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APPENDIXBAnswers to Selected ExercisesChapter 11.1 $27,456.151.3 I(5) = 300, A(6) = 2,0401.4 A(3) = 321, i(4) = 4.36%1.5 (a) $1,315.79 (b) $1,240.00 (c) $1,262.48(d) $1,268.99 (e) $1,272.01 (f) $1,271.251.6 (a) i(2) = 32.34%, i(3) = 26.85% (b) I(3) = $519.761.7 (b) $9.5971.8 Only (c)1.9 (a) 10.488% (b) 9.729% (c) 10.098% (d) 9.973% (e) (1.104876) t1.10 7.39%1.12 $1,740.20, $240.201.13 (a) $25 (b) $312.61.14 18 years, 17.67 years1.15 (a) $434.83 (b) $434.06 (c) $455.84 (d) $443.731.16 8%1.17 Lender A1.18 15%
334 APPENDIX B1.19 Present value = 2,366.28, future value = 2,612.561.20 (b) $2,9021.21 (a) 0.05, 0.04762, 0.04545 (b) Simple interest at 5%1.22 (a) $441.18 (b) $438.711.23 $3,999.301.24 (b) i =18.73% or 1.07%1.25 15.1029 years1.26 15.0984 years1.27 All but the upper right-hand figure1.28 2.422%1.29 4%1.30 (a) $8,500 (b) $4,545.051.31 41.32 1.2144%1.33 (b) Simple rate of discount of 1% per year for 100 years1.34 0.30771.35 Only (a)1.36 0.0641.37 (a) 4.3000 (b) 4.3076 (c) 4.32831.38 (a) 1.8682 (b) 0.1251.39 131.451.40 Option (b)1.42 t =8.871.43 (a) δ =ln(1+i) (b) δ = − ln(1 − d)
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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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Page 348 and 349: APPENDIXAReview of Mathematics and
Page 350 and 351: Review of Mathematics and Statistic
Page 352 and 353: Review of Mathematics and Statistic
Page 356 and 357: Answers to Selected Exercises 335Ch
Page 358 and 359: Answers to Selected Exercises 337Ch
Page 360 and 361: Answers to Selected Exercises 3394.
Page 368 and 369: Answers to Selected Exercises 34710
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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