## PROBLEM SET:ANNUITIES AND SINKING FUNDS

Each of the following problems involve an annuity - a sequence of payments.

1) Find the future value of an annuity of $200 per month for 5 years at 6% compounded monthly. | 2) How much money should be deposited at the end of each month in an account paying 7.5% for it to amount to $10,000 in 5 years? |

3) At the end of each month Rita deposits $300 in an account that pays 5%. What will the final amount be in 4 years? | 4) Mr. Chang wants to retire in 10 years and can save $650 every three months. If the interest rate is 7.8%, how much will he have (a) at the end of 5 years? (b) at the end of 10 years? |

5) A firm needs to replace most of its machinery in five years at a cost of $500,000. The company wishes to create a sinking fund to have this money available in five years. How much should the quarterly deposits be if the fund earns 8%? | 6) Mrs. Brown needs $5,000 in three years. If the interest rate is 9%, how much should she save at the end of each month to have that amount in three years? |

7) A company has a $120,000 note due in 4 years. How much should be deposited at the end of each quarter in a sinking fund to payoff the note in four years if the interest rate is 8%? | 8) You are now 20 years of age and decide to save $100 at the end of each month until you are 65. If the interest rate is 9.2%, how much money will you have when you are 65? |

9) Is it better to receive $400 at the beginning of each month for six years, or a lump sum of $25,000 today if the interest rate is 7%? Explain. | 10) To save money for a vacation, Jill decided to save $125 at the beginning of each month for the next 8 months. If the interest rate is 7%, how much money will she have at the end of 8 months? |

11) Mrs. Gill puts $2200 at the end of each year in her IRA account that earns 9% per year. How much total money will she have in this account after 20 years? | 12) If the inflation rate stays at 6% per year for the next five years, how much will the price be of a $15,000 car in five years? How much must you save at the end of each month at an interest rate of 7.3% to buy that car in 5 years? |

## Annuities

An annuity is a **fixed income over a period of time**.

### Example: You get $200 a week for 10 years.

How do you get such an income? **You buy it!**

**you pay them**one large amount, then**they pay you**back a series of small payments over time

### Example: You buy an annuity

And in return you get $400 a month for 5 years

*Is that a good deal?*

### Example (continued):

$400 a month for 5 years = $400 × 12 × 5 = **$24,000**

Seems like a good deal . you get back more than you put in.

Why do you get **more** income *($24,000)* than the annuity originally cost *($20,000)*?

Because **money now** is more valuable than money later.

The people who got your $20,000 can invest it and earn interest, or do other clever things to make more money.

So how much *should* an annuity cost?

## Features

**MathXL® and MyMathLab® for Business Math** provide a powerful classroom management, homework, tutorial, and assessment tools. Students can take chapter quizzes or tests in MathXL and MyMathLab and receive personalized study plans based on their test results. The study plan diagnoses weaknesses and links students directly to tutorial exercises for the outcomes they need to study and retest. All student work can be tracked in MathXL’s online gradebook. Three packaging options--MyMathLab, MathXL, or MathXL Tutorials on CD--provide flexible platforms to fit your course goals. For more information, visit our websites at www.mymathlab.com and www.mathxl.com, or contact your sales representative.

### New to This Edition

**New and Updated Features:**

**Case Studies**are one-page features that highlight a business and provide questions that relate the company's business practices to the chapter concepts. Selected Case Studies have additional video content available on the**Classroom Lectures and Case Studies on DVD-ROM**.**Quick Check Exercises**follow each example in the text to reinforce understanding of specific concepts. Answers to these exercises are given at the bottom of the page.**Application problems**have been updated throughout to be relevant to today’s students, and they reference well-known companies such as Subway, The Home Depot, Jackson and Perkins Company, REI, FTD, Ford Motor Company, Bank of America, General Motors, Citigroup, Century 21, The Hershey Company, and Mattel.**The new design**and trim size provides an easy-to-read, engaging text for students.

**New Student Resources:**

- The new
**Classroom Lectures and Case Studies on DVD**offer a short lecture for each section of the text, along with Case Study company profile videos tied to select Case Studies from the text.

## Mathematics (part 1)

According to the ILO's (prerequisite of the program), the student will globally learn to use mathematical tools to solve management problems. Particularly, the main objectives are: - learning of rigor in mathematics - applying mathematics in management - solving concrete problems - using and applying mathematical models.

The target competences are: - analyzing scientifically situations, - solving problems, - modelizing, - arguing, - communicating.

### Prerequisite knowledge and skills

Elementary algebra : fractions, powers, operations priority, proper use of parentheses first and second degree functions and their graphs.

### Planned learning activities and teaching methods

Each notion of the contents is illustrated by exercises.

### Mode of delivery (face to face, distance learning, hybrid learning)

- Face-to-face lectures.
- Practice sessions.
- Possibility to attend "questions-and-answers" sessions weekly.

### Organisational adjustments related to the current health context

If in-site exams are forbidden (during any session), written or oral exams might be replaced by on-line multiple choice questions.

### Recommended or required readings

Lecture notes, slides and exercices are available via [email protected]

### Assessment methods and criteria

* Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.*

Written and/or oral exam with theory and exercises.

The 1st choice is a written on site exam with open questions.

Marginal sections students could have other exam methods.

If there is an oral exam, students have to register according to the rules (including dates) communicated via [email protected] Any sudent not fulfilling these requirements can be considered "Absent" at the exam.

If the marks N_T for the theory and the marks N_P for the exercises are both greater than or equal to 05/20, the final marks are N = 0.4 x N_T + 0.6 x N_P otherwise, N = min

