Answers to Supplementary Exercises

Chapter 1

  1. \(\quad 9\)

  2. \(\quad 3\,000\)

  3. \(\quad 1\,191\)

  4. \(\quad 320\)

  5. \(\quad 3.\overline{33}\)

  6. \(\quad 583\)

  7. \(\quad\) (a) \(35.294\%\), (b) \(35\,035\,000\)

  8. \(\quad\) (a) \(314.25\), (b) \(2\,713.27\)

  9. \(\quad 16\)

  10. \(\quad 3\,456\)

  11. \(\quad 950\)

  12. \(\quad 8\,756\)

  13. \(\quad 1\,978\)

  14. \(\quad 13.187\%\)

  15. \(\quad 47\,619\)

  16. \(\quad 1\,052\)

  17. \(\quad 1\,147\)

  18. \(\quad 8\)

  19. \(\quad 20\)

  20. \(\quad 0.95238\)

  21. \(\quad 1\,568\)

  22. \(\quad 0.01005\)

  23. \(\quad 3\,170\)

  24. \(\quad 832\)

  25. \(\quad 0.11036\)

  26. \(\quad 5.83\)

  27. \(\quad 6.9\) years

  28. \(\quad 6.378\%\) by linear interpolation between \(0.03\) y \(0.05\).

  29. \(\quad 2\,800\)

  30. \(\quad 7.607\%\)

  31. \(\quad 17\,936\)

  32. \(\quad 700\)

  33. \(\quad 81\)

  34. \(\quad 3\,932\)

  35. \(\quad 4\,226\)

  36. \(\quad 12.91\%\)

Chapter 2

  1. \(\quad 652\)

  2. \(\quad 8.298\%\)

  3. \(\quad 2\,390\)

  4. \(\quad 9\,173\)

  5. \(\quad 5\,695\)

  6. \(\quad 3\,276\)

  7. \(\quad 146.07\)

  8. \(\quad 32.41\)

  9. \(\quad 9\)

  10. \(\quad 29\)

  11. \(\quad 50\)

  12. \(\quad 1\,220\)

  13. \(\quad 35\,824\)

  14. \(\quad 6\%\)

  15. \(\quad 4\,040\)

  16. \(\quad 20\%\)

  17. \(\quad 27.46\)

  18. \(\quad 4.76\%\)

  19. \(\quad 16\,607\)

  20. \(\quad 7\,851\)

  21. \(\quad 48\,000\)

  22. \(\quad 3\,343\)

  23. \(\quad 61\,947\)

  24. \(\quad 1\,410\)

  25. \(\quad 2\,085\)

  26. \(\quad 139\)

  27. \(\quad 0.1225\)

  28. \(\quad 201\)

  29. \(\quad 122\,634\)

  30. \(\quad 18\,371\)

  31. \(\quad 2\,431\)

  32. \(\quad 77\,979\)

  33. \(\quad 5\,522\)

  34. \(\quad 142.72\)

  35. \(\quad 4\,000\)

  36. \(\quad 22\,831\)

  37. \(\quad 39\,729\)

  38. \(\quad 84.50\)

  39. \(\quad 42\,000\)

  40. \(\quad 4\,069.22\)

  41. \(\quad 6\,523\)

Chapter 3

  1. \(\quad 635\)

  2. \(\quad 4\,198\)

  3. \(\quad 16\,514\)

  4. \(\quad 642\)

  5. \(\quad 13\)

  6. \(\quad 72\)

  7. \(\quad 676\)

  8. \(\quad 76\,105\)

  9. \(\quad 14\,709\)

  10. \(\quad 846\)

  11. \(\quad 796\)

  12. \(\quad 1\,557\)

  13. \(\quad 1\,132\)

  14. \(\quad 10\,814\)

  15. \(\quad 171\,429\)

  16. \(\quad 3\,413\)

  17. \(\quad 36\,454\)

  18. \(\quad 2\,221\)

  19. \(\quad 1\,029\)

  20. \(\quad 934\)

  21. \(\quad 32\,456\)

  22. \(\quad 482\)

  23. \(\quad 253\) and the loan should not be refinanced

  24. \(\quad 367\)

  25. \(\quad 2\,400\)

  26. \(\quad 15\,649.67\)

