

      The estimate for 2010's earnings are

      The estimate for 2011's earnings are

      *Estimates from Reuters.com/finance, accessed December 25, 2008.

      After five years:

      And after 10 years:

      You can see the difference between compounded and simple interest in Figure 4.3, in which we show the growth of $1,000 at 6 percent using both types of interest.