## Table of Contents

The Business Mathematics, 13th Edition, Learning System

Learning Tips for Students

Business Mathematics Pretest

**1. Whole Numbers and Decimals**

1.4 Addition and Subtraction of Decimals

1.5 Multiplication and Division of Decimals

Case Study: Cost of Getting Married

Case in Point Summary Exercise: Subway

2.2 Addition and Subtraction of Fractions

2.3 Addition and Subtraction of Mixed Numbers

2.4 Multiplication and Division of Fractions

2.5 Converting Decimals to Fractions and Fractions to Decimals

Case Stdy: Operating Expenses at Woodline Moldings and Trim

Case in Point Summary Exercise: Home Depot

3.1 Writing Decimals and Fractions as Percents

Supplementary Application Exercises on Base and Part

Supplementary Application Exercises on Base, Rate, and Part

3.5 Increase and Decrease Problems

Case Study: Self Employed Retirement Plan

Case in Point Summary Exercise: Century 21

**4. Equations and Formulas**

4.2 Applications of Equations

Case Study: Forecasting Sales at Alcorns Boutique

Case in Point Summary Exercise: General Motors

Chapters 14 Cumulative Review

5.1 Electronic Banking, Checking Accounts, and Check Registers

5.2 Checking Services and Credit-Card Transactions

5.3 Bank Statement Reconciliation

Case Study: Banking Activities of a Retailer

Case in Point Summary Exercise: Jackson & Perkins

6.1 Gross Earnings: Wages and Salaries

6.2 Gross Earnings: Piecework and Commissions

6.3 Social Security, Medicare, and Other Taxes

6.4 Income Tax Withholding

Case Study: Payroll: Finding Your Take-Home Pay

Case in Point Summary Exercise: Payroll at Starbucks

**7. Mathematics of Buying**

7.1 Invoices and Trade Discounts

7.2 Series Discounts and Single Discount Equivalents

7.3 Cash Discounts: Ordinary Dating Methods

7.4 Cash Discounts: Other Dating Methods

Case Study: George Foreman

Case in Point Summary Exercise: Discounts at Bed Bath & Beyond

**8. Mathematics of Selling**

8.2 Markup on Selling Price

Supplementary Application Exercises on Markup

8.4 Turnover and Valuation of Inventory

Case Study: Markdown: Reducing Prices to Move

Case in Point Summary Exercise: Recreational Equipment Inc. (REI)

Chapters 5 Cumulative Review

9.1 Basics of Simple Interest

9.2 Finding Principal, Rate, and Time

9.4 Discounting a Note Before Maturity

Supplementary Application Exercises on Simple Interest and Simple Discount

## AnnuityF

Chapter 1 Linear Equations And Graphs

Future Value of an Annuity Sinking Funds Barnett/Ziegler/Byleen Finite Mathematics 12e Sinking Fund Payment Formula To derive the sinking fund payment formula, we use algebraic techniques to rewrite the formula for the future value of an annuity and solve for the variable PMT: . Document Viewer

MATH 1003 Calculus And Linear Algebra (Lecture 3)

Future Value of an Annuity Formula for the Future Value of an Annuity We now introduce the formula of the future value of an annuity in the term of the notations used in ﬁnance. Theorem Sinking Fund Formula for Sinking Fund Payment . View Doc

Section 11.6 Ordinary **Annuities** **Formula** - YouTube

5:46 Computing payment for sinking fund by Arthur Weiss 574 views 8:03 Annuity - future value (monthly savings) 6:19 Present Value of an annuity: Deriving the formula by TeachThemToThink 906 views Loading more suggestions Load more suggestions . Language: English . View Video

Present Value Of An Ordinary **Annuity** - Www.atcmathprof.com .

Http://www.atcmathprof.com - Present Value of An Ordinary Annuity, annuities, retirement account, present value, future value, sinking funds, stocks, bonds, 401(k), 401(b), dividends, mature, Dow Jones Industrial Average, IRA, mutual fund, Roth IRA, stockbrokers, stock certificates . View Video

Mathematics Of Compound Interest

Application to Personal Decision Making Ex. Corporation sets up sinking fund of some type. If company issues bond worth $100,000,000 that must be redeemed at par Last deposit earns no interest at all because annuity formula set up so that deposits are made at end of each year. . Access Content

FM Lial 9th 5.2 Notes F09 - NWACC - Faculty

At the end of a regular time period, they form an ordinary annuity. B. Formula for a Sinking Fund Payment. or Example 2. Find the amount of each payment to be made into a sinking fund so that enough will be. present to accumulate the following amount. . Fetch Document

CL&rsquos Handy **Formula** Sheet - Arkansas Tech University

Formula Sheet (Useful formulas from Marcel Finan&rsquos FM/2 Book) Compiled by Charles Lee Hence the total number of annuity payments is in the sinking fund method, the borrower both deposits . Document Retrieval

Finding Principal Using The Interest **formula**

Find the principal using the interest formula. Simple interest formula. Page 5. . Read Article

Ch. 11.5: **Annuities** - Washington State University

Ordinary Annuity Formula: A = m " 1 + r n nt 1 r n # Example 2: Say you intend to deposit $200.00 at thte end of every 6 months into a Sinking Funds A sinking fund (in its modern business usage) is basically an annuity set up for the purpose of paying o a debt. . Doc Retrieval

Theory Of Interest - **Formula** Sheet II Continuous **annuities** F T

Theory of Interest - Formula Sheet II 1. Continuous annuities. If the payments are being made continuously at the rate f(t)at exact moment t, then the present value of an n-period continuous varying annuity is . Retrieve Content

Chapter 9, Section I

12-8 Calculating the amount of an amortization by table an annuity by using table. 12-9 (Optional) Calculating sinking fund payments by formula certain Contingent annuities Ordinary annuity Annuity due Future value of an annuity Present value of an annuity Sinking fund . Fetch Document

**Annuities** - Arizona State University

Sinking Funds A sinking fund is when we know the future value of the annuity and we wish to compute the monthly payment. For an ordinary unity this formula is For an annuity due the formula is Sinking Fund Example Suppose you decide to use a sinking fund to save $10,000 for a car. If you . Return Document

Installment payments are in the form of an annuity. synonymous terms. outstanding you will remember our formula from chapter 3. amount to Sinking Fund For A $10,000 5 Year Loan At 10% Interest But Sinking Fund Earning 8% Year Interest Paid On Loan Sinking Fund Deposit Interest . Fetch Full Source

Amortization Schedule - Wikipedia, The Free Encyclopedia

Again, the Present Value of an Annuity formula should be used. This means that at the end of year seven the loan can be paid off in full for the amount of $79,268.02. Typically mortgage lenders will have a balloon payment clause in the contract that will charge a fee for early payment. . Read Article

Uniform Payment Series **Sinking** **Fund** Factor (Difficulty .

Uniform Payment Series Sinking Fund Factor 19:24 Chapter 13- Annuity & Sinking Funds by InstructorOverly 1,104 views 5:46 Computing payment for sinking fund by Arthur Weiss 574 views 3:56 Should I exit some LIC plans by MyInsuranceClub 1,869 views . View Video

Financial Formulae 2012 - Real Estate Defined

Sinking-Fund (s.f.) Factor .. 5 as a function of: Amount of One or Future Value (An) .. 5 Capitalisation income, i.e. of an annuity certain. Given by the formula: () n ()n n i . View Doc

Mississippi State University

Imbedded Annuities Sometimes uneven streams of cash flows will have annuities embedded within them We can use the annuity formula Problem is to determine the periodic deposit to have the needed amount at the bond&rsquos maturity&mdasha future value of an annuity problem The Sinking Fund . Content Retrieval

Finance **Formula** Sheet - University Of South Dakota

Sinking Fund: Present Value: Amortization: Time left Determining Which Formula to Use: 1: Are we comparing two different compound Are we creating a lump sum? Yes: Future value annuity (we know R finding the amount of $ saved) Sinking fund (we know the $ saved finding R) No: We are . Fetch Doc

Definition Of **Annuity** Chapter 3 Mathematics Of Finance

Future Value of an Annuityy g Sinking Funds Definition of Annuity To derive the sinking fund payment formula we useTo derive the sinking fund payment formula, we use algebraic techniques to rewrite the formula for the future . Get Content Here

Chapter 1 Linear Equations And Graphs - Pellissippi State .