  27. \(\quad 23\,554.38\)

  28. \(\quad 7\,246\)

  29. \(\quad 704.96\)

  30. \(\quad 168\,653\)

  31. \(\quad 5\,900\)

  32. \(\quad 229.87\)

  33. \(\quad 7\%\)

  34. \(\quad 6\,183.69\)

  35. \(\quad 36\,920.75\)

  36. \(\quad 4.19\)

  37. \(\quad 13\)

  38. \(\quad 30\,975.11\)

  39. \(\quad 7\,964.25\)

  40. \(\quad 8\,263.99\)

  41. \(\quad 442.36\)

Chapter 4

  1. \(\quad 894\)

  2. \(\quad 1\,019\)

  3. \(\quad 1\,159\)

  4. \(\quad 1.43\)

  5. \(\quad 0.04322317\)

  6. \(\quad 945\)

  7. \(\quad 1\,200\)

  8. \(\quad 1\,100\)

  9. \(\quad 1\,495\)

  10. \(\quad 1\,360\)

  11. \(\quad 30.65\)

  12. \(\quad 9.07\)

  13. \(\quad 58.66\)

  14. \(\quad 1\,000\)

  15. \(\quad 1\,045\)

  16. \(\quad 3.6\%\)

  17. \(\quad 7.48\)

  18. \(\quad 8.322\%\)

  19. \(\quad 171\)

  20. \(\quad 1\,605\)

  21. \(\quad 1\,487\)

  22. \(\quad 40\)

  23. \(\quad 15.709\%\)

  24. \(\quad 25.32\)

  25. \(\quad\) (a) \(66.70\), (b) \(14\,067\)

  26. \(\quad 12.389\%\)

  27. \(\quad 895.35\)

  28. \(\quad 922.05\)

  29. \(\quad 1\,119.25\)

  30. \(\quad 846.28\)

  31. \(\quad 58.65\)

  32. \(\quad 1\,086\)

  33. \(\quad 1\,024.88\)

  34. \(\quad 18\) years

  35. \(\quad 14\,269.84\)

  36. \(\quad 635\) basis points

  37. \(\quad 4.90\)

  38. \(\quad 928.64\)

  39. \(\quad 881.53\)

  40. \(\quad 868.11\)

Chapter 5

  1. \(\quad 26\)

  2. \(\quad 6\%\)

  3. \(\quad 5\%\)

  4. \(\quad 10.619\%\)

  5. \(\quad 18.785\%\)

  6. \(\quad 9.778\%\)

  7. \(\quad 9\,430\)

  8. \(\quad 9.545\%\)

  9. \(\quad 10.506\%\)

  10. \(\quad 2\,524.07\)

  11. \(\quad 50\)

  12. \(\quad 7.247\)

  13. \(\quad 4.871\)

  14. \(\quad 13.5\)

  15. \(\quad 27\)

  16. \(\quad 2.706\)

  17. \(\quad 16.77\)

  18. \(\quad 10\)

  19. \(\quad 9.3\)

  20. \(\quad 5.496\)

  21. \(\quad 312.5\)

  22. \(\quad 1\,250\)

  23. \(\quad 0.979\)

  24. \(\quad 92.952\)

  25. \(\quad 0\)

  26. \(\quad -35.6\%\)

  27. \(\quad +20\%\)

  28. \(\quad A=280.5\), \(B=78.2\).

  29. \(\quad 6\,415\)

  30. \(\quad M=32\,805\), \(N=40\,500\).

  31. \(\quad 4\,450\).

  32. \(\quad 47\,826\) in \(4\)-year bonds and \(9\,457\) in the \(10\)-year bonds.

  33. \(\quad 75.36\) and the program does satisfy Redington immunization.

  34. \(\quad 28\,072\)

  35. \(\quad\) (a) \(\text{vp}_{A}=2\,192.48=\text{vp}_{L}\) and \(\text{MacDur}_{A}=3.246=\text{MacDur}_{L}\), thus conditions are met.

  36. \(\quad\) (a) \(\text{ModCon}_{A}=12.17\) and \(\text{MacCon}_{L}=12.16\), thus conditions are met.

  37. \(\quad\) (a) \(10.16\), \(0.595\) and \(2.20\)