Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Dick Schwanke Finite Math 111 Harford Community College Fall 2013"

Transcription

1 Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of Exponents and Logarithms Calculating Compound Interest Comparing different Compounding Periods Computing the Present Value of A Dollars About Zero-Coupon Bonds 2 Time Value of Money Problems Exercise 6.2, pp Recall P = A(1+(r/n)) -nt or A = P(1+(r/n)) nt Present value is the P dollars (at the start) Future value is the A dollars (at the end) Find the present value: #20, 22, 26 Find the effective rate of interest: #34, 36 Find investment amounts: #48, 50 Find value of zero-coupon bond: #86, 88 Discuss the approach to question #97 with four banks, summary data on p End Sections of Chapter 6; Using Excel for Financial Calculations Page 1 of 6

2 Annuities Definition: Annuity is a sequence of equal periodic deposits Investing money in small amounts at periodic intervals is typical method Annual life insurance premiums (whole life) Monthly savings deposits at the bank perhaps for a college fund or house down payment Installment loan payments perhaps for a car 401(k) dollar averaging in the stock market Funding for a sinking fund payback Amount of annuity is the sum of all deposits plus all interest accumulated 4 Finding the amount of an Annuity Using compound interest A = P(1+(r/n)) nt Where t is the number of years P is the principal invested r is the annual interest rate n is the times per year it is compounded First deposit is worth A 1 = P(1+i) n Second deposit worth A 2 = P(1+i) (n-1) Third deposit worth A 3 = P(1+i) (n-2) until final deposit is P without interest 5 Finding the amount of an Annuity Add all those deposits and interest Total A = A 1 + A 2 + A A (n-1) + A n A= P(1+i) n + P(1+i) (n-1) + P(1+i) (n-2) + P(1+i) (n-3) P(1+i) + P Factor out the P and reverse the order Total A = P[ 1+ (1+i) (1+i) (n-1) ] The (1+i) terms geometric sequence = [1-(1+i) n ] / [1-(1+i)] (from Appendix 4) 6 End Sections of Chapter 6; Using Excel for Financial Calculations Page 2 of 6

3 Finding the amount of an Annuity Simply the sequence to get the value of the annuity after n deposits is A = P [ ((1+i) n -1)/ i ] Note: when the n th deposit is made the first deposit has earned interest for n-1 compounding periods Note: be careful with your arithmetic, e.g.: n deposits using (n-1) periods e.g. : multiple nested parenthesis 7 Working a few examples: page 326 Saving for a house (or one year at Harvard) #28 Funding a Keogh Plan for retirement #30 Sinking Fund to pay off bonds #32 (also see using Excel in examples #10-11, on pages ; website) Value of an IRAs #36 So you want to be a millionaire #40 8 Finding Present Value of an Annuity (recall) Present Value is the amount of money needed now, to obtain an amount A in the future. Present Value of an annuity is the sum of present values of the withdraws. Alternately: Present Value of an annuity is the money need now, so that if invested at i percent, n equal dollar amounts can be withdrawn to zero left 9 End Sections of Chapter 6; Using Excel for Financial Calculations Page 3 of 6

4 Finding Present Value of an Annuity Similar to earlier method Recall we defined a -n = 1/ a n if a 0 Sum the present values (V n ) for all of the planned withdraws First withdraw is worth V 1 = P(1+i) -1 Second withdraw is worth V 2 = P(1+i) -2 until final (n th ) withdraw is V 2 = P(1+i) -n 10 Finding Present Value of an Annuity Add Present Values for all withdraws Total V = V 1 + V 2 + V V (n-1) + V n V = P(1+i) -1 + P(1+i) P(1+i) -n Factor out the P(1+i) -n and substitute the geometric sequence (as before) to get Present Value of the Annuity is V = P[1-(1+i) -n ]/ i] 11 Work some examples Retirement Account, page 342, #16 How much to invest today? At age 65, can expect to live 25 years Invested at 4% PA, compound monthly Need to guarantee $300 / month Corporate Leasing page 342, #46 Which piece is the better investment? Model A costs $50K, saves $12K/year in labor, has a useful life of 10 years Model B costs $42K, saves $10K/year in labor costs, has useful life of 8 years Time value of money is 10% per annum 12 End Sections of Chapter 6; Using Excel for Financial Calculations Page 4 of 6