Future Value of an Annuity Sinking Funds Sinking Fund Payment Formula To derive the sinking fund payment formula, we use algebraic techniques to rewrite the formula for the future value of an annuity and solve for the variable PMT: . View Full Source

FINANCIAL MATHEMATICS : GRADE 12

The year i.e. when payments made at the beginning of the time period (Annuity due), then the following formula is used: have set up an annuity called a sinking fund. Important terms: Book Value of an asset is its value after depreciation has been taken into account. . Document Retrieval

The Time Value Of Money (contd.) - MIT - Massachusetts .

Factor Name Factor Notation Formula Cash Flow Diagram Future worth Uniform series compound amount factor (aka future-worth-of-an-annuity factor) (F/A, i, N) F=A (1+i)N-1 i È Î Í ˘ ˚ ˙ Sinking fund factor(A/F, i, N) A=F i (1+i (A/P, r%, N) Continuous annuity from a present amount . Read More

The difference between an annuity and a sinking fund is: You currently (presently) have amassed the total value of a sinking fund, while with an annuity you have to wait till you&rsquove made all your payments into it to know the total value. The Present Value formula applied to credit cards: . Read More

The Mathematics Of Real Estate Appraisal - Commercial Appraiser

Sinking fund factor and the discount rate so we have: s(n,i) 1 a(n,i) 1 i I I V + = = . Cross-multiplying shows that each income I is the sum of the amount V/s(n,i) and iV. The straight line changing annuity formula for this sum was previously derived. [][]. i . Document Viewer

14-1 SECTION EXERCISES

3 Find the sinking fund payment or the present value of an annuity using a formula or a calculator application. Businesses and individuals often use sinking funds to accumulate a desired amount of money by . Get Document

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The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

### Program Details

**CHAPTER 1** Problem Solving with Math **CHAPTER 2** Fractions **CHAPTER 3** Percents and Their Applications **CHAPTER 4** Solving for the Unknown **CHAPTER 5** Business Statistics **CHAPTER 6** Banking and Budgeting **CHAPTER 7** Payroll and Income Tax **CHAPTER 8** Sales, Excise, and Property Taxes **CHAPTER 9** Risk Management **CHAPTER 10** Installment Buying and Revolving Charge Credit Cards **CHAPTER 11** Discounts: Trade and Cash **CHAPTER 12** Markups and Markdowns: Perishables and Breakeven Analysis **CHAPTER 13** How to Read, Analyze, and Interpret Financial Reports **CHAPTER 14** Depreciation **CHAPTER 15** Inventory and Overhead **CHAPTER 16** Simple Interest **CHAPTER 17** Promissory Notes, Simple Discount Notes, and the Discount Process **CHAPTER 18** The Cost of Home Ownership **CHAPTER 19** Compound Interest and Present Value **CHAPTER 20** Annuities and Sinking Funds **CHAPTER 21** Stocks, Bonds, and Mutual Funds

## AnnuityF

5.2 Future Value Of An **Annuity** - Marquette High School .

An Annuity Objectives: By the end of this lesson you should be able to: Explain what an annuity is. Explain the different types of annuities. Find the future value of an annuity. Calculate the payment of a sinking fund. Use the TVM Solver in your graphing calculator to solve annuity problems. . Retrieve Full Source

A **sinking** **fund** Is An **annuity** Where A Specific Value In The .

Hp calculators . HP 35s Sinking Funds . Sinking Funds . The Time Value of Money on the HP 35s . Practice solving for payment required to . achieve a goal . Access This Document

FinancialMathematics - YouTube

4:27 Annuity (Sinking Fund: Find Payment) by ChattState Math 611 views 2:09 Rainbow Otea by CarolaT18 261 views 4:53 present value of an annuity by DeltaMATHtv 3,446 views 3:35 HP 50G Financial Mathematics: Annuity / Pension / Investment by software49g 3,258 views . View Video

Financial Mathematics For Actuaries - Singapore Management .

Annuity-immediate using the sinking fund method. The loan charges 6% interest and the sinking fund credits 4% interest. What is the annual installment? If this installment is used to pay back a loan of the same amount by amortization, what is the rate of interest? . Retrieve Doc

User:Arael2/wikislice-economics - Wikipedia, The Free .

- account - accounting - accrual - acquisition - actuary - administration - advance - allocation - allowance - amortisation - annuity - appeal - apportionment - appraisal - appreciation - asociation - assets - associate - attorney (ERDF) - European Single Act - European Social Fund (ESF . Read Article

Manistee Area Public Scools **Sinking** **Fund** - Part 1 - YouTube

Presentation by the MAPS Superintendent and Business Manager about the sinking fund bond proposal to be voted upon May 8th. More information is available at . View Video

5.3 Future Value Of An **Annuity** And **Sinking** **Funds**

5.3 Future Value of an Annuity and Sinking Funds Definition: A sequence is a function whose domain is the set of positive integers. . Doc Retrieval

Section F.3: **Annuities** And **Sinking** **Funds** De Nitions: An .

