A Basic Course in the Theory of Interest and Derivatives - Actuarial Exam FM/2 - Study Guide

Sep 27, 2026

Introductory course material for the theory of interest and annuity, designed for junior-level study of the mathematics of finance. Presents a structured progression from interest meaning, accumulation and amount functions, effective/nominal rates, and present value, through discounting, force of interest, and time-varying rates. Extends into annuity-immediate and annuity-due, deferred and perpetuities, solving for unknown payments or rates, and detailed analysis of varying and continuous annuities. Includes later coverage of discounted cash flow, IRR uniqueness, loan repayment methods, bond pricing, and interest-rate sensitivity measures.

LanguageEnglish

CategoryExam

FormatPDF

Pages647

Reading Time27 h 10 min

AccessFree to download

Preface

The Basics of Interest Theory

The Meaning of Interest

Accumulation and Amount Functions

Effective Interest Rate (EIR)

Linear Accumulation Functions: Simple Interest

Date Conventions Under Simple Interest

Exponential Accumulation Functions: Compound Interest

Present Value and Discount Functions

Interest in Advance: Effective Rate of Discount

Nominal Rates of Interest and Discount

Force of Interest: Continuous Compounding

Time Varying Interest Rates

Equations of Value and Time Diagrams

Solving for the Unknown Interest Rate

Solving for Unknown Time

The Basics of Annuity Theory

Present and Accumulated Values of an Annuity-Immediate

Annuity in Advance: Annuity Due

Annuity Values on Any Date: Deferred Annuity

Annuities with Infinite Payments: Perpetuities

Solving for the Unknown Number of Payments of an Annuity

Solving for the Unknown Rate of Interest of an Annuity

Varying Interest of an Annuity

Annuities Payable at a Different Frequency than Interest is Convertible

Analysis of Annuities Payable Less Frequently than Interest is Convertible

Rate of Return of an Investment

Discounted Cash Flow Technique

Uniqueness of IRR

Interest Reinvested at a Different Rate

Dollar-Weighted Interest Rate

Time-Weighted Rate of Interest

Bonds and Related Topics

Types of Bonds

Various Pricing Formulas of a Bond

Amortization of Premium or Discount

Valuation of Bonds Between Coupon Payment Dates

Loan Repayment Methods

Finding the Loan Balance Using Prospective and Retrospective Methods

Amortization Schedules

Sinking Fund Method

Loans Payable at a Different Frequency than Interest is Convertible

Measures of Interest Rate Sensitivity

Effect of Inflation on Interest Rates

Term Structure and Yield Curves

Macaulay and Modified Durations

Redington Immunization and Convexity

A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 Marcel B. Finan Arkansas Tech University 􀀍cAll Rights Reserved Preliminary Draft Last updated February 27, 2011 2 In memory of my parents August 1, 2008 January 7, 2009 Preface This manuscripts is designed for an introductory course in the theory of interest and annuity. This manuscript is suitablefor a junior level course in the mathematics of 􀀌nance. A calculator, such as TI BA II Plus, either the solar or battery version, will be useful in solving many of the problems in this book. A recommended resource link for the use of this calculator can be found at [http://www.scribd.com/doc/517593/TI-BA-II-PLUS-MANUAL](http://www.scribd.com/doc/517593/TI-BA-II-PLUS-MANUAL). The recommended approach for using this book is to read each section, work on the embedded examples, and then try the problems. Answer keys are provided so that you check your numerical answers against the correct ones. Problems taken from previous exams will be indicated by the symbol z: This manuscript can be used for personal use or class use, but not for commercial purposes. If you 􀀌nd any errors, I would appreciate hearing from you: m􀀌nan@atu.edu This project has been supported by a research grant from Arkansas Tech University. Marcel B. Finan Russellville, Arkansas March 2009 4 PREFACE Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest ................................... 10 2 Accumulation and Amount Functions ............................ 14 3 E􀀋ective Interest Rate (EIR) ................................ 22 4 Linear Accumulation Functions: Simple Interest ...................... 28 5 Date Conventions Under Simple Interest .......................... 35 6 Exponential Accumulation Functions: Compound Interest ................ 41 7 Present Value and Discount Functions ........................... 50 8 Interest in Advance: E􀀋ective Rate of Discount ...................... 56 9 Nominal Rates of Interest and Discount .......................... 66 10 Force of Interest: Continuous Compounding ....................... 78 11 Time Varying Interest Rates ................................ 93 12 Equations of Value and Time Diagrams .......................... 100 13 Solving for the Unknown Interest Rate .......................... 107 14 Solving for Unknown Time ................................. 116 The Basics of Annuity Theory 143 15 Present and Accumulated Values of an Annuity-Immediate ............... 144 16 Annuity in Advance: Annuity Due ............................. 157 17 Annuity Values on Any Date: Deferred Annuity ..................... 168 18 Annuities with In􀀌nite Payments: Perpetuities ...................... 176 19 Solving for the Unknown Number of Payments of an Annuity .............. 184 20 Solving for the Unknown Rate of Interest of an Annuity ................. 192 21 Varying Interest of an Annuity ............................... 202 22 Annuities Payable at a Di􀀋erent Frequency than Interest is Convertible ........ 206 23 Analysis of Annuities Payable Less Frequently than Interest is Convertible ....... 210 6 CONTENTS 24 Analysis of Annuities Payable More Frequently than Interest is Convertible ...... 218 25 Continuous Annuities .................................... 228 26 Varying Annuity-Immediate ................................ 234 27 Varying Annuity-Due .................................... 249 28 Varying Annuities with Payments at a Di􀀋erent Frequency than Interest is Convertible 257 29 Continuous Varying Annuities ............................... 268 Rate of Return of an Investment 275 30 Discounted Cash Flow Technique ............................. 276 31 Uniqueness of IRR ..................................... 285 32 Interest Reinvested at a Di􀀋erent Rate .......................... 292 33 Interest Measurement of a F

FAQs

Who is this course designed for and what level of math is expected?

It is designed for an introductory course in the theory of interest and annuity, suitable for a junior level course in the mathematics of finance.

How should the study guide be used to learn the material efficiently?

Read each section, work through the embedded examples, then attempt the problems. Answer keys are provided to check numerical answers.

How are problems from previous actuarial exams identified?

Problems taken from previous exams are indicated by the symbol z.

Sep 27, 2026

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