1 6-1 Chapter 6 Time Value of Money Concepts 6-2 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in one year. 6-3 Simple Interest Interest amount = P i n Assume you invest $1,000 at 6% simple interest for 3 years. You would earn $180 interest. ($1, = $180) (or $60 each year for 3 years)
2 Compound Interest When we compound interest, we assume you earn interest on both principal and interest. Principal Interest 6-5 Compound Interest Assume we will save $1,000 for three years and earn 6% interest compounded annually. What is the balance in our account at the end of three years? 6-6 Compound Interest Original balance $ 1, First year interest Balance, end of year 1 $ 1, Balance, beginning of year 2 $ 1, Second year interest Balance, end of year 2 $ 1, Balance, beginning of year 3 $ 1, Third year interest Balance, end of year 3 $ 1,191.02
3 Future Value of a Single Amount Multiply a year s beginning principal by the interest rate and add that year s interest to the account balance. $1, = $1, and $1, = $1, and $1, = $1, Future Value of a Single Amount Writing in a more efficient way, we can say.... $1, = $1, or $1,000 [1.06] 3 = $1, Future Value of a Single Amount $1,000 [1.06] 3 = $1, We can generalize this as... FV = PV (1 + i) n Future Present Interest Value Value Rate Number of Periods
4 Future Value of a Single Amount Find the Future Value of $1 table in your textbook Future Value of a Single Amount Find the factor for 6% and 3 periods. Solve our problem like this... FV = $1, FV = $1, FV $ Future Value of a Single Amount You invest $10,000 today and earn 8% interest for 8 years. What will the balance in your account be at the end of 8 years if.... A. Interest is simple. B. Interest is compounded annually.
5 Future Value of a Single Amount A - Simple Interest $10, = $6,400 $10,000 + $6,400 = $16,400 B - Compound Annually $10, = $18, Present Value of a Single Amount Instead of asking what is the future value of a current amount, we might want to know what amount we must invest today to accumulate a known future amount. This is a present value question Present Value of a Single Amount Remember our equation? FV = PV [1 + i] n We can solve for PV and get.... FV PV = [1 + i] n
6 Present Value of a Single Amount We can rearrange the equation... PV = FV or 1 [1 + i] n PV = FV [1 + i] -n 6-17 Present Value of a Single Amount Find the Present Value of $1 table in your textbook. Hey, it looks familiar! 6-18 Present Value of a Single Amount Assume you plan to buy a new car in 5 years and you think it will cost $20,000 at that time. What amount must you invest today in order to accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually?
7 Present Value of a Single Amount i =.08, n = 5 Present Value Factor = $20, = $13, If you deposit $13, now, at 8% annual interest, you will have $20,000 at the end of 5 years Time Value of Money Example If you deposit $5,000 in a bank at 8% interest compounded annually, how much will you have in 5 years?... in 10 years? 5 Years 10 Years a. $7,387 $8,144 b. $7,347 $10,795 c. $7,347 $9,471 d. $6,984 $9, Time Value of Money Example If you deposit $5,000 in a bank at 8% interest compounded annually, how much will you have in 5 years?... in 10 years? 5 Years 10 Years a. $7,387 $8,144 b. $7,347 $10,795 c. $7,347 $9,471 d. $6,984 $9,186 Future Value of $1 Table $5, = $ 7, $5, = $10,794.60
8 Time Value of Money Example What amount must you deposit today at 6% interest compounded annually, to have $10,000 for your first year of college 5 years from now? a. $7,462 b. $7,921 c. $7,473 d. $7, Time Value of Money Example What amount must you deposit today at 6% interest compounded annually, to have $10,000 for your first year of college 5 years from now? a. $7,462 b. $7,921 c. $7,473 d. $7,581 Present Value of $1 Table $10,000 x = $7, Present Value On June 1, your company purchases equipment by paying $5,000 down and issuing a $27,000 noninterest-bearing note payable that is due in three years. Similar transactions carry a stated interest rate of 6%. What is the purchase price of the equipment?