Section F.3: Annuities and Sinking Funds De nitions: An annuity is a sequence of equal payments made at regular intervals of time. An ordinary annuity is one in which the payments are made Example 2: Finding Payment Amount You create a sinking fund that . Access Doc

**Annuities** - Arizona State University

Sinking Funds A sinking fund is when we know the future value of the annuity and we wish to compute the monthly payment. For an ordinary unity this formula is For an annuity due the formula is Sinking Fund Example Suppose you decide to use a sinking fund to save $10,000 for a car. If you . Document Viewer

Installment payments are in the form of an annuity. synonymous terms. outstanding loan balance. outstanding principal. Sinking Fund For A $10,000 5 Year Loan At 10% Interest Year Interest Paid On Loan Sinking Fund Deposit Interest Earned On Sinking Fund Sinking Fund Net Loan 0 10,000 .00 1 . Read Content

5

Annuity. If payments are made at the end Find the amount of each payment to be made into a sinking fund to accumulate $11,000. Assume the money earns 5% compounded semiannually for 8 years. 1 . Title: 5 Author: leeh Last modified by: . View Full Source

CHAPTER 7 FI A CIAL MATHEMATICS

7.2 Compound Value of an Annuity 118 7.3 Sinking Funds 119 7.4 Present Value 122 7.5 Present Value of an Annuity 122 7.6 Term Loans and Amortization 123 Exercise set up a sinking fund schedule and explain some of the applications of sinking funds. Chapter 7: Financial Mathematics 117 . Doc Retrieval

Amortization Schedule - Wikipedia, The Free Encyclopedia

Annuity Bullet (all at once) Balloon (amortization payments and large end payment) Increasing balance (negative amortization) Amortization schedules run in chronological order. . Read Article

Internal Rate Of Return - Wikipedia, The Free Encyclopedia

In the case that the cash flows are random variables, such as in the case of a life annuity, the expected values are put into the above formula. Often, the value of cannot be found analytically. In this case, numerical methods or graphical methods must be used. . Read Article

**Annuities** - Overview Of **Annuities** - Advantages And .

An annuity is a contract between the buyer and an insurance company. In general, the insurance company promises to do something with the buyer&rsquos money. This page should serve as a general overview of annuities. After you understand the concept you can look into the various annuity types. . Read Article

Chapter 8: The Time Value Of Money - Thomson Nelson .

Annuities The Future Value of an Annuity The Future Value of an Annuity&mdashDeveloping a Formula The Future Value of an Annuity&mdashSolving Problems The Sinking Fund Problem Compound Interest and Non-Annual Compounding The Effective Annual Rate The Present Value of an Annuity&mdashDeveloping a . Retrieve Doc

Annuity Annuity &ndash a sequence of payments made at regular time intervals. Ordinary Annuity &ndash payments made at the end of each payment period. Simple Annuity &ndash payment period coincides with the interest conversion period. Sinking Fund Payment . Fetch Here

Amortization Method And **Sinking** **Funds** - McGraw-Hill

Solution The sinking-fund deposits form an ordinary simple annuity with S =25800, i =2 3 %, n =60. We calculate the total monthly sinking-fund deposit R =25800 s 602/3% sinking fund are made at the same times as the interest payments on the debt are . Read More

**Sinking** **Funds** - **About.com** Money In Your 20s

Definition: Sinking funds are used to pay for large expenses that you are planning for. You may use different sinking funds to pay for home repairs, save for a new car, pay for your vacation or to cover large medical bills. . Read Article

BF01 **Sinking** **Fund** - University Of Rhode Island

HP 50g Sinking Fund The FINANCE menu Sinking Funds Practice solving for payment required to achieve a goal . hp calculators Sinking Funds A sinking fund is an annuity where a specific value in the future is needed, which is accumulated through a series of regular . Fetch Full Source

Hp Calculators

Sinking Funds A sinking fund is an annuity where a specific value in the future is needed, which is accumulated through a series of regular payments. These types of problems often occur when saving for a goal, such as retirement or college tuition. . Access Content

Math 125 Section 5.3 &ndash Annuities, Future Value and Sinking Funds So far, we have only discussed one-time payments. This section turns our attention to REGULAR payments. DEF: Ordinary annuity One where regular Do Examples 2 and 3 ** A Sinking fund is a fund set up to RECEIVE regular . Visit Document

What Is The Difference Between A **Sinking** **Fund** And An .

People often confuse sinking funds and emergency funds. They also use their emergency fund, when they should be setting up a sinking fund to cover that particular expense. . Read Article

Derivation Of Time V Alue Of Money Formulas

The Annuity Case The third time value of money factor is more difficult to derive. A level annuity ally have presented the sinking fund and loan constant factors as separate tools, perhaps because of the importance in real estate analysis of computing loan pay- . Access Full Source

Annunities Objectives

Tax-deferred annuity sinking fund present value of an annuity Formulas: Ordinary Annuity Formula: Present Value of Annuity Formula Possible Classroom Examples: On March 19, Rachael Westlake joined a Christmas club. Her bank will . Doc Retrieval

## Mathematics (MATH)

Mathematics used in solving business problems related to simple and compound interest, annuities, payroll, taxes, promissory notes, consumer credit, insurance, markup and markdown, mortgage loans, discounting, financial statement ratios and break-even analysis. Course is not applicable toward the undergraduate Mathematics major requirements.

**Term Offered:** Fall

**MATH 1180 Reasoning With Mathematics**

Reasoning with Mathematics will prepare students for an increasingly information-based society. Students will acquire the skills necessary to make rational decisions based on real data and evaluate numerical information. They will be exposed to general methods of inquiry that apply in a wide variety of settings. They will be able to critically assess arguments and make rational decisions. Finally, students will develop the ability to judge the strengths and limitations of quantitative approaches.

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1200 Mathematical Modeling and Problem Solving**

Mathematical modeling of data using linear, quadratic, rational, and radical functions in their numerical, symbolic, graphic, and verbal forms. Problem solving methods and strategies will be emphasized. Course is not applicable toward the undergraduate Mathematics major requirements. Math core course.

**Term Offered:** Spring, Summer, Fall

**MATH 1210 Mathematics For Education Majors I**

Principles of elementary number theory, base systems, foundations of arithmetic operations, fractions, decimals and problem solving techniques. Course is not applicable toward the undergraduate Mathematics major requirements.

**Prerequisites:** MATH 1180 with a minimum grade of C- or MATH 1200 with a minimum grade of C- or Aleks Math Placement Test with a score of 46 or Aleks Math Placement Retest with a score of 46 or ACT Math with a score of 20 or Math - Coll Algebra Placement with a score of 10 or Math - Elem Algebra Placement with a score of 12 or SAT Mathematics with a score of 480 or MATH SECTION SCORE with a score of 510

**Term Offered:** Spring, Fall

**MATH 1220 Mathematics For Education Majors II**

Development of integers, rational numbers and real numbers probability, statistics, informal geometry, geometric figures and measurements. Course is not applicable toward the undergraduate Mathematics major requirements.

**Prerequisites:** MATH 1210 with a minimum grade of C-

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1320 College Algebra**

Number system elementary theory of equations and inequalities functions and relations exponentials and logarithms systems of equations and topics in analytic geometry. Course is not applicable toward the undergraduate Mathematics major requirements. No credit given for students who have credit for MATH 1340.