5 Amortization, or who is Mort? A fixed interest rate loan is said to be amortized, if both principal and interest are paid by sequence of equal payments made over equal periods of time Take Present Value of the Annuity V = P[1-(1+i) -n ] / i], solve for Payment Payment required to pay off a loan of V dollars, borrowed for n payment periods, at i interest rate per period is P = V[ i / (1-(1+i) -n ] 13 Work an example Mortgage Payments, page 343 #32 What will the monthly payment be? Summer home will cost $180,000 $60,000 in present home equity for down payment Finance 25 years at 5.1% compounded monthly BTY, the Refinancing Mortgage #30 would make a great test question Note: we will return to mortgage payments with Excel later 14 Pricing Bonds Definition: Face Amount (or Face Value or Par Value or Denomination) of a bond is the amount paid to the bond holder at maturity. Note: often this is the amount paid by the bondholder at original issue Nominal Interest (or Coupon Rate) is the contractual interest paid on the bond Note: normally quoted as annual percentage rate of the face amount Note: conventionally paid semi-annually 15 End Sections of Chapter 6; Using Excel for Financial Calculations Page 5 of 6

6 More About Bond Pricing Prices of Corporate Bonds fluctuate Reasons might include Trading at a Premium means price is higher than face amount Trading at a Discount means price is lower than face amount 16 Still More About Bond Pricing True Yield means the combination of trading price and interest rate To calculate the true interest rate = sum an annuity of semiannual interest payments (for now until maturity date) plus the present value of a single future payment at maturity Work example, page 344, #48 (also see using Excel in examples #11-12, on pages ; website) 17 Notes of the Day Session #3 - got to slide #8 problems Resume this same set of session #3 slides at session #4 Session #4 do slide #12 problems Session #4 discuss discount and premium pricing for bonds 18 End Sections of Chapter 6; Using Excel for Financial Calculations Page 6 of 6

Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Dick Schwanke Finite Math 111 Harford Community College Fall 2013 Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

More information

300 Chapter 5 Finance

300 Chapter 5 Finance 300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for $200,000 with a down payment of $40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which

More information

Compound Interest Formula

Compound Interest Formula Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At

More information

Finite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan

Finite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan Finite Mathematics Helene Payne CHAPTER 6 Finance 6.1. Interest savings account bond mortgage loan auto loan Lender Borrower Interest: Fee charged by the lender to the borrower. Principal or Present Value:

More information

Finance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization

Finance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need

More information

Mathematics. Rosella Castellano. Rome, University of Tor Vergata

Mathematics. Rosella Castellano. Rome, University of Tor Vergata and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings

More information

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved. 2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical defined-contribution

More information

Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows 1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter

More information

Chapter 22: Borrowings Models

Chapter 22: Borrowings Models October 21, 2013 Last Time The Consumer Price Index Real Growth The Consumer Price index The official measure of inflation is the Consumer Price Index (CPI) which is the determined by the Bureau of Labor

More information

E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is

E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =

More information

Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition

Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future

More information

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM-09-05. January 14, 2014: Questions and solutions 58 60 were

More information

Chapter 16. Debentures: An Introduction. Non-current Liabilities. Horngren, Best, Fraser, Willett: Accounting 6e 2010 Pearson Australia.

Chapter 16. Debentures: An Introduction. Non-current Liabilities. Horngren, Best, Fraser, Willett: Accounting 6e 2010 Pearson Australia. PowerPoint to accompany Non-current Liabilities Chapter 16 Learning Objectives 1. Account for debentures payable transactions 2. Measure interest expense by the straight line interest method 3. Account

More information

Click Here to Buy the Tutorial

Click Here to Buy the Tutorial FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin-534/fin-534-week-4-quiz-3- str/ For more course tutorials visit www.tutorialoutlet.com Which of the following

More information

1. Annuity a sequence of payments, each made at equally spaced time intervals.

1. Annuity a sequence of payments, each made at equally spaced time intervals. Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology

More information

Bonds. Describe Bonds. Define Key Words. Created 2007 By Michael Worthington Elizabeth City State University

Bonds. Describe Bonds. Define Key Words. Created 2007 By Michael Worthington Elizabeth City State University Bonds OBJECTIVES Describe bonds Define key words Explain why bond prices fluctuate Compute interest payments Calculate the price of bonds Created 2007 By Michael Worthington Elizabeth City State University

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective

More information

Discounted Cash Flow Valuation

Discounted Cash Flow Valuation 6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

More information

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

More information

ANALYSIS OF FIXED INCOME SECURITIES

ANALYSIS OF FIXED INCOME SECURITIES ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its

More information

Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1

Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1 Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation

More information

Appendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C- 1

Appendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C- 1 C Time Value of Money C- 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C- 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.

More information

Fin 3312 Sample Exam 1 Questions

Fin 3312 Sample Exam 1 Questions Fin 3312 Sample Exam 1 Questions Here are some representative type questions. This review is intended to give you an idea of the types of questions that may appear on the exam, and how the questions might

More information

Finance 197. Simple One-time Interest

Finance 197. Simple One-time Interest Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for

More information

Check off these skills when you feel that you have mastered them.

Check off these skills when you feel that you have mastered them. Chapter Objectives Check off these skills when you feel that you have mastered them. Know the basic loan terms principal and interest. Be able to solve the simple interest formula to find the amount of

More information

Chapter F: Finance. Section F.1-F.4

Chapter F: Finance. Section F.1-F.4 Chapter F: Finance Section F.1-F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given

More information

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM-09-05. April 28, 2014: Question and solutions 61 were added. January 14, 2014:

More information

You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?

You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy? 1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each

More information

Module 1: Corporate Finance and the Role of Venture Capital Financing TABLE OF CONTENTS

Module 1: Corporate Finance and the Role of Venture Capital Financing TABLE OF CONTENTS 1.0 ALTERNATIVE SOURCES OF FINANCE Module 1: Corporate Finance and the Role of Venture Capital Financing Alternative Sources of Finance TABLE OF CONTENTS 1.1 Short-Term Debt (Short-Term Loans, Line of

More information

Time-Value-of-Money and Amortization Worksheets

Time-Value-of-Money and Amortization Worksheets 2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or

More information

Chapter 6 Interest rates and Bond Valuation. 2012 Pearson Prentice Hall. All rights reserved. 4-1

Chapter 6 Interest rates and Bond Valuation. 2012 Pearson Prentice Hall. All rights reserved. 4-1 Chapter 6 Interest rates and Bond Valuation 2012 Pearson Prentice Hall. All rights reserved. 4-1 Interest Rates and Required Returns: Interest Rate Fundamentals The interest rate is usually applied to

More information

Topics. Chapter 5. Future Value. Future Value - Compounding. Time Value of Money. 0 r = 5% 1

Topics. Chapter 5. Future Value. Future Value - Compounding. Time Value of Money. 0 r = 5% 1 Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series

More information

Chapter 6. Interest Rates And Bond Valuation. Learning Goals. Learning Goals (cont.)

Chapter 6. Interest Rates And Bond Valuation. Learning Goals. Learning Goals (cont.) Chapter 6 Interest Rates And Bond Valuation Learning Goals 1. Describe interest rate fundamentals, the term structure of interest rates, and risk premiums. 2. Review the legal aspects of bond financing

More information

1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?

1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? Chapter 2 - Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in

More information

Present Value Concepts

Present Value Concepts Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts

More information

Chapter The Time Value of Money

Chapter The Time Value of Money Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

More information

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26 Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.

More information

Example. L.N. Stout () Problems on annuities 1 / 14

Example. L.N. Stout () Problems on annuities 1 / 14 Example A credit card charges an annual rate of 14% compounded monthly. This month s bill is $6000. The minimum payment is $5. Suppose I keep paying $5 each month. How long will it take to pay off the

More information

Undergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics

Undergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics A Semester Course in Finite Mathematics for Business and Economics Marcel B. Finan c All Rights Reserved August 10,

More information

Vilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis

Vilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis Vilnius University Faculty of Mathematics and Informatics Gintautas Bareikis CONTENT Chapter 1. SIMPLE AND COMPOUND INTEREST 1.1 Simple interest......................................................................

