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Answers to Selected Exercises 3394.25 (a) −0.508 (b) Weight = 0.2085, expected return = 12.117%4.26 (a) Expected return = 14.4%, standard deviation = 21.72%(b) Expected return = 9.6%, standard deviation = 10.92%4.29 (a) $95.38 (b) −9.1%4.30 (a) $67 (b) $70.64.31 20%4.32 (a) 22% (b) 20% (c) 16%4.33 X = 8.0157%, Y = 5.6054%4.34The investment-year rates are i 20081 =6.7%, i 20072 =6.3% andi 20063 =6.0%The portfolio rate is i 2008 =6.2%4.35 $108.484.36 5.725%4.37 $3.36344.38 5.54%4.39 $153.554.40 −$129.284.41 $28.3896, not acceptable4.46 −$85.8223, profitable4.47 Pay cash4.48 15.48%4.49 (a) 7.863% (b) 7.570%4.50 (a) 32.25% (b) $1,727.824.51 (a) 11.5% (b) $20.20
340 APPENDIX BChapter 55.2 (a) $8,982.59 (b) $8,982.595.3 $2,118.685.4 (a) $2,855.44 (b) $2,855.445.5 (a) 7%, $1,552.175.6 (a) $1,584.72 (b) $2,523.385.7 $3,4895.10 The effective annual rate is 4.04%.5.13 $3,880.965.14 $461.885.15 (a) $8,956.30 (b) $8,956.30,The interest portion in the 7th annual payment is $537.38.5.16 (a) $9,670.26 (b) $878.255.17 $62,004.605.18 $18,852.505.19 (a) $1,170.45 (b) $1,077.205.20 $361.165.21 (a) $254.163 (b) 4.91%5.22 (a) $13,507.98 (b) $13,523.615.26 The first level instalment is $1,250, other results follow5.27 The first level instalment is $1,750, other results follow5.28 The first level instalment is $1,200, other results follow5.30 500i5.31 P = $176.55
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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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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 358 and 359: Answers to Selected Exercises 337Ch
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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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