**Prerequisites:** MATH 1200 with a minimum grade of C- or ACT Math with a score of 20 or SAT Mathematics with a score of 480 or Aleks Math Placement Test with a score of 46 or Aleks Math Placement Retest with a score of 46 or Math - Coll Algebra Placement with a score of 10 or MATH SECTION SCORE with a score of 510

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1330 Trigonometry**

Definitions and graphs of trigonometric functions and their inverses, solving trigonometric equations, applications and topics in analytic geometry. Course is not applicable toward the undergraduate Mathematics major requirements. No credit given for students who have credit for MATH 1340.

**Prerequisites:** MATH 1320 with a minimum grade of C- or ACT Math with a score of 22 or SAT Mathematics with a score of 520 or Aleks Math Placement Test with a score of 61 or Aleks Math Placement Retest with a score of 61 or Math - Coll Algebra Placement with a score of 15 or MATH SECTION SCORE with a score of 550

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1340 College Algebra And Trigonometry**

Functions and graphs, exponential and logarithmic functions, trigonometric functions and applications, systems of equations and topics in analytic geometry. No credit for students who have credit for MATH 1320 or 1330.

**Prerequisites:** ACT Math with a score of 24 or SAT Mathematics with a score of 560 or Aleks Math Placement Test with a score of 68 or Aleks Math Placement Retest with a score of 68 or (Math - Coll Algebra Placement with a score of 12 and Math - Trigonometry Placement with a score of 9) or MATH SECTION SCORE with a score of 580

**Term Offered:** Spring, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1730 Calculus with Applications to Business and Finance**

An introduction to differential and integral calculus. Topics include limits, derivatives, maxima/minima, indefinite and definite integrals with an emphasis on business applications and technology use.

**Prerequisites:** MATH 1320 with a minimum grade of C- or MATH 1340 with a minimum grade of C- or Math - Coll Algebra Placement with a score of 15 or ACT Math with a score of 24 or SAT Mathematics with a score of 560 or Aleks Math Placement Test with a score of 68 or Aleks Math Placement Retest with a score of 68 or MATH SECTION SCORE with a score of 580

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1750 Calculus For The Life Sciences With Applications I**

Definitions of trigonometric functions, solving trigonometric equations, functions, limits and derivatives, exponential and logarithmic functions, and applications. Course is not applicable toward the undergraduate Mathematics major requirements.

**Prerequisites:** MATH 1320 with a minimum grade of C- or MATH 1340 with a minimum grade of C- or Math - Coll Algebra Placement with a score of 15 or ACT Math with a score of 24 or SAT Mathematics with a score of 560 or Aleks Math Placement Test with a score of 68 or Aleks Math Placement Retest with a score of 68 or MATH SECTION SCORE with a score of 580

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1760 Calculus For The Life Sciences With Applications II**

Indefinite and definite integrals, probability, vectors, least squares, differential equations. Course is not applicable toward the undergraduate Mathematics major requirements.

**Prerequisites:** MATH 1750 with a minimum grade of C- or MATH 1850 with a minimum grade of C- or MATH 1830 with a minimum grade of C-

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1830 Calculus I For Mathematicians, Scientists And Educators**

Limits, differentiation, Fundamental Theorem of Calculus, Mean Value Theorem, curve sketching, maxima/minima, definite and indefinite integrals, applications. The emphasis is on the rigorous aspects and foundational ideas of calculus. Of interest to students requiring a conceptual understanding of calculus. Course is not applicable toward the undergraduate Mathematics major requirements.

**Prerequisites:** (MATH 1340 with a minimum grade of C- or Aleks Math Placement Test with a score of 76 or Aleks Math Placement Retest with a score of 76) or (MATH 1320 with a minimum grade of C- or ACT Math with a score of 27 or SAT Mathematics with a score of 610 or MATH SECTION SCORE with a score of 630 or Math - Coll Algebra Placement with a score of 15) and (MATH 1330 with a minimum grade of C- or Math - Trigonometry Placement with a score of 12)

**Term Offered:** Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1840 Calculus II For Mathematicians, Scientists And Educators**

Applications and techniques of integration, polar coordinates and calculus of plane curves, infinite series and Taylor series, vectors and geometry of space. The emphasis is on the rigorous aspects and foundational ideas of calculus. Of interest to students requiring a conceptual understanding of calculus.

**Prerequisites:** MATH 1830 with a minimum grade of C- or MATH 1850 with a minimum grade of C- or MATH 1920 with a minimum grade of C-

**Term Offered:** Spring, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1850 Single Variable Calculus I**

Limits, differentiation, Fundamental Theorem of Calculus, curve sketching, maxima/minima, definite and indefinite integrals, applications. Course is not applicable toward the undergraduate Mathematics major requirements.

**Prerequisites:** (MATH 1340 with a minimum grade of C- or Aleks Math Placement Test with a score of 76 or Aleks Math Placement Retest with a score of 76) or (MATH 1320 with a minimum grade of C- or ACT Math with a score of 27 or SAT Mathematics with a score of 610 or MATH SECTION SCORE with a score of 630 or Math - Coll Algebra Placement with a score of 15) and (MATH 1330 with a minimum grade of C- or Math - Trigonometry Placement with a score of 12)

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1860 Single Variable Calculus II**

Applications and techniques of integration, polar coordinates and calculus of plane curves, infinite series and Taylor series, vectors and geometry of space.

**Prerequisites:** MATH 1830 with a minimum grade of C- or MATH 1850 with a minimum grade of C-

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1890 Elementary Linear Algebra**

Matrix algebra, systems of linear equations, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, applications, additional topics chosen from Google's page rank algorithm, Digital Image Compression, and others.

**Prerequisites:** MATH 1840 with a minimum grade of C- or MATH 1860 with a minimum grade of C-

**Term Offered:** Spring, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 1980 Topics In Mathematics**

Selected topics in mathematics.

**Term Offered:** Spring, Fall

**MATH 2190 Foundations of Mathematics**

This course lays the logical and set-theoretic foundations for upper level mathematics courses. Topics include: logical connectives, quantifiers techniques of proof set operations functions equivalence classes partitions, cardinality, natural numbers, rationals, real numbers.

**Prerequisites:** MATH 1830 with a minimum grade of C- or MATH 1850 with a minimum grade of C-

**Term Offered:** Spring

**MATH 2450 Calculus For Engineering Technology I**

Differential calculus of algebraic and trigonometric functions, including limits, curve sketching, motion, maxima/minima, related rates, integral calculus of algebraic functions.

**Prerequisites:** (MATH 1340 with a minimum grade of C- or Aleks Math Placement Test with a score of 76 or Aleks Math Placement Retest with a score of 76) or (MATH 1320 with a minimum grade of C- or ACT Math with a score of 27 or SAT Mathematics with a score of 610 or MATH SECTION SCORE with a score of 630 or Math - Coll Algebra Placement with a score of 15) and (MATH 1330 with a minimum grade of C- or Math - Trigonometry Placement with a score of 12)

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 2460 Calculus For Engineering Technology II**

Transcendental functions, methods of integration, applications of the integral, polar coordinates, vectors and vector operation, lines and planes, parametric equations.

