Theory of Interest / Edition 2

by Stephen G. Kellison, Kay Fulton, Karen Murphy

Overview

The new and improved third edition of The Theory of Interest is significantly revised and expanded from previous editions. The text covers the basic mathematical theory of interest as traditionally developed. The book is a thorough treatment of the mathematical theory and practical applications of compound interest or mathematics of finance. The popular pedagogical approach remains the focal point for this text as the narrative emphasizes both the importance of conceptual understanding and the ability to apply the techniques to practical problems.

New Features: Expanded coverage in a number of areas, including three new chapters devoted to: the term structure of interest rates; duration, convexity and immunization; and options and other derivatives. Computational approaches in the third edition have been modernized to reflect the widespread availability of calculators with exponential logarithmic capability, including those with built-in financial functions. 545 end-of-chapter exercises-Each exercise is intended to illustrate a somewhat different point to keep the number of repetitious exercises to a minimum.

Product Details

ISBN-13:	9780256091502
Publisher:	McGraw-Hill Companies, The
Publication date:	05/01/1991
Edition description:	Older Edition
Pages:	448
Product dimensions:	6.00(w) x 9.00(h) x 0.93(d)

Table of Contents

The measurement of interest     1
Introduction     1
The accumulation and amount functions     2
The effective rate of interest     5
Simple interest     7
Compound interest     8
Present value     13
The effective rate of discount     15
Nominal rates of interest and discount     22
Forces of interest and discount     28
Varying interest     35
Summary of results     38
Appendix 1     39
Simple interest for fractional periods     39
Compound interest for fractional periods     40
Exercises     42
Solution of problems in interest     49
Introduction     49
The basic problem     50
Equations of value     52
Unknown time     55
Unknown rate of interest     58
Determining time periods     60
Practical examples     62
Appendix 2     66
Derivation involving method of equated time     66
Exercises     67
Basic annuities     73
Introduction     73
Annuity-immediate     74
Annuity-due     79
Annuity values on any date     83
Perpetuities     86
Unknown time     89
Unknown rate of interest     93
Varying interest     95
Annuities not involving compound interest     98
Appendix 3     106
Approximate formula for unknown rate of interest     106
Exercises     107
More general annuities     114
Introduction     114
Differing payment and interest conversion periods     114
Annuities payable less frequently than interest is convertible     117
Annuities payable more frequently than interest is convertible     121
Continuous annuities     125
Payments varying in arithmetic progression     127
Payments varying in geometric progression     133
More general varying annuities     137
Continuous varying annuities     140
Summary of results     142
Appendix 4     143
Other formulas for annuities payable more frequently than interest is convertible     143
Alternative approach for payments varying in arithmetic progression     144
Exercises     146
Amortization schedules and sinking funds     152
Introduction     152
Finding the outstanding loan balance     153
Amortization schedules     156
Sinking funds     164
Differing payment periods and interest conversion periods     170
Varying series of payments     172
Amorization with continuous payments     178
Step-rate amounts of principal     181
Exercises     185
Bonds and other securities     194
Introduction     194
Types of securities     194
Price of a bond     200
Premium and discount     206
Valuation between coupon payment dates     213
Determination of yield rates     219
Callable and putable bonds     222
Serial bonds     226
Some generalizations     228
Other securities     231
Valuation of securities     234
Appendix 6     238
Derivation of the bond salesman's formula     238
Exercises     240
Yield rates     248
Introduction     248
Discounted cash flow analysis     249
Uniqueness of the yield rate     255
Reinvestment rates     258
Interest measurement of a fund     264
Time-weighted rates of interest     269
Portfolio methods and investment year methods     274
Short sales     277
Capital budgeting - basic techniques     281
Capital budgeting - other techniques     286
Appendix 7     295
Uniqueness of the yield rate     295
Further analysis of the simple interest assumption in Section 7.5     296
Interest measurement using continuous functions     297
Exercises     299
Practical applications     309
Introduction     309
Truth in lending     310
Automobile financing     316
Real estate mortgages     326
Approximate methods     333
Depreciation methods     344
Capitalized cost     352
Modern financial instruments     355
Exercises     364
More advanced financial analysis     373
Introduction     373
An economic rationale for interest     374
Determinants of the level of interest rates     376
Recognition of inflation     379
Consideration of expenses      385
Effect of taxes     391
Currency exchange rates     397
Reflecting risk and uncertainty     400
Interest rate assumptions     408
Exercises     411
The term structure of interest rates     419
Introduction     419
Yield curves     420
Spot rates     424
Relationship with bond yields     426
Forward rates     431
Arbitrage     437
A continuous model     440
Exercises     444
Duration, convexity and immunization     450
Introduction     450
Duration     451
Convexity     458
Interest sensitive cash flows     467
Analysis of portfolios     470
Matching assets and liabilities     476
Immunization     480
Full immunization     486
A more general model     488
Appendix 11     491
Further analysis of varying annuities     491
Exercises     492
Stochastic approaches to interest     500
Introduction     500
Independent rates of interest     501
The lognormal model     509
Time series models     515
Binomial lattices     520
Continuous stochastic models     527
Scenario testing     535
More advanced models     540
Appendix 12     542
Derivation of the variance of annuity     542
Exercises     545
Options and other derivatives     551
Introduction     551
Definitions and concepts     552
Position and profit diagrams     556
Determinants of option value     559
Combination positions     563
Binomial lattices     566
Black-Scholes formula     574
Some extensions     576
Appendix 13     579
Derivation of the Black-Scholes formula     579
Exercises     582
Table numbering the days of the year     587
Illustrative mortgage loan amortization schedule     588
Basic mathematical review     592
Statistical background     595
Iteration methods     599
Answers to the exercises     601
Glossary of notation     625
Index     635