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List of Mathematical SymbolsxviiSymbol(Ia) n⌉(Iä) n⌉(Iā) n⌉(Īā) n⌉(Is) n⌉(I¨s) n⌉(I¯s) n⌉(Ī¯s) n⌉r (m)¯rr Ir Nr RR AR BR DR GR LR PR SR Ts n⌉s n⌉ iq|s n⌉ is (m)n⌉s (m)n⌉iMeaningpresent value of an increasing annuity-immediatepresent value of an increasing annuity-duepresent value of an increasing continuous annuitypresent value of a continuously increasing continuous annuityfuture value of an increasing annuity-immediatefuture value of an increasing annuity-duefuture value of an increasing continuous annuityfuture value of a continuously increasing continuous annuitynominal rate of interest payable m times a yearcontinuously compounded rate of interestrate of inflationnominal rate of interestreal rate of interestarithmetic mean rate of returninterest rate for borrowingone-period DWRR (dollar-weighted rate of return)geometric mean rate of returninterest rate for lendingrate of return for a portfolioswap rate of an interest rate swapone-period TWRR (time-weighted rate of return)same as s n⌉when the rate of interest is understoodifuture value of an annuity-immediatefuture value of a q-period deferred annuity-immediatesame as s (m) when the rate of interest is understoodn⌉ifuture value of an mn-payment annuity-immediate withm payments per interest-conversion period
xviiiList of Mathematical SymbolsSymbolq|s (m)n⌉i¨s n⌉¨s n⌉ iq|¨s n⌉ i¨s (m)n⌉¨s (m)n⌉iq|¨s (m)n⌉i¯s n⌉q|¯s n⌉vv(t)Meaningfuture value of an q-period deferred, mn-paymentannuity-immediate with m payments per interest-conversion periodsame as ¨s n⌉when the rate of interest is understoodifuture value of an annuity-duefuture value of a q-period deferred annuity-duesame as ¨s (m) when the rate of interest is understoodn⌉ifuture value of an mn-payment annuity-due withm payments per interest-conversion periodfuture value of a q-period deferred, mn-payment annuity-duewith m payments per interest-conversion periodpresent value of a continuous annuitypresent value of a q-period deferred continuous annuitydiscount factorpresent value of 1 to be paid at time t
Page 2 and 3: Financial Mathematics forActuaries
Page 4 and 5: Financial Mathematics forActuaries
Page 6 and 7: To Bonnie, Nikki and Kevinfor their
Page 8 and 9: About the AuthorsWai-Sum Chan, PhD,
Page 10 and 11: Preface to the Second EditionA good
Page 12 and 13: ContentsAbout the AuthorsPreface to
Page 14 and 15: ContentsxiiiChapter 7 Bond Yields a
Page 16 and 17: List of Mathematical SymbolsSymbola
Page 20 and 21: 1InterestAccumulation andTime Value
Page 22 and 23: Interest Accumulation and Time Valu
Page 48: Table 1.3:Summary of accumulated va
Page 59 and 60: 2AnnuitiesAn annuity is a series of
Page 61 and 62: Annuities 41Figure 2.1 illustrates
Page 63 and 64: Annuities 43Solution: The rate of i
Page 65 and 66: Annuities 45As an annuity-due of n
Page 67 and 68: 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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10Stochastic Interest RatesIn previ
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Stochastic Interest Rates 307Table
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Stochastic Interest Rates 309ands 5
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Stochastic Interest Rates 311Next,
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Stochastic Interest Rates 313Theref
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Stochastic Interest Rates 315which
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Stochastic Interest Rates 317There
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Stochastic Interest Rates 319We use
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Stochastic Interest Rates 32110.3 W
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Stochastic Interest Rates 32310.13
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Stochastic Interest Rates 32510.24
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APPENDIXAReview of Mathematics and
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Review of Mathematics and Statistic
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Review of Mathematics and Statistic
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APPENDIXBAnswers to Selected Exerci
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Answers to Selected Exercises 335Ch
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Answers to Selected Exercises 337Ch
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Answers to Selected Exercises 3394.
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Answers to Selected Exercises 34710
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IndexAaccrued interest, 187, 198-20
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Index 351RATE, 63, 70XIRR, 109-111,
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Index 353dollar-weighted, 105, 112,
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