**Prerequisites:** MATH 2450 with a minimum grade of C- or MATH 1850 with a minimum grade of C-

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 2600 Introduction To Statistics**

An introduction to descriptive and inferential statistical methods including point and interval estimation, hypothesis testing and regression. No credit allowed if taken after MATH 3610 or 4680 credit not allowed for both MATH 2600 and 2630. Course is not applicable toward the undergraduate Mathematics major requirements.

**Prerequisites:** MATH 1200 with a minimum grade of C- or ACT Math with a score of 20 or SAT Mathematics with a score of 480 or Aleks Math Placement Test with a score of 46 or Aleks Math Placement Retest with a score of 46 or Math - Coll Algebra Placement with a score of 10 or MATH SECTION SCORE with a score of 510

**Term Offered:** Spring, Summer, Fall

Core Mathematics, Trans Mod Mathematics

**MATH 2620 Discrete Probability**

Sample spaces, events, counting techniques, probability distributions and their applications. No credit if taken after 4680. Course is not applicable toward the undergraduate Mathematics major requirements.

**Prerequisites:** MATH 1180 with a minimum grade of C- or MATH 1200 with a minimum grade of C- or Math - Coll Algebra Placement with a score of 10 or Math - Elem Algebra Placement with a score of 12 or ACT Math with a score of 20 or SAT Mathematics with a score of 480 or Aleks Math Placement Test with a score of 46 or Aleks Math Placement Retest with a score of 46 or MATH SECTION SCORE with a score of 510

**Term Offered:** Spring

**MATH 2640 Statistics for Applied Science**

Introduction to statistical methods. Modeling relationships between variables. Basic concepts in probability. Introduction to design of experiments, surveys and observational studies. Overview of statistical procedures used in applied science literature.

**Prerequisites:** (MATH 1200 with a minimum grade of C-) or ACT Math with a score of 20 or SAT Mathematics with a score of 510 or Aleks Math Placement Test with a score of 46 or Aleks Math Placement Retest with a score of 46 or Math - Coll Algebra Placement with a score of 10

**Term Offered:** Spring, Fall

**MATH 2850 Elementary Multivariable Calculus**

Geometry of functions of several variables, partial differentiation, multiple integrals, vector algebra and calculus (including Theorems of Green, Gauss and Stokes), and applications.

**Prerequisites:** MATH 1840 with a minimum grade of C- or MATH 1860 with a minimum grade of C-

**Term Offered:** Spring, Summer, Fall

**MATH 2860 Elementary Differential Equations**

An introduction to the analysis and solution of ordinary differential equations with emphasis on the fundamental techniques for solving linear differential equations.

**Prerequisites:** MATH 2850 with a minimum grade of C-

**Term Offered:** Spring, Summer, Fall

**MATH 2890 Numerical Methods And Linear Algebra**

Topics include: matrices, characteristic roots, solution of linear and nonlinear equations, curve fitting, integration, differentiation and numerical solution of ordinary differential equations. MATLAB is introduced and used to analyze problems. Additional topics are chosen from Google's page rank algorithm, Digital Image Compression, and others.

**Prerequisites:** MATH 1830 with a minimum grade of C- or MATH 1850 with a minimum grade of C- or MATH 1920 with a minimum grade of C-

**Term Offered:** Spring, Summer, Fall

**MATH 3000 Symbolic Logic**

A study of propositional and predicate logic, the symbolic techniques used to evaluate deductive arguments. Topics may include computability, set theory, Bayesianism and other formal systems with mathematical or philosophical relevance.

**Prerequisites:** MATH 1180 with a minimum grade of C-

**Term Offered:** Spring, Fall

**MATH 3190 Introduction To Mathematical Analysis**

This course is intended to introduce students to mathematical analysis. The focus will be on learning to write clear, rigorous proofs. Topics include set theory and logic, the real number system and its topology, sequences, limits and continuity.

**Prerequisites:** MATH 1840 with a minimum grade of C- or MATH 1860 with a minimum grade of C-

**Term Offered:** Fall

**MATH 3200 Number Theory**

Divisibility, congruences, diophantine equations, numerical functions, quadratic reciprocity.

**Prerequisites:** MATH 2190 with a minimum grade of C- or MATH 3190 with a minimum grade of C-

**Term Offered:** Spring, Fall

**MATH 3320 Introduction To Abstract Algebra**

Sets and mappings, integers, groups, rings and applications.

**Prerequisites:** MATH 2190 with a minimum grade of C- or MATH 3190 with a minimum grade of C-

**Term Offered:** Spring

**MATH 3440 Fundamentals Of Modern Geometry I**

Euclidean geometry from a modern viewpoint, constructions and transformations. Primarily for students in secondary education.

**Prerequisites:** MATH 1840 with a minimum grade of C- or MATH 1860 with a minimum grade of C-

**Term Offered:** Fall

**MATH 3450 Fundamentals Of Modern Geometry II**

Euclidean geometry from a modern viewpoint, constructions and transformations. Primarily for students in secondary education.

**Prerequisites:** MATH 3440 with a minimum grade of C-

**Term Offered:** Spring

**MATH 3510 History Of Mathematics**

Contributions to the development of mathematics by various groups and individuals from the earliest history to the present, with special emphasis on the elementary branches: arithmetic, algebra, geometry and calculus.

**Prerequisites:** MATH 1840 with a minimum grade of C- or MATH 1860 with a minimum grade of C-

**Term Offered:** Fall

**MATH 3610 Statistical Methods I**

Basic probability, sampling, descriptive statistics, statistical inference, regression, correlation, analysis of variance, goodness of fit, model formulation and testing.

**Prerequisites:** MATH 1840 with a minimum grade of C- or MATH 1860 with a minimum grade of C- or MATH 3190 with a minimum grade of C-

**Term Offered:** Fall

**MATH 3620 Statistical Methods II**

Multiple regression, analysis of covariance, standard experimental designs, contingency tables, nonparametric methods and methods for sample surveys.

**Prerequisites:** MATH 3610 with a minimum grade of C-

**Term Offered:** Spring

**MATH 3920 Junior Readings**

Selected subjects in mathematics of special interest to students and the professor.

**Term Offered:** Spring, Summer, Fall

**MATH 4300 Linear Algebra I**

Theory of vector spaces and linear transformations, including such topics as matrices, determinants, inner products, eigenvalues and eigenvectors, and rational and Jordan canonical forms.

