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Answers to Selected Exercises 3458.18 (a) P = $26,638.05, D =6.9216 years, C =52.5392(b) $9,495, $15,8578.19 Bond X8.21 Bond X: $2,004.682, Bond Y : $2,141.7478.22 (a) 48.3472% (b) Liability: 9 years, Assets: 9.167 years8.23 Bond M8.24 (a) Liability: D =19.3642, C = 497.9611Bond A: D =17.6013, C = 371.0864Bond B: D =26.4562, C = 879.9213(b) $1,212.11 in Bond A and $301.31 in Bond B8.26 E :$4,218.3680, F :$4,513.6538, G :$4,513.6538, H :$4,739.33658.27 (b) D ∗ =(i − g) −1 , C =2(i − g) −28.28 (a) $66,255.08, 5 years (b) Yes8.29 (a) −1.92%, 2.45%, 5.15% for n =1, 2 and 5, respectively8.32 Statement (c) only8.35 (a) $921.659 (b) Up: $1,834.88, Down: $1,851.878.37 (a) D F = 2.882 years for Bond A and 4.332 years for Bond B∑Wt = 2.711 years (A) and 4.069 years (B)(b) Actual price changes: –1.873% (A) and –2.796% (B)Predicted price changes: –1.898% (A) and –2.848% (B)(c) D F = 2.881 years (A) and 4.322 years (B)8.38 21.3384, 813.21498.39(a) No (b) 1,617.20 (1-year bond), 0 (3-year bond), 1,388.60(4-year bond)8.40 (a) E(T )=D
346 APPENDIX BChapter 99.1 4.5%9.2 $98.109.3 0.97%9.4 $395.249.5 $183,845.68Chapter 1010.1 7.7%10.2 (a) 5.3633, 5.8666 (b) 5.4875, 0.174610.4 7.5544, 0.256510.5 “Pop-up” scenario10.6 2.6191, 0.057510.7 10.3662, 0.011510.9 (b) 1.0932, 0.00355210.10 1.6289, 0.049110.11 12.5795, 0.440610.12 21.55, 0.2809 for n =13; 36.38, 0.5699 for n =1810.14 (a) 7.7884% (b) 0.7985, 0.687310.15 (a) 1.2214, 0.1243 (b) 0.8869, 0.065510.16 (a) 1.2713, 0.2064 (b) 0.8869, 0.100310.17 (a) 6.2196, 2.1994 (b) 6.4090, 1.475810.18 (a) 7.5546, 3.5302 (b) 7.7459, 5.651410.19 (1.8616, 3.2407)
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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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Table 1.3:Summary of accumulated va
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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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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 175rem
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Loans and Costs of Borrowing 177Yea
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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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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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Page 346 and 347: Stochastic Interest Rates 32510.24
Page 348 and 349: APPENDIXAReview of Mathematics and
Page 350 and 351: Review of Mathematics and Statistic
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Page 354 and 355: APPENDIXBAnswers to Selected Exerci
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Page 370 and 371: IndexAaccrued interest, 187, 198-20
Page 372 and 373: Index 351RATE, 63, 70XIRR, 109-111,
Page 374: Index 353dollar-weighted, 105, 112,
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