9 Present Value Face of note $ 27,000 Present value of $1 (i = 6%, n = 3) Present value of note $ 22,670 Cash paid 5,000 Cost of equipment $ 27,670 Journal entry to record the note and equipment 6-26 Present Value GENERAL JOURNAL Page 25 Date Description Post. Ref. Debit Credit Jun. 1 Equipment 27,670 Discount on Notes Payable 4,330 Notes Payable 27,000 Cash 5, Solving for Other Values FV = PV (1 + i) n Future Present Interest Value Value Rate Number of Periods There are four variables needed when determining the time value of money. If you know any three of these, the fourth can be determined.
10 Solving for Other Variables Example Suppose a friend wants to borrow $1,000 today and promises to repay you $1,092 two years from now. What is the annual interest rate you would be agreeing to? a. 3.5% b. 4.0% c. 4.5% d. 5.0% 6-29 Solving for Other Variables Example Suppose a friend wants to borrow $1,000 today and promises to repay you $1,092 two years from now. What is the annual interest rate you would be agreeing to? a. 3.5% b. 4.0% c. 4.5% d. 5.0% Present Value of $1 Table $1,000 = $1,092? $1,000 $1,092 = Search the PV of $1 table in row 2 (n=2) for this value No Explicit Interest Some notes do not include a stated interest rate. We call these notes noninterest-bearing notes. Even though the agreement states it is a noninterest-bearing note, the note does, in fact, include interest. We impute an appropriate interest rate for a loan of this type to use as the interest rate.
11 Expected Cash Flow Approach Statement of Financial Accounting Concepts No. 7 Using Cash Flow Information and Present Value in Accounting Measurements The objective of valuing an asset or liability using present value is to approximate the fair value of that asset or liability. Expected Cash Flow Risk-Free Rate of Interest Present Value 6-32 Basic Annuities An annuity is a series of equal periodic payments Ordinary An annuity with payments at the end of the period is known as an ordinary annuity. End End
12 Due An annuity with payments at the beginning of the period is known as an annuity due. Beginning Beginning Beginning 6-35 Future Value of an Ordinary The equation to find the future value of an annuity is... n FVA = (1 + i) i Because this is the equation for the FV of $1, the equation for FVA should be easy to remember Future Value of an Ordinary To find the future value of an ordinary annuity, multiply the amount of a single payment or receipt by the future value factor.
13 Future Value of an Ordinary We plan to invest $2,500 at the end of each of the next 10 years. We can earn 8%, compounded annually, on all invested funds. What will be the fund balance at the end of 10 years? 6-38 Future Value of an Ordinary Amount of annuity $ 2, Future value of ordinary annuity of $1 (i = 8%, n = 10) Balance $ 36, Find the Future Value of Ordinary of $1 factor in your textbook Future Value of an Due Compute the future value of $10,000 received at the beginning of each of the next four years with interest at 6% compounded annually.
14 Future Value of an Due Compute the future value of $10,000 received at the beginning of each of the next four years with interest at 6% compounded annually. Amount of annuity $ 10,000 FV of annuity due of $1 (i=6%, n=4) Present value of annuity $ 46, Present Value of an Ordinary Rats! More Present Value Present Value of an Ordinary The equation to find the present value of a series of $1 payments is.... PV = 1-1 [1+i] i n This is the equation for the PV of $1
15 Present Value of an Ordinary You wish to withdraw $10,000 at the end of each of the next 4 years from a bank account that pays 10% interest compounded annually. How much do you need to invest today to meet this goal? 6-44 Present Value of an Ordinary Today $10,000 $10,000 $10,000 $10,000 PV1 PV2 PV3 PV Present Value of an Ordinary PV Present Factor Value PV1 $ 10, $ 9, PV2 10, , PV3 10, , PV4 10, , Total $ 31, If you invest $31, today you will be able to withdraw $10,000 at the end of each of the next four years.