**Prerequisites:** MATH 2190 with a minimum grade of C- or MATH 3190 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4310 Linear Algebra II**

Hermitian and normal operators, multilinear forms, spectral theorem and other topics.

**Prerequisites:** MATH 4300 with a minimum grade of C-

**MATH 4330 Abstract Algebra I**

Arithmetic of the integers, unique factorization and modular arithmetic group theory including normal subgroups, factor groups, cyclic groups, permutations, homomorphisms, the isomorphism theorems, abelian groups and p-groups.

**Prerequisites:** MATH 2190 with a minimum grade of C- or MATH 3190 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4340 Abstract Algebra II**

Ring theory including integral domains, field of quotients, homomorphisms, ideals, Euclidean domains, polynomial rings, vector spaces, roots of polynomials and field extensions.

**Prerequisites:** MATH 4330 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4350 Applied Linear Algebra**

Matrices, systems of equations, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, singular value decomposition, pseudoinverses, rank, numerical methods and applications to various areas, e.g., the Google Matrix or Digital Image Compression or others.

**Prerequisites:** MATH 1890 with a minimum grade of C- or MATH 2890 with a minimum grade of C-

**Term Offered:** Spring, Summer

**MATH 4380 Discrete Structures And Analysis Of Algorithms**

Discrete mathematical structures for applications in computer science such as graph theory, combinatorics, and groups theory, asymptotics, recurrence relations and analysis of algorithms.

**Prerequisites:** MATH 3320 with a minimum grade of C- or MATH 4330 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4450 Introduction To Topology I**

Metric spaces, topological spaces, continuous maps, bases and subbases, closure and interior operators, products, subspaces, sums, quotients, separation axioms, compactness and local compactness.

**Prerequisites:** MATH 2190 with a minimum grade of C- or MATH 3190 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4460 Introduction To Topology II**

Connectedness and local connectedness, convergence, metrization, function spaces. The fundamental groups and its properties, covering spaces, classical applications, e.g. Jordan Curve Theorem, Fundamental Theorem of Algebra, Brouwer's Fixed Point Theorem.

**Prerequisites:** (MATH 4450 with a minimum grade of C- and MATH 3320 with a minimum grade of C-) or (MATH 4450 with a minimum grade of C- and MATH 4330 with a minimum grade of C-)

**Term Offered:** Spring

**MATH 4540 Classical Differential Geometry I**

Smooth curves in Euclidean space including the Frenet formulae. Immersed surfaces with the Gauss map, principal curvatures and the fundamental forms. Special surfaces including ruled surfaces and minimal surfaces. Intrinsic Geometry including the Gauss Theorem Egregium.

**Prerequisites:** MATH 2860 with a minimum grade of C-

**MATH 4550 Classical Differential Geometry II**

Tensors, vector fields, and the Cartan approach to surface theory, Bonnet's Theorem and the construction of surfaces via solutions of the Gauss Equation. Geodesics parallel transport, and Jacobi Fields. Theorems of a global nature such as Hilbert's Theorem or the Theorem of Hopf-Rinow.

**Prerequisites:** MATH 4540 with a minimum grade of C-

**MATH 4600 Advanced Statistical Methods I**

Basics of descriptive statistics, study designs and statistical inference. Properties of, and assumptions required for, inference for means, variances, and proportions from one and two-sample paired and unpaired studies. Introduction to ANOVA with multiple comparisons. Model assessment and diagnostics. Statistical software will be employed. Opportunities to apply procedures to real data. Emphasis placed on the foundations to approaches in introductory statistics.

**Prerequisites:** MATH 2600 with a minimum grade of D- or MATH 2640 with a minimum grade of D- or MATH 3610 with a minimum grade of D- or MATH 4690 with a minimum grade of D-

**Term Offered:** Fall

**MATH 4610 Applications Of Statistics II**

Continuation of Applications of Statistics I.

**Prerequisites:** MATH 4600 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4620 Theory Of Interest**

This course covers the measurement of interest, certain annuities, yield rates, amortization and sinking funds, bonds and other securities and application of interest theory.

**Prerequisites:** MATH 1840 with a minimum grade of C- or MATH 1860 with a minimum grade of C-

**Term Offered:** Spring, Fall

**MATH 4640 Statistical Computing**

Modern statistical computing, including programming tools, modern programming methodologies, design of data structures and algorithms, numerical computing and graphics. Additional topics selected from simulation studies, rejection sampling, importance sampling, Monte Carlo integration, and bootstrapping.

**Prerequisites:** MATH 3610 with a minimum grade of C- or MATH 4600 with a minimum grade of C- or MATH 4690 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4680 Introduction To Theory Of Probability**

Probability spaces, random variables, probability distributions, moments and moment generating functions, limit theorems, transformations and sampling distributions.

**Prerequisites:** MATH 2850 with a minimum grade of C-

**Term Offered:** Summer, Fall

**MATH 4690 Introduction To Mathematical Statistics**

Sampling distributions, point and interval estimation, hypothesis testing, regression and analysis of variance.

**Prerequisites:** MATH 4680 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4710 Methods Of Numerical Analysis I**

Floating point arithmetic polynomial interpolation numerical solution of nonlinear equations Newton's method. Likely topics include: numerical differentiation and integration solving systems of linear equations Gaussian elimination LU decomposition Gauss-Seidel method.

**Prerequisites:** MATH 2860 with a minimum grade of C-

**Term Offered:** Spring, Fall

**MATH 4720 Methods Of Numerical Analysis II**

Likely topics include: Computation of eigenvalues and eigenvectors solving systems of nonlinear equations least squares approximations rational approximations cubic splines fast Fourier transforms numerical solutions to initial value problems ordinary and partial differential equations.

**Prerequisites:** MATH 4710 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4740 Advanced Applied Mathematics I**

Series and numerical solutions to ordinary differential equations, special functions, orthogonal functions, Sturm-Liouville problems, self-adjointness, vector analysis.

**Prerequisites:** MATH 2860 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4750 Advanced Applied Mathematics II**

Continuation of vector analysis, introduction to complex analysis, partial differential equations, Fourier series and integrals.

**Prerequisites:** MATH 4740 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4760 Actuarial Mathematics I**

Survival distributions and life tables, life insurance, life annuities, benefit premiums and reserves and multiple life functions are some topics covered in this course.

**Prerequisites:** MATH 4680 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4770 Actuarial Mathematics II**

Continuation of Actuarial Mathematics I. Multiple decrement models, collective risk models and applications of risk theory.

