Ch01 part 3 finance

288 views

Published on

Published in: Business, Economy & Finance
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
288
On SlideShare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
2
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Ch01 part 3 finance

  1. 1. Sequences, Series, FinanceCHAPTER 1
  2. 2. Chapter 1: Sequences, Series, Finance • Content: – Introduction – Sequences • Basic definitions • Limit of a sequence – Series • Partial sums • Series and convergence of seriesBCOR 110, A-2011 2
  3. 3. Chapter 1: Sequences, Series, Finance • Content-continued – Finance • Simple interest and compound interest • Periodic payments • Loan repayments, redemption tables • Investment projects • DepreciationBCOR 110, A-2011 3
  4. 4. 1. Introduction • Sequences and Series play important roles in business applications • Several finance problems are approached through sequences and series • This chapter will treat some of these topicsBCOR 110, A-2011 4
  5. 5. CH01-PART 3 APPLICATIONS TO FINANCEBCOR 110, A-2011 5
  6. 6. Simple interest and compound interest • Let P denote the principal, i.e. it is the total amount of money borrowed (e.g. by an individual from a bank in the form of a loan) or invested (e.g. by an individual at a bank in the form of a savings account). • Interest can be interpreted as money paid for the use of moneyBCOR 110, A-2011 6
  7. 7. Simple interest and compound interest • The rate of interest is the amount charged for the use of the principal for a given length of time, usually on a yearly (or per annum, abbreviated p.a.) basis, given either as a percentage ( p per cent) or as a decimal i:BCOR 110, A-2011 7
  8. 8. Simple interest • Simple interest is interest computed on the principal for the entire period it is borrowed or invested • It is assumed that this interest is not reinvested with the original capital • If a principal P is invested at a simple interest rate of i per annum, then i is given byBCOR 110, A-2011 8
  9. 9. Simple InterestBCOR 110, A-2011 9
  10. 10. BCOR 110, A-2011 10
  11. 11. Compound Interest Next, we assume that at the end of each year, the interest which is due at this time is added to the principal so that the interest computed for the next year is based on this new amount (of old principal plus interest). This is known as compound interest.BCOR 110, A-2011 11
  12. 12. • Let Ak be the amount accrued on the principal at the end of year k. Then we obtain the followingBCOR 110, A-2011 12
  13. 13. BCOR 110, A-2011 13
  14. 14. BCOR 110, A-2011 14
  15. 15. BCOR 110, A-2011 15
  16. 16. BCOR 110, A-2011 16
  17. 17. ExamplesBCOR 110, A-2011 17
  18. 18. ExamplesBCOR 110, A-2011 18
  19. 19. BCOR 110, A-2011 19
  20. 20. BCOR 110, A-2011 20
  21. 21. ExamplesBCOR 110, A-2011 21
  22. 22. BCOR 110, A-2011 22
  23. 23. Effective Rate of InterestBCOR 110, A-2011 23
  24. 24. BCOR 110, A-2011 24
  25. 25. ExampleBCOR 110, A-2011 25
  26. 26. Combined simple & Compound InterestsBCOR 110, A-2011 26
  27. 27. BCOR 110, A-2011 27
  28. 28. BCOR 110, A-2011 28
  29. 29. Periodic Payments • In the previous subsection, we considered the computation of the future value of one investment when a fixed amount of money is deposited in an account that pays interest compounded periodically. • In many situations, there are periodic payments (i.e. deposits or withdrawals) and the question is which amount is accrued (or left over) after a number of payment periods. • Such situations occur, for example, in connection with annual life insurance premiums, monthly deposits at a bank, loan repaymentsBCOR 110, A-2011 29