16 Present Value of an Ordinary PV Present Factor Value PV1 $ 10, $ 9, PV2 10, , PV3 10, , PV4 10, , Total $ 31, Can you find this value in the Present Value of Ordinary of $1 table? 6-47 Present Value of an Ordinary How much must a person 65 years old invest today at 8% interest compounded annually to provide for an annuity of $20,000 at the end of each of the next 15 years? a. $153,981 b. $171,190 c. $167,324 d. $174, Present Value of an Ordinary How much must a person 65 years old invest today at 8% interest compounded annually to provide for an annuity of $20,000 at the end of each of the next 15 years? a. $153,981 b. $171,190 c. $167,324 d. $174,680 PV of Ordinary $1 Payment $ 20, PV Factor Amount $171,189.60
17 Present Value of an Ordinary Assume the person only has $140,000. What annuity will this amount provide at the end of each of the next 15 years if it is invested today at 8% interest compounded annually? a. $15,891 b. $16,356 c. $17,742 d. $18, Present Value of an Ordinary Assume the person only has $140,000. What annuity will this amount provide at the end of each of the next 15 years if it is invested today at 8% interest compounded annually? a. $15,891 b. $16,356 c. $17,742 d. $18,123 PV of Ordinary of $1 Amount $ 140,000 Divided by $16, Present Value of an Due Compute the present value of $10,000 received at the beginning of each of the next four years with interest at 6% compounded annually.
18 Present Value of an Due Compute the present value of $10,000 received at the beginning of each of the next four years with interest at 6% compounded annually. Amount of annuity $ 10,000 PV of annuity due of $1 (i=6%, n=4) Present value of annuity $ 36, Present Value of Annuities Western Gas, Inc. lost a lawsuit requiring the company to pay $2,250,000 immediately or $260,000 ($3,900,000 total) at the end of each of the next 15 years. Assume Western Gas can earn 9% on all funds available. Which settlement option would you recommend? 6-54 Present Value of Annuities Annual payment $ 260,000 PV factor for ordinary annuity, n = 15, i = 9% PV of annuity payments $ 2,095,779 Because the present value of the payments is less than the lump sum payment, you would recommend that Western Gas make the annual payments of $260,000.
19 Present Value of a Deferred In a deferred annuity, the first cash flow is expected to occur more than one period after the date of the agreement Present Value of a Deferred On January 1, 2003, you are considering an investment that will pay $12,500 a year for 2 years beginning on December 31, If you require a 12% return on your investments, how much are you willing to pay for this investment? Cost Today? $12,500 $12,500 1/1/03 12/31/03 12/31/04 12/31/05 12/31/06 12/31/ Present Value of a Deferred Payment PV of $1 i = 12% PV n 1 $ 12, $ 8, , ,944 4 $ 16,841 Cost Today? $12,500 $12,500 1/1/03 12/31/03 12/31/04 12/31/05 12/31/06 12/31/
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
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
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
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.
Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
Format Exam 3 Review http://fates.cns.muskingum.edu/~ plaube/acct301/default.htm 15 questions Multiple choice (12) Essay (2) Problem (1) What to Bring/Remember What to bring Calculator I ll bring scrap
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
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
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
Present Value and Annuities Chapter 3 Cont d Present Value Helps us answer the question: What s the value in today s dollars of a sum of money to be received in the future? It lets us strip away the effects
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
Finance Formulas for College Algebra (LCU - Fall 2013) ---------------------------------------------------------------------------------------------------------------------------------- Formula 1: Amount
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
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.
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17 2. Use of
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
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
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value
D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of
Sample Examination Questions CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY MULTIPLE CHOICE Conceptual Answer No. Description d 1. Definition of present value. c 2. Understanding compound interest tables.
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
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
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
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
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
EYK 15-1 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,
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
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
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
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
CHAPTER 6 Accounting and the Time Value of Money 6-1 LECTURE OUTLINE This chapter can be covered in two to three class sessions. Most students have had previous exposure to single sum problems and ordinary
Accounting Building Business Skills Paul D. Kimmel Appendix B: Time Value of Money PowerPoint presentation by Kate Wynn-Williams University of Otago, Dunedin 2003 John Wiley & Sons Australia, Ltd 1 Interest
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
BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?
ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular
CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equal-sized
ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return
9. Time Value of Money 1: Present and Future Value Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this language, because
Integrated Case 5-42 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
Time Value of Money, Part 5 Present Value aueof An Annuity Intermediate Accounting II Dr. Chula King 1 Learning Outcomes The concept of present value Present value of an annuity Ordinary annuity versus
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
Exercise 1 for Time Value of Money MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing
2 Time Value of Money BASIC CONCEPTS AND FORMULAE 1. Time Value of Money 2. Simple Interest 3. Compound Interest 4. Present Value of a Sum of Money 5. Future Value It means money has time value. A rupee
Week 4 Time Value of Money Chonga Zangpo, DFB What is time value of money? It is based on the belief that people have a positive time preference for consumption. It reflects the notion that people prefer
KEATMX01_p001-008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with
Applying Time Value Concepts C H A P T E R 3 based on the value of two packs of cigarettes per day and a modest rate of return? Let s assume that Lou will save an amount equivalent to the cost of two packs
Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest $1,000 it becomes $1,050 $1,000 return of $50 return on Factors to consider when assessing Return on
USING THE SHARP EL 738 FINANCIAL CALCULATOR Basic financial examples with financial calculator steps Prepared by Colin C Smith 2010 Some important things to consider 1. These notes cover basic financial
Chapter Discounted Cash Flow Valuation Compounding Periods Other Than Annual Let s examine monthly compounding problems. Future Value Suppose you invest $9,000 today and get an interest rate of 9 percent
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
In following we will introduce one of the most important and powerful concepts you will learn in your study of finance; the time value of money. It is generally acknowledged that money has a time 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
Interests on Transactions Chapter 10 13 PV & FV of Annuities PV & FV of Annuities An annuity is a series of equal regular payment amounts made for a fixed number of periods 2 Problem An engineer deposits
8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded
CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists
Key Concepts and Skills Chapter 4 Introduction to Valuation: The Time Value of Money Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received
Ch. 4 - The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation
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
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
MAT116 Project 2 Chapters 8 & 9 1 8-1: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the
5 More on Annuities and Loans 5.1 Introduction This section introduces Annuities. Much of the mathematics of annuities is similar to that of loans. Indeed, we will see that a loan and an annuity are just
EXERCISE 6-4 (15 20 minutes) (a) (b) (c) (d) Future value of an ordinary annuity of $4,000 a period for 20 periods at 8% $183,047.84 ($4,000 X 45.76196) Factor (1 +.08) X 1.08 Future value of an annuity
#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
Six Functions of a Dollar Made Easy! Business Statistics AJ Nelson 8/27/2011 1 Six Functions of a Dollar Here's a list. Simple Interest Future Value using Compound Interest Present Value Future Value of
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate
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
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
CHAPTER 8 INTEREST RATES AND BOND VALUATION Answers to Concept Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury securities have substantial
1.-1.3 ime Value of Money and Discounted ash Flows ime Value of Money (VM) - the Intuition A cash flow today is worth more than a cash flow in the future since: Individuals prefer present consumption to
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,
1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned
Time Value of Money Revisited: Part 1 Terminology Intermediate Accounting II Dr. Chula King 1 Learning Outcomes Definition of Time Value of Money Components of Time Value of Money How to Answer the Question
Texas Instruments Graphing Calculators have a built in app that may be used to compute quantities involved in compound interest, annuities, and amortization. For the examples below, we ll utilize the screens
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
FNE 215 Financial Planning Chris Leung, Ph.D., CFA, FRM Email: email@example.com Chapter 2 Planning with Personal Financial Statements Chapter Objectives Explain how to create your personal cash flow
CHAPTER 2 Time Value of Money 2-1 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 2-2 Time lines 0 1 2 3