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# Ch01 part 3 finance

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### 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
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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
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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
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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
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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
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94. 94. Investment ProjectsBCOR 110, A-2011 94
95. 95. BCOR 110, A-2011 95
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97. 97. Method of Net Present ValueBCOR 110, A-2011 97
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102. 102. Method of Internal Rate of RevenueBCOR 110, A-2011 102
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106. 106. Comparison of both methodsBCOR 110, A-2011 106
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111. 111. DepreciationBCOR 110, A-2011 111
112. 112. Linear DepreciationBCOR 110, A-2011 112
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114. 114. Degressive DepreciationBCOR 110, A-2011 114
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