  30. 30. Periodic Payments • The notion annuity is used in the following for a sequence of (usually equal) periodic payments. • Here we consider only the case when payment periods and the periods for interest payments coincide. • Moreover, the interest is always credited at the end of a payment period.BCOR 110, A-2011 30
  31. 31. Periodic Payments • First, we consider a so-called ordinary annuity, where the payments (deposits) are made at the same time the interest is credited, namely at the end of the period. • We mark all values by the superscript ‘E’ which stands for ‘end of the period’.BCOR 110, A-2011 31
  32. 32. Annual PaymentsBCOR 110, A-2011 32
  33. 33. Annual PaymentsBCOR 110, A-2011 33
  34. 34. BCOR 110, A-2011 34
  35. 35. BCOR 110, A-2011 35
  36. 36. BCOR 110, A-2011 36
  37. 37. BCOR 110, A-2011 37
  38. 38. BCOR 110, A-2011 38
  39. 39. BCOR 110, A-2011 39
  40. 40. BCOR 110, A-2011 40
  41. 41. BCOR 110, A-2011 41
  42. 42. BCOR 110, A-2011 42
  43. 43. BCOR 110, A-2011 43
  44. 44. BCOR 110, A-2011 44
  45. 45. BCOR 110, A-2011 45
  46. 46. BCOR 110, A-2011 46
  47. 47. BCOR 110, A-2011 47
  48. 48. BCOR 110, A-2011 48
  49. 49. BCOR 110, A-2011 49
  50. 50. BCOR 110, A-2011 50
  51. 51. BCOR 110, A-2011 51
  52. 52. BCOR 110, A-2011 52
  53. 53. BCOR 110, A-2011 53
  54. 54. BCOR 110, A-2011 54
  55. 55. BCOR 110, A-2011 55
  56. 56. BCOR 110, A-2011 56
  57. 57. BCOR 110, A-2011 57
  58. 58. BCOR 110, A-2011 58
  59. 59. BCOR 110, A-2011 59
  60. 60. BCOR 110, A-2011 60
  61. 61. BCOR 110, A-2011 61
  62. 62. BCOR 110, A-2011 62
  63. 63. BCOR 110, A-2011 63
  64. 64. BCOR 110, A-2011 64
  65. 65. Loan Repayments, Redemption Tables • One application of periodic payments is loan repayments. • First, we again consider annual payments and later we briefly discuss the modifications in the case of several payments per year.BCOR 110, A-2011 65
  66. 66. Notations for year kBCOR 110, A-2011 66
  67. 67. Definition • A loan is said to be amortized if both Principal (i.e., the amount of the loan) and Interest are paid by a sequence of payments made over equal time periodsBCOR 110, A-2011 67
  68. 68. BCOR 110, A-2011 68
  69. 69. BCOR 110, A-2011 69
  70. 70. BCOR 110, A-2011 70
  71. 71. BCOR 110, A-2011 71
  72. 72. BCOR 110, A-2011 72
  73. 73. BCOR 110, A-2011 73
  74. 74. BCOR 110, A-2011 74
  75. 75. BCOR 110, A-2011 75
  76. 76. BCOR 110, A-2011 76
  77. 77. BCOR 110, A-2011 77
  78. 78. BCOR 110, A-2011 78
  79. 79. BCOR 110, A-2011 79
  80. 80. BCOR 110, A-2011 80
  81. 81. BCOR 110, A-2011 81
  82. 82. BCOR 110, A-2011 82
  83. 83. BCOR 110, A-2011 83
  84. 84. BCOR 110, A-2011 84
  85. 85. BCOR 110, A-2011 85
  86. 86. BCOR 110, A-2011 86
  87. 87. BCOR 110, A-2011 87
  88. 88. BCOR 110, A-2011 88
  89. 89. BCOR 110, A-2011 89
  90. 90. BCOR 110, A-2011 90
  91. 91. BCOR 110, A-2011 91
  92. 92. BCOR 110, A-2011 92
  93. 93. BCOR 110, A-2011 93
  94. 94. Investment ProjectsBCOR 110, A-2011 94
  95. 95. BCOR 110, A-2011 95
  96. 96. BCOR 110, A-2011 96
  97. 97. Method of Net Present ValueBCOR 110, A-2011 97
  98. 98. BCOR 110, A-2011 98
  99. 99. BCOR 110, A-2011 99
  100. 100. BCOR 110, A-2011 100
  101. 101. BCOR 110, A-2011 101
  102. 102. Method of Internal Rate of RevenueBCOR 110, A-2011 102
  103. 103. BCOR 110, A-2011 103
  104. 104. BCOR 110, A-2011 104
  105. 105. BCOR 110, A-2011 105
  106. 106. Comparison of both methodsBCOR 110, A-2011 106
  107. 107. BCOR 110, A-2011 107
  108. 108. BCOR 110, A-2011 108
  109. 109. BCOR 110, A-2011 109
  110. 110. BCOR 110, A-2011 110
  111. 111. DepreciationBCOR 110, A-2011 111
  112. 112. Linear DepreciationBCOR 110, A-2011 112
  113. 113. BCOR 110, A-2011 113
  114. 114. Degressive DepreciationBCOR 110, A-2011 114
  115. 115. BCOR 110, A-2011 115
  116. 116. BCOR 110, A-2011 116
  117. 117. BCOR 110, A-2011 117
  118. 118. BCOR 110, A-2011 118
  119. 119. BCOR 110, A-2011 119
  120. 120. BCOR 110, A-2011 120

×