IndexAaccrued interest, 187, 198–200, 202, 206,208, 210accumulation function, 2–4, 8, 11, 14–17,21–22, 24, 27, 30, 36, 49, 56, 64, 73,84–87, 98, 101, 215, 220, 240, 292affine models, 317amortization, 147–148, 152–157,159–161, 170, 173–174, 176–178, 184,187–188, 193–197, 203, 206–211, 238amount function, 2–3, 27, 33amount of interest, 2, 6–7, 9, 28, 30, 34,65, 67, 90–91, 141, 143, 159, 180,184–185, 195annual percentage rate (APR), 148, 169,171–172annuity, 39, 40-49, 51–61, 63–67, 69, 73,80–85, 88, 99–101, 148–159, 161, 166,169, 191, 257, 282–283, 292, 315, 320decreasing, 58, 283deferred, 40, 45–46, 54, 56–57, 64,66, 84, 88due, 40, 44–45, 51, 55, 57–58, 63–66,82–84, 169immediate, 53in arrears, 40increasing, 57–58, 60, 158level, 58, 60, 257, 280, 282ordinary, 40perpetuity, 45–46, 65–66, 69term of, 60varying, 40, 56–57autoregressive model, 305, 314, 320Bbond, 39, 56, 116–119, 122–123, 136,139, 145, 187–231, 233–267, 269–273,275, 281–290, 292, 294–295, 297–298,320–321callable, 187–189, 202–204, 206,210–211, 213, 216–217, 223,238–239, 241, 273, 281, 285–287coupon-paying, 188–189, 191inflation-indexed, 187, 294investment-grade, 189, 209, 237, 287junk, 145, 189, 207zero-coupon, 187, 189, 193,207–208, 228, 230–231, 233–234,239, 240, 242–244, 256, 259, 263,265, 267, 270–272, 286–289, 320bond amortization schedule, 187–188,193, 195–197, 203, 206–211, 238bond discount, 194–196bond premium, 194–195effective interest method, 194straight-line method, 194, 211bond management, 213, 221, 236, 245,247, 249, 251, 253, 255, 257, 277–278active, 221, 236, 277–278passive, 245, 277bond price, 191, 193, 197, 199, 201, 207,212, 215, 225, 229, 233, 236–237, 245,250, 252–255, 260–262, 273, 278, 287clean price, 198, 214, 218–219dirty price, 198, 209–210, 214, 216,238349
350 Indexpurchase price, 187, 190, 192, 195quoted price, 187, 198–201, 206,208, 214, 219bond yield, 212, 214, 251, 298current yield, 214, 222, 236holding-period yield, 222, 224, 234,279nominal yield, 214, 236yield to maturity, 213, 216, 218,236–239, 241, 248, 252bootstrap method, 213–214, 225–226,237, 242–243, 297borrowing rate, 75, 111, 130, 142Ccallable bond, 187–189, 202–204, 206,211, 213, 217, 223, 239, 241, 273, 281call premium, 202call price, 189, 202–204, 217call protection period, 202call protection, 189, 202call risk, 189, 202, 206first call date, 202–203, 206capital budgeting, 106, 127, 130, 132cash-flow matching, 245, 259, 263, 269,272, 278certificate of deposit (CD), 207commercial paper, 297–299compounding period, 5, 7–8, 28, 36, 40,51continuous compounding, 8, 10, 99, 213,228, 237coupon, 39, 56, 112, 119, 136, 187–223,225–234, 236–249, 251–253, 256–265,267, 270–272, 276, 278, 280–281,283–289, 294, 320coupon rate, 56, 188–194, 196–197,201–203, 205–206, 208–210, 212,214–216, 218, 220, 225–227, 236–238,240, 242–245, 249, 251, 253–259, 262,276, 278, 280–281, 283–285, 287–288conversion period, 5, 7, 31, 33, 51–55, 64,66, 108convexity, 245–246, 252, 254–256,265–267, 273, 278–280, 282–286, 289Ddedication strategy, 245, 263, 278, 287derivatives, 252, 296, 317dirty price, 198, 209–210, 214, 216, 238discount, 1–2, 12–15, 20–21, 24, 27–31,33, 37, 41, 48, 67–68, 88, 109, 111,118, 120, 127, 129–133, 148, 165–166,187, 189–191, 194–198, 203, 206,210–212, 214–215, 227–228, 249, 258,273, 286–287, 296–300, 302discount factor, 20–21, 24, 27, 41,227–228, 249, 287rate of discount, 1–2, 12-13, 31, 68discount window, 296–300, 302duration, 111, 131–132, 245–267,271–276, 278–279, 250–272, 274–287effective (option-adjusted/stochastic),246, 273, 279Fisher–Weil, 245–246, 275–276, 279,288–289Macaulay, 245–254, 256–265, 267,272, 275, 278–287, 289modified, 245–246, 250–255, 257,272, 275, 278–280, 282–284, 286rules for duration, 246, 256duration matching, 246, 263–266,271–273, 275, 279, 288–289dynamic term structure model, 305–306,316, 320EEuro Interbank Offered Rate (Euribor),300effective capital, 113, 135effective principal, 12–14, 27equation of value, 24-28, 32, 60–62, 64,107–108, 226–227, 230–231, 295equivalent nominal rate (ENR), 164–169,182Excel functions, 63, 251DURATION, 251, 280IRR, 106–112, 118–120, 127–130,133, 142–144MDURATION, 251PRICE, 200–201
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Financial Mathematics forActuaries
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Financial Mathematics forActuaries
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To Bonnie, Nikki and Kevinfor their
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About the AuthorsWai-Sum Chan, PhD,
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Preface to the Second EditionA good
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ContentsAbout the AuthorsPreface to
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ContentsxiiiChapter 7 Bond Yields a
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List of Mathematical SymbolsSymbola
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List of Mathematical SymbolsxviiSym
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1InterestAccumulation andTime Value
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Table 1.3:Summary of accumulated va
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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Interest Accumulation and Time Valu
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2AnnuitiesAn annuity is a series of
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Annuities 41Figure 2.1 illustrates
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Annuities 43Solution: The rate of i
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Annuities 45As an annuity-due of n
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Annuities 47Figure 2.3: Illustratio
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Annuities 49Also, it can be checked
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Annuities 512.5 Payment Periods, Co
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Annuities 53Note that (2.20) has a
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Annuities 55Example 2.11: Solve the
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Annuities 57Figure 2.8:Increasing a
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Annuities 59Second, we may consider
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Annuities 61n is an integer and 0 <
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Annuities 63Exhibit 2.1: Use of Exc
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Annuities 652.2 Let d (2) =2%. Eval
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Annuities 672.23 Express s(52) n⌉
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Annuities 692.37 A paused rainbow i
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Annuities 71(c) Find the amount of
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3SpotRates, Forward Ratesand the Te
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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Spot Rates, Forward Rates and the T
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4Rates of ReturnThe performance of
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Rates of Return 107Example 4.1: A p
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Rates of Return 109where y 4 is the
