## Example 38 Back to Kangaroo Autos

Let us return to Kangaroo Autos for (almost) the last time. Most installment plans call for level streams of payments. So let us suppose that this time Kangaroo offers an "easy payment" scheme of \$4,000 a year at the end of each of the next 3 years. First let's do the calculations the slow way, to show that if the interest rate is 10%, the present value of the three payments is \$9,947.41. The time line in Figure 3.9 shows these calculations. The present value of each cash flow is calculated and then the three present values are summed. The annuity formula, however, is much quicker:

You can use a calculator to work out annuity factors or you can use a set of annuity tables. Table 3.4 is an abridged annuity table (an extended version is shown in Table A.3 at the end of the book). Check that you can find the 3-year annuity factor for an interest rate of 10 percent.

chapter 3 The Time Value of Money 77

figure 3.9

Time line for Kangaroo Autos

Present value

4,000 1.10

Total

,947.41

Year

► self-test 3.7 If the interest rate is 8 percent, what is the 4-year discount factor? What is the 4-year annuity factor? What is the relationship between these two numbers? Explain.