**Prerequisites:** MATH 4760 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4780 Advanced Calculus**

Extrema for functions of one or more variables, Lagrange multipliers, indeterminate forms, inverse and implicit function theorems, uniform convergences, power series, transformations, Jacobians, multiple integrals.

**Prerequisites:** MATH 2850 with a minimum grade of C-

**MATH 4800 Ordinary Differential Equations**

Modern theory of differential equations transforms and matrix methods existence theorems and series solutions and other selected topics.

**Prerequisites:** MATH 2860 with a minimum grade of C-

**Term Offered:** Spring, Fall

**MATH 4810 Partial Differential Equations**

First and second order equations numerical methods separation of variables solutions of heat and wave equations using eigenfunction techniques and other selected topics.

**Prerequisites:** MATH 2860 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4820 Introduction To Real Analysis I**

The real number system continuity and differentiability of functions convergence of sequences and series applications.

**Prerequisites:** MATH 2190 with a minimum grade of C- or MATH 3190 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4830 Introduction To Real Analysis II**

Riemann Integral limits of functions elementary metric space theory including compactness, connectedness and completeness. Optional topics include differentiable functions on Rn the Implicit and Inverse Function Theorems.

**Prerequisites:** MATH 4820 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4860 Calculus Of Variations And Optimal Control I**

Conditions for an extrema (Euler's equations, Erdman corner conditions, conditions of Legendre, Jacobi, and Weierstrass, fields of extremals, Hilbert's invariant integral) Raleigh-Ritz method isoperimetric problems Lagrange, Mayer-Bolza problems. Recommended: MATH 4820.

**Prerequisites:** MATH 1890 with a minimum grade of C- or MATH 2890 with a minimum grade of C-

**Term Offered:** Fall

**MATH 4870 Calculus Of Variations And Optimal Control II**

Pontryagin's maximum principle necessary and sufficient conditions for optimal control, controllability, time optimal control, existence of optimal controls, relationship to the calculus of variations.

**Prerequisites:** MATH 4860 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4880 Complex Variables**

Analytic functions Cauchy's theorem Taylor and Laurent series residues contour integrals conformal mappings, analytic continuation and applications.

**Prerequisites:** MATH 2860 with a minimum grade of C-

**Term Offered:** Spring

**MATH 4900 Senior Seminar**

Seminar on a topic not usually covered in a course. Library research and paper to be expected.

**Term Offered:** Spring, Summer, Fall

**MATH 4920 Senior Readings**

Selected subjects in mathematics of special interest to students and the professor. (By arrangement with professor and student.)

**Term Offered:** Spring, Summer, Fall

**MATH 4940 Internship in the Mathematical Sciences**

MATH 4940 Co-Op Experience [3 credit hours] Approved internship experience. Course may be repeated for credit with departmental permission. Terms Offered: Spring, Summer, Fall

**Term Offered:** Spring, Summer, Fall

**MATH 4960 Actuarial Science Problem Seminar**

The primary activity will be student solution and presentation of problems of a type given on actuarial exams.

**Term Offered:** Spring, Fall

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## 8.3E: Exercises - Annuities and Sinking Funds - Mathematics

**FINITE MATHEMATICS (Math 120B) - Mathematics of Finance**

**Annuities: terminology, issues, and problem types**

ANNUITIES ARE SEQUENCES OF (MULTIPLE) PAYMENTS WITH COMPOUND INTEREST

MULTIPLE PAYMENTS ===> ANNUITY FORMULAS

TYPE OF COMPOUNDING: ONLY PERIODIC

Distinguish from:

SINGLE PAYMENT ===> COMPOUND AMOUNT FORMULAS

TYPE OF COMPOUNDING: PERIODIC OR CONTINUOUS

CATEGORIZATION OF ANNUITIES (See page 70 in __Mathematics of Finance__, 2d ed, by Petr Zima and Robert L. Brown, Schaum's Outlines McGraw-Hill, 1996.

Contingent Annuities (term depends upon an uncertain event) vs Annuities Certain (dates of payments are fixed)

General Annuities vs Simple Annuities (payment interval and interest compounding interval coincide)

Annuities Due (payments at beginning of intervals) vs Ordinary Annuities (payments at end of intervals)

Deferred Annuities (the first payment is due at some later, deferred date)

IN MATH 141, WE WILL ONLY DEAL WITH ANNUITIES CERTAIN WHICH ARE SIMPLE ANNUITIES. WE WILL TREAT SIMPLE ANNUITIES CERTAIN OF ALL THREE TYPES: ANNUITIES DUE, ORDINARY ANNUITIES, AND DEFERRED ANNUITIES.

ANNUITY FORMULAS: [formulas readily derived from others are in italics]

FUTURE VALUE OF AN ORDINARY ANNUITY (p. 458 in textbook)

REQUIRED PAYMENT INTO AN ORDINARY ANNUITY FOR SINKING FUND (p. 461)

FUTURE VALUE OF AN ANNUITY DUE (p. 463)

PRESENT VALUE OF AN ORDINARY ANNUITY (p. 468)

PRESENT VALUE OF AN ANNUITY DUE (p. 472)

PRESENT VALUE OF A DEFERRED ORDINARY ANNUITY (p. 474)

PAYMENT SIZE FOR AN AMORTIZED LOAN (P. 480)

UNPAID BALANCE OR PAYOFF AMOUNT OF AN AMORTIZED LOAN (p. 482)

POSSIBLE PARAMETERS FOR FORMULAS [All relate to periodic compounding of interest on the annuity payments]

NOMINAL (ANNUAL) RATE ["APR"]

PERIOD (YEAR, HALF-YEAR,QUARTER (3 MO'S) TWO-MONTHS, MONTH, … )

NUMBER OF PERIODS IN ONE YEAR

PERIODIC RATE

NUMBER OF YEARS

TOTAL NUMBER OF PERIODS

PERIODS FOR WHICH AN ORDINARY ANNUITY IS DEFERRED

SIZE OF REGULAR PAYMENT IN AN ANNUITY

PRESENT VALUE

FUTURE VALUE

1. Each of the parameters above has a commonly used letter consistent with those used in our textbook. You should be able to associate each of the parameters with a letter (or in some cases more than one) such as: A, FV, i , k, m, n, P, PV, r, R, or S, some of these with subscripts. Also, in each of the examples in class and homework exercises you do, you should be able to confidently identify the procedure from those listed above under formulas and solutions. You should also be familiar with the "s, n angle i" and "a, n angle i" notation used in finance mathematics (textbook, pp. 458, 468 respectively), as it relates to the annuity formulas. You will not be required to memorize those formulas you will be expected to understand their notation and to apply them in appropriate contexts, including determining when to use each formula.