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Rates of Return 111Exhibit 4.3:Solu
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Rates of Return 113Figure 4.1: Cash
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Rates of Return 115Hence, from (4.5
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Rates of Return 117Calculate the ar
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Rates of Return 119denote it as R D
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Rates of Return 1214.4 Portfolio Re
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Rates of Return 123Solution: For (a
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Rates of Return 125To calculate the
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Rates of Return 127Finally, for (d)
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Rates of Return 129Figure 4.4: NPV
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Rates of Return 131When the project
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Rates of Return 133measure of the r
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Rates of Return 1354.7 Which of the
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Rates of Return 1374.19 A 7-year pr
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Rates of Return 139(a) Calculate th
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Rates of Return 141Assume all inves
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Rates of Return 143(a) Draw a graph
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Rates of Return 1454.50 Judy is con
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5Loans andCosts of BorrowingLoans a
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Loans and Costs of Borrowing 149can
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Loans and Costs of Borrowing 151Due
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Loans and Costs of Borrowing 153Tab
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Loans and Costs of Borrowing 155Exa
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Loans and Costs of Borrowing 157We
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Loans and Costs of Borrowing 159Exa
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Loans and Costs of Borrowing 161For
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Loans and Costs of Borrowing 1635.5
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Loans and Costs of Borrowing 165the
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Loans and Costs of Borrowing 167its
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Loans and Costs of Borrowing 169Not
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Table 5.5:Summary of reference rate
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Loans and Costs of Borrowing 1735.5
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Loans and Costs of Borrowing 175rem
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Loans and Costs of Borrowing 177Yea
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Loans and Costs of Borrowing 1795.3
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Loans and Costs of Borrowing 1815.4
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Loans and Costs of Borrowing 1835.6
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Loans and Costs of Borrowing 185let
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6Bondsand Bond PricingA bond is a c
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Bonds and Bond Pricing 189hand, bon
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Bonds and Bond Pricing 191Figure 6.
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Bonds and Bond Pricing 193Example 6
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Bonds and Bond Pricing 195Table 6.1
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Bonds and Bond Pricing 197Note that
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Bonds and Bond Pricing 199Figure 6.
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Bonds and Bond Pricing 201The Excel
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Bonds and Bond Pricing 203Assuming
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Bonds and Bond Pricing 205cash flow
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Bonds and Bond Pricing 2076. When t
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Bonds and Bond Pricing 209Half- Cou
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Bonds and Bond Pricing 2116.23 Show
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7Bond Yields andthe Term StructureW
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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Bond Yields and the Term Structure
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8Bond ManagementThe rate of interes
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Bond Management 247Using PV(C t ) a
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Bond Management 249again is less th
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Bond Management 251To use the modif
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Bond Management 253Example 8.5: A 1
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Bond Management 255Figure 8.2:Bond-
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Bond Management 257Rule 3: Other th
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Bond Management 259the duration D P
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Bond Management 261Example 8.8: A c
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Bond Management 263Figure 8.4:Illus
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Bond Management 265Example 8.10: A
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Bond Management 267of the asset and
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Bond Management 269Figure 8.5:Illus
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Bond Management 271Solving the abov
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Bond Management 273First, in classi
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Bond Management 275wherePV(C t )=C
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Bond Management 277Example 8.14: Co
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Bond Management 2795. Immunization
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Bond Management 281Time toCoupon ra
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Bond Management 2838.15 Using Exerc
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Bond Management 2858.22 Revisit Exe
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Bond Management 2878.29 Suppose you
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Bond Management 289(c) Calculate th
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9Interest Rates andFinancial Securi
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Interest Rates and Financial Securi
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Interest Rates and Financial Securi
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Interest Rates and Financial Securi
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- Page 348 and 349: APPENDIXAReview of Mathematics and
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