Mathematical Interest Theory

494 Pages·2014·12.658 MB·English

by  Daniel, James W.;Vaaler, Leslie Jane Federer

Second Edition
MATHEMATICAL INTEREST THEORY
® Mathematical Association of America
MAA ®
Leslie Jane Federer Vaaler & James W. Daniel
Second Edition
Mathematical Interest Theory is among the recommended reading
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options for the Society of Actuaries/Casualty Actuarial Society FM/2 exam.
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Students pursuing an actuarial career as well as those seeking a mathematically based T INTEREST
finances course stand to benefit from this informative, up-to-date, and, above all,
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skillfully written treatise. Instructors and students of interest theory owe Daniel and
Vaaler a debt of gratitude for their fine efforts. E THEORY
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—Susan Staples, Texas Christian University
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We use the Vaaler and Daniel text as our primary learning resource for actuarial L
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students master the big ideas in interest theory. The accessible exercises reinforce the e
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—Mark Maxwell, Director of Actuarial Science, Robert Morris University V I
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Mathematical Interest Theorygives an introduction to how investments grow Ja E
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over time. This is done in a mathematically precise manner. The emphasis is on e
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practical applications that give the reader a concrete understanding of why the various W
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relationships should be true. Among the modern financial topics are: arbitrage,
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options, futures, and swaps. The content of the book, along with an understanding of ie
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probability, will provide a solid foundation for readers embarking on actuarial careers.

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Mathematical Interest Theoryincludes more than 240 carefully worked examples.
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There are over 430 problems, and numerical answers are included in an appendix.
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ISBN978-0-88385-754-0
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Y
9 780883 857540
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Mathematical
Interest Theory
Second Edition
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OriginallypublishedbyPearsonPrenticeHall.
c 2007PearsonEducation,Inc.
(cid:13)
SecondEdition
c 2009by
(cid:13)
TheMathematicalAssociationofAmerica(Incorporated)
LibraryofCongressCatalogCardNumber2008935286
PrintISBN:978-0-88385-754-0
ElectronicISBN:978-1-61444-600-2
PrintedintheUnitedStatesofAmerica
CurrentPrinting(lastdigit):
1098765432
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Mathematical
Interest Theory
Second Edition
Leslie Jane Federer Vaaler
James W. Daniel
The University of Texas at Austin
Publishedanddistributedby
TheMathematicalAssociationofAmerica
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CouncilonPublications
PaulM.Zorn,Chair
MAATextbooksEditorialBoard
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GeorgeExner
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Investorsreceive interest.
ToAbigailLouiseVaalerandDouglasQuinnVaaler,
thebestinterestever.
ToJeffreyDavidVaaler,myco-investor.
–LeslieJaneFedererVaaler
Tomywife,AnnDaniel;myteacher,PaulMielke;
andmyactuarialguide,GeneWisdom.
–JamesW.Daniel
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Contents
Preface xiii
0 AnintroductiontotheTexasInstrumentsBAIIPlus 1
0.1 Choosingacalculator . . . . . . . . . . . . . . . . . . . . . . . . 1
0.2 Fontconvention . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
0.3 BAIIPlusbasics . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
0.4 Problems,Chapter0. . . . . . . . . . . . . . . . . . . . . . . . . . 7
1 Thegrowthofmoney 9
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Whatisinterest? . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Accumulationandamountfunctions . . . . . . . . . . . . . . . . . 11
1.4 Simpleinterest/Linearaccumulationfunctions . . . . . . . . . . . 15
1.5 Compoundinterest(Theusualcase!) . . . . . . . . . . . . . . . . . 19
1.6 Interestinadvance/Theeffectivediscountrate . . . . . . . . . . . 24
1.7 Discountfunctions/Thetimevalueofmoney . . . . . . . . . . . . 28
1.8 Simplediscount . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.9 Compounddiscount . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.10 Nominalratesofinterestanddiscount . . . . . . . . . . . . . . . . 43
1.11 Afriendlycompetition(Constantforceofinterest) . . . . . . . . . 51
1.12 Forceofinterest . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.13 NoteforthosewhoskippedSections(1.11)and(1.12) . . . . . . . 57
1.14 Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
1.15 Problems,Chapter1. . . . . . . . . . . . . . . . . . . . . . . . . . 61
2 Equationsofvalueandyieldrates 73
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.2 Equationsofvalueforinvestmentsinvolvinga
singledepositmadeundercompoundinterest . . . . . . . . . . . . 74
2.3 Equationsofvalueforinvestmentswithmultiple
contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.4 Investmentreturn . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.5 Reinvestmentconsiderations . . . . . . . . . . . . . . . . . . . . . 90
2.6 Approximatedollar-weightedyieldrates . . . . . . . . . . . . . . . 91
2.7 Fundperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
2.8 Problems,Chapter2. . . . . . . . . . . . . . . . . . . . . . . . . . 100
ix
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