More information

APPENDIX 3 TIME VALUE OF MONEY. Time Lines and Notation. The Intuitive Basis for Present Value

APPENDIX 3 TIME VALUE OF MONEY. Time Lines and Notation. The Intuitive Basis for Present Value 1 2 TIME VALUE OF MONEY APPENDIX 3 The simplest tools in finance are often the most powerful. Present value is a concept that is intuitively appealing, simple to compute, and has a wide range of applications.

More information

Index Numbers ja Consumer Price Index

Index Numbers ja Consumer Price Index 1 Excel and Mathematics of Finance Index Numbers ja Consumer Price Index The consumer Price index measures differences in the price of goods and services and calculates a change for a fixed basket of goods

More information

FinQuiz Notes 2 0 1 4

FinQuiz Notes 2 0 1 4 Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

More information

Lesson 4 Annuities: The Mathematics of Regular Payments

Lesson 4 Annuities: The Mathematics of Regular Payments Lesson 4 Annuities: The Mathematics of Regular Payments Introduction An annuity is a sequence of equal, periodic payments where each payment receives compound interest. One example of an annuity is a Christmas

More information

TVM Applications Chapter

TVM Applications Chapter Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (long-term receivables) 7 Long-term assets 10

More information

Introduction to Real Estate Investment Appraisal

Introduction to Real Estate Investment Appraisal Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has

More information

A = P [ (1 + r/n) nt 1 ] (r/n)

A = P [ (1 + r/n) nt 1 ] (r/n) April 23 8.4 Annuities, Stocks and Bonds ---- Systematic Savings Annuity = sequence of equal payments made at equal time periods i.e. depositing $1000 at the end of every year into an IRA Value of an annuity

More information

Activity 3.1 Annuities & Installment Payments

Activity 3.1 Annuities & Installment Payments Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.

More information

Chapter 21: Savings Models

Chapter 21: Savings Models October 16, 2013 Last time Arithmetic Growth Simple Interest Geometric Growth Compound Interest A limit to Compounding Problems Question: I put $1,000 dollars in a savings account with 2% nominal interest

More information

CHAPTER 17 ENGINEERING COST ANALYSIS

CHAPTER 17 ENGINEERING COST ANALYSIS CHAPTER 17 ENGINEERING COST ANALYSIS Charles V. Higbee Geo-Heat Center Klamath Falls, OR 97601 17.1 INTRODUCTION In the early 1970s, life cycle costing (LCC) was adopted by the federal government. LCC

More information

Discounted Cash Flow Valuation

Discounted Cash Flow Valuation Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

More information

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value. Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values

More information

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the Hewlett-Packard

More information

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued 6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

More information

, plus the present value of the $1,000 received in 15 years, which is 1, 000(1 + i) 30. Hence the present value of the bond is = 1000 ;

, plus the present value of the $1,000 received in 15 years, which is 1, 000(1 + i) 30. Hence the present value of the bond is = 1000 ; 2 Bond Prices A bond is a security which offers semi-annual* interest payments, at a rate r, for a fixed period of time, followed by a return of capital Suppose you purchase a $,000 utility bond, freshly

More information

Bond Price Arithmetic

Bond Price Arithmetic 1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously

More information

The Time Value of Money (contd.)

The Time Value of Money (contd.) The Time Value of Money (contd.) February 11, 2004 Time Value Equivalence Factors (Discrete compounding, discrete payments) Factor Name Factor Notation Formula Cash Flow Diagram Future worth factor (compound

More information

A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%

A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.

