Chapter 4 12. The times lines are: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PV | $4,500 | $4,500 | $4,500 | $4,500 | $4,500 | $4,500 | $4,500 | $4,500 | $4,500 | | | 0 | 1 | 2 | 3 | 4 | 5 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PV | $7,000 | $7,000 | $7,000 | $7,000 | $7,000 | | | | | | PVA = C({1 – [1/(1 + r)]t } / r ) At a 5 percent interest rate: X@5%: PVA = $4,500{[1 – (1/1.05)9 ] / .05 } = Y@5%: PVA = $30,306.34 And at a 22 percent interest rate: X@22%: PVA = $4,500{[1 – (1/1.22)9 ] / .22 } = Y@22%: PVA = $20,045.48

17. For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m)]m – 1 So, for each bank, the EAR is: First National: EAR = [1 + (.1120 / 12)]12 – 1 = First United: EAR = 0.1172, or 11.72%

19. The time line is: | 0 | 1 | | | | … | | | | | ? | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | –$21,500 | $700 | $700 | $700 | $700 | | $700 | $700 | $700 | $700 | $700 |

PVA = C({1 – [1/(1 + r)]t } / r)

Now, we solve for t: 1/1.013t = 1 – [($21,500)(.013) / ($700)] 1.013t = 1/(0.601) = 1.665

23. Although the stock and bond accounts have different interest rates, we can draw one time line, but we need to remember to apply different interest rates. The time line is: