Theory of Interest
Author: Stephen G Kellison
The book is a thorough treatment of the mathematical theory and practical applications of compound interest, or mathematics of finance.
Table of Contents:
The measurement of interest 1Introduction 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
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Inflation, Unemployment, and Monetary Policy
Author: Robert M M Solow
The connection between price inflation and real economic activity has been a focus of macroeconomic research--and debate--for much of the past century. Although this connection is crucial to our understanding of what monetary policy can and cannot accomplish, opinions about its basic properties have swung widely over the years.
Today, virtually everyone studying monetary policy acknowledges that, contrary to what many modern macroeconomic models suggest, central bank actions often affect both inflation and measures of real economic activity, such as output, unemployment, and incomes. But the nature and magnitude of these effects are not yet understood.
In this volume, Robert M. Solow and John B. Taylor present their views on the dilemmas facing U.S. monetary policymakers. The discussants are Benjamin M. Friedman, James K. Galbraith, N. Gregory Mankiw, and William Poole. The aim of this lively exchange of views is to make both an intellectual contribution to macroeconmics and a practical contribution to the solution of a public policy question of central importance.
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