5.1 We need to calculate the future value of S10,000 at 6 percent for five years. The future value factor is: 1.06 1.3382 The future value is thus $10,000x 1.3382 We need the present value of $150,000 to be paid in 11 years at 9 percent. The discount factor is: $13,382.26. 5.2 1/1.091 1/2.5804 3875 The present value is thus about S58,130. Suppose you invest $1,000. You will have $2,000 in 10 years with this investment. So, $1,000 is the amount you have today, or the present value, and $2,000 is the amount you will have in 10 years, or the future value. From the basic present value equation, we have 5.3 $2,000$1,000 x (1)10 2(1 r) From here, we need to solve for r, the unknown rate. As shown in the chapter, there are several different ways to do this. We will take the 10th root of 2 (by raising 2 to the power of 1/10): 21/101+r 1.07181+r r ,0718, or 7.18% Using the Rule of 72, we have 72t = ,%, or 72/10= .072, or 7.2%; so, our answer looks good (remember that the Rule of 72 is only an approximation). 5.4The basic equation is this $30,000$15,000 x (1 .09) 2 (1+.09)' = If we solve for t, we find that-8.04 years. Using the Rule of 72, we get 72/9 8 years, so once again our answer looks good. To get $45,000, verify for yourself that you will have to wait 12.75 years