More information

Chapter 2 Present Value

Chapter 2 Present Value Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted

More information

FinQuiz Notes 2 0 1 5

FinQuiz Notes 2 0 1 5 Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

More information

FI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY

FI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY FI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY 1. (3 points) BS16 What is a 401k plan Most U.S. households single largest lifetime source of savings is

More information

Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010

Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010 P a g e 1 Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010 P a g e 2 Background The purpose of my senior project is to prepare myself, as well as other students who may read my senior

More information

Time Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)

Time Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F) Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for

More information

Module 8: Current and long-term liabilities

Module 8: Current and long-term liabilities Module 8: Current and long-term liabilities Module 8: Current and long-term liabilities Overview In previous modules, you learned how to account for assets. Assets are what a business uses or sells to

More information

PowerPoint. to accompany. Chapter 5. Interest Rates

PowerPoint. to accompany. Chapter 5. Interest Rates PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When

More information

Chapter 3 Equivalence A Factor Approach

Chapter 3 Equivalence A Factor Approach Chapter 3 Equivalence A Factor Approach 3-1 If you had $1,000 now and invested it at 6%, how much would it be worth 12 years from now? F = 1,000(F/P, 6%, 12) = $2,012.00 3-2 Mr. Ray deposited $200,000

More information

averages simple arithmetic average (arithmetic mean) 28 29 weighted average (weighted arithmetic mean) 32 33

averages simple arithmetic average (arithmetic mean) 28 29 weighted average (weighted arithmetic mean) 32 33 537 A accumulated value 298 future value of a constant-growth annuity future value of a deferred annuity 409 future value of a general annuity due 371 future value of an ordinary general annuity 360 future

More information

8.1 Simple Interest and 8.2 Compound Interest

8.1 Simple Interest and 8.2 Compound Interest 8.1 Simple Interest and 8.2 Compound Interest When you open a bank account or invest money in a bank or financial institution the bank/financial institution pays you interest for the use of your money.

More information

substantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus

substantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society

More information

Excel Financial Functions

Excel Financial Functions Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint() Future Value How much will your money

More information

OHIO TREASURER S FINANCIAL EDUCATION GLOSSARY OF TERMS

OHIO TREASURER S FINANCIAL EDUCATION GLOSSARY OF TERMS OHIO TREASURER S FINANCIAL EDUCATION GLOSSARY OF TERMS 401(k) An employer qualified retirement plan set up by a private company in which eligible employees may make salary-deferral (salary-reduction) contributions

More information

Annuities and Sinking Funds

Annuities and Sinking Funds Annuities and Sinking Funds Sinking Fund A sinking fund is an account earning compound interest into which you make periodic deposits. Suppose that the account has an annual interest rate of compounded

More information

Basic Financial Tools: A Review. 3 n 1 n. PV FV 1 FV 2 FV 3 FV n 1 FV n 1 (1 i)

Basic Financial Tools: A Review. 3 n 1 n. PV FV 1 FV 2 FV 3 FV n 1 FV n 1 (1 i) Chapter 28 Basic Financial Tools: A Review The building blocks of finance include the time value of money, risk and its relationship with rates of return, and stock and bond valuation models. These topics

More information

Practice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.

Practice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4. PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor

More information

The Institute of Chartered Accountants of India

The Institute of Chartered Accountants of India CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY- APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able

More information

Section 8.1. I. Percent per hundred

Section 8.1. I. Percent per hundred 1 Section 8.1 I. Percent per hundred a. Fractions to Percents: 1. Write the fraction as an improper fraction 2. Divide the numerator by the denominator 3. Multiply by 100 (Move the decimal two times Right)

More information

Prepared by: Dalia A. Marafi Version 2.0

Prepared by: Dalia A. Marafi Version 2.0 Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC-200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version

More information

Chapter 02 How to Calculate Present Values

Chapter 02 How to Calculate Present Values Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00

More information

Understand the relationship between financial plans and statements.

Understand the relationship between financial plans and statements. #2 Budget Development Your Financial Statements and Plans Learning Goals Understand the relationship between financial plans and statements. Prepare a personal balance sheet. Generate a personal income

More information

FIN 3000. Chapter 6. Annuities. Liuren Wu

FIN 3000. Chapter 6. Annuities. Liuren Wu FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate

More information

Financial Math on Spreadsheet and Calculator Version 4.0

Financial Math on Spreadsheet and Calculator Version 4.0 Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS

More information

Chapter 8. Present Value Mathematics for Real Estate

Chapter 8. Present Value Mathematics for Real Estate Chapter 8 Present Value Mathematics for Real Estate Real estate deals almost always involve cash amounts at different points in time. Examples: Buy a property now, sell it later. Sign a lease now, pay

More information

The explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.

The explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off. USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas

More information

10.6 Functions - Compound Interest

10.6 Functions - Compound Interest 10.6 Functions - Compound Interest Objective: Calculate final account balances using the formulas for compound and continuous interest. An application of exponential functions is compound interest. When

More information

Bonds. Accounting for Long-Term Debt. Agenda Long-Term Debt. 15.501/516 Accounting Spring 2004

Bonds. Accounting for Long-Term Debt. Agenda Long-Term Debt. 15.501/516 Accounting Spring 2004 Accounting for Long-Term Debt 15.501/516 Accounting Spring 2004 Professor S. Roychowdhury Sloan School of Management Massachusetts Institute of Technology April 5, 2004 1 Agenda Long-Term Debt Extend our

More information

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

More information

Module 5: Interest concepts of future and present value

Module 5: Interest concepts of future and present value Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities

More information

BA-35 Solar Quick Reference Guide

BA-35 Solar Quick Reference Guide BA-35 Solar Quick Reference Guide Table of Contents General Information... 2 The Display... 4 Arithmetic Operations... 6 Correcting Errors... 7 Display Formats... 8 Memory Operations... 9 Math Operations...

More information

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is

More information

Time Value Conepts & Applications. Prof. Raad Jassim

Time Value Conepts & Applications. Prof. Raad Jassim Time Value Conepts & Applications Prof. Raad Jassim Chapter Outline Introduction to Valuation: The Time Value of Money 1 2 3 4 5 6 7 8 Future Value and Compounding Present Value and Discounting More on

More information

Assist. Financial Calculators. Technology Solutions. About Our Financial Calculators. Benefits of Financial Calculators. Getting Answers.

Assist. Financial Calculators. Technology Solutions. About Our Financial Calculators. Benefits of Financial Calculators. Getting Answers. Assist. Financial s Technology Solutions. About Our Financial s. Helping members with their financial planning should be a key function of every credit union s website. At Technology Solutions, we provide

More information

Chapter 3. Understanding The Time Value of Money. Prentice-Hall, Inc. 1

Chapter 3. Understanding The Time Value of Money. Prentice-Hall, Inc. 1 Chapter 3 Understanding The Time Value of Money Prentice-Hall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,

More information

CHAPTER 5. Interest Rates. Chapter Synopsis

CHAPTER 5. Interest Rates. Chapter Synopsis CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)

More information

Time Value of Money. Nature of Interest. appendix. study objectives

Time Value of Money. Nature of Interest. appendix. study objectives 2918T_appC_C01-C20.qxd 8/28/08 9:57 PM Page C-1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.

More information

Basic financial arithmetic

Basic financial arithmetic 2 Basic financial arithmetic Simple interest Compound interest Nominal and effective rates Continuous discounting Conversions and comparisons Exercise Summary File: MFME2_02.xls 13 This chapter deals

More information

The Time Value of Money C H A P T E R N I N E

The Time Value of Money C H A P T E R N I N E The Time Value of Money C H A P T E R N I N E Figure 9-1 Relationship of present value and future value PPT 9-1 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure

More information

Statistical Models for Forecasting and Planning

Statistical Models for Forecasting and Planning Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information

More information

Learning Objectives. Learning Objectives. Learning Objectives. Principles Used in this Chapter. Simple Interest. Principle 2:

Learning Objectives. Learning Objectives. Learning Objectives. Principles Used in this Chapter. Simple Interest. Principle 2: Learning Objectives Chapter 5 The Time Value of Money Explain the mechanics of compounding, which is how money grows over a time when it is invested. Be able to move money through time using time value

More information

Manual for SOA Exam FM/CAS Exam 2.

Manual for SOA Exam FM/CAS Exam 2. Manual for SOA Exam FM/CAS Exam 2. Chapter 5. Bonds. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics. Fall 2009 Edition,

More information

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be

More information