Mathematical Interest Theory

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

• ISBN13: 9780131472853
• ISBN10: 0131472852
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-01-01
• Publisher: Prentice Hall

Summary

Written in a reader-friendly manner, this reference is designed to meet the needs of readers who want to master the interest theory and finance topics addressed in the Financial Mathematics exam. Requires an algebra background; calculus not a prerequisite. Encourages readers to practice writing throughout, and more than 30 end-of-chapter writing exercises are included. Provides more than 240 worked examples in a wide range of difficulty. Features abundant examples, discussion, and problems throughout.A useful guide for readers planning to take the Financial Mathematics exam. Mathematical Interest Theory, 1/E James W. Daniel Leslie Jane Federer Vaaler

Author Biography

James W. Daniel, ASA, Ph.D., Sc.D., is Director of Actuarial Studies, University Distinguished Teaching Professor, and the Paul V. Montgomery Professor of Actuarial Mathematics at The University of Texas at Austin Leslie Jane Federer Vaaler, Ph.D., is Buck Consultants Assistant Director of Actuarial Studies, and Lecturer in Mathematics at The University of Texas at Austin

Table of Contents

Preface	p. xi
An introduction to the Texas Instruments BA II Plus	p. 1
Choosing a calculator	p. 1
Font convention	p. 2
BA II Plus basics	p. 2
Problems, Chapter 0	p. 7
The growth of money	p. 9
Introduction	p. 9
What is interest?	p. 10
Accumulation and amount functions	p. 11
Simple interest / Linear accumulation functions	p. 15
Compound interest (The usual case!)	p. 20
Interest in advance / The effective discount rate	p. 25
Discount functions / The time value of money	p. 29
Simple discount	p. 39
Compound discount	p. 41
Nominal rates of interest and discount	p. 46
A friendly competition (Constant force of interest)	p. 54
Force of interest	p. 57
Note for those who skipped Sections (1.11) and (1.12)	p. 60
Inflation	p. 61
Problems, Chapter 1	p. 64
Equations of value and yield rates	p. 76
Introduction	p. 76
Equations of value for investments involving a single deposit made under compound interest	p. 77
Equations of value for investments with multiple contributions	p. 79
Investment return	p. 87
Reinvestment considerations	p. 94
Approximate dollar-weighted yield rates	p. 95
Fund performance	p. 100
Problems, Chapter 2	p. 103
Annuities (annuities certain)	p. 112
Introduction	p. 112
Annuities - immediate	p. 114
Annuities - due	p. 128
Perpetuities	p. 131
Deferred annuities and values on any date	p. 133
Outstanding loan balances	p. 138
Nonlevel annuities	p. 144
Annuities with payments in geometric progression	p. 146
Annuities with payments in arithmetic progression	p. 149
Yield rate examples involving annuities	p. 156
Annuity symbols for nonintegral terms	p. 161
Annuities governed by general accumulation functions	p. 164
The investment year method	p. 168
Problems, Chapter 3	p. 172
Annuities with different payment and conversion periods	p. 186
Introduction	p. 186
Level annuities with payments less frequent than each interest period	p. 187
Level annuities with payments more frequent than each interest period	p. 191
Annuities with payments less frequent than each interest period and payments in arithmetic progression	p. 198
Annuities with payments more frequent than each interest period and payments in arithmetic progression	p. 201
Continuously paying annuities	p. 205
A yield rate example	p. 210
Problems, Chapter 4	p. 213
Loan repayment	p. 220
Introduction	p. 220
Amortized loans and amortization schedules	p. 220
The Sinking Fund method	p. 229
Loans with other repayment patterns	p. 236
Yield rate examples and replacement of capital	p. 239
Problems, Chapter 5	p. 247
Bonds	p. 255
Introduction	p. 255
Bond alphabet soup and the basic price formula	p. 256
The premium-discount formula	p. 262
Other pricing formulas for bonds	p. 264
Bond amortization schedules	p. 266
Valuing a bond after its date of issue	p. 276
Selling a bond after its date of issue	p. 283
Yield rate examples	p. 292
Callable bonds	p. 296
Floating-rate bonds	p. 301
The BA II Plus calculator Bond worksheet	p. 302
Problems, Chapter 6	p. 308
Stocks and financial markets	p. 316
Common and preferred stock	p. 316
Brokerage accounts	p. 320
Going long: buying stock with borrowed money	p. 326
Selling short: selling borrowed stocks	p. 329
Problems, Chapter 7	p. 334
Arbitrage, the term structure of interest rates, and derivatives	p. 338
Introduction	p. 338
Arbitrage	p. 339
The term structure of interest rates	p. 342
Forward contracts	p. 353
Commodity futures held until delivery	p. 355
Offsetting positions and liquidity of futures contracts	p. 362
Price discovery and more kinds of futures	p. 367
Options	p. 369
Using replicating portfolios to price options	p. 374
Using weighted averages to price options	p. 387
Swaps	p. 394
Problems, Chapter 8	p. 401
Interest rate sensitivity	p. 412
Overview	p. 412
Duration	p. 416
Convexity	p. 430
Immunization	p. 437
Other types of duration	p. 445
Problems, Chapter 9	p. 449
Appendices
Some useful formulas	p. 455
Answers to end of chapter problems	p. 461
Bibliography	p. 485
Index	p. 487
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