10.3 Future Value and Present Value of an Ordinary General Annuity


 Leslie Roberts
 6 years ago
 Views:
Transcription
1 360 Chapter 10 Annuities 10.3 Future Value and Present Value of an Ordinary General Annuity 29. In an ordinary general annuity, payments are made at the end of each payment period and the compounding period is not equal to the payment period. In this case, if we find the equivalent periodic rate, i 2, that matches the payment period, then using this equivalent periodic rate we can use the ordinary simple annuity formula to calculate the future value and present value. To calculate this, we first find the number of compounding periods per payment period (c) and then the equivalent periodic interest rate per payment period (i 2 ) using the following two formulas: Formula 10.3(a) Number of Compounding Periods per Payment Period c = Formula 10.3(b) Equivalent Periodic Interest Rate per Payment Period i 2 = (1 + i) c  1 Note: The value of 'c' as calculated from Formula 10.3(a) is used in calculating 'i 2 ' in Formula 10.3(b). Substitute the value of 'i 2 ' for 'i' in the ordinary simple annuity formulas, Formula 10.2(a) and Formula 10.2(b), to solve for 'FV' and 'PV' of an ordinary general annuity: n n ^1+ h ^1+ h FV = PMT ; E  and PV = PMT ; E Example 10.3(a) Calculating the Compounding Periods per Payment Period (c) and the Equivalent Periodic Interest Rate (i 2 ) that Matches the Payment Period Complete the table by calculating the number of compounding periods per payment period (c) and the equivalent periodic interest rate (i 2 ) that matches the payment period for the related interest rates: Solution Interest Rate 8% compounded quarterly Payment Period c i 2 Monthly = per month 9% compounded semiannually Quarterly = per quarter 6% compounded monthly Semiannually = per half year 5% compounded annually Monthly = per month
2 Chapter 10 Annuities 361 The following two examples will demonstrate future value and present value calculations of an ordinary general annuity. Example 10.3(b) Calculating the Future Value of an Ordinary General Annuity Rachel would like to save $100 every month for the next four years in a savings account at 2% compounded quarterly. (i) What would be the accumulated value of the investments at the end of four years? (ii) What would be the amount of interest earned? Solution This is an ordinary general annuity as: Payments are made at the end of each payment period (monthly) Compounding period (quarterly) payment period (monthly) (i) Using Formula 10.3(a), Number of compounding periods per year 4 c = = Number of payments per year 12 Using Formula 10.3(b), i 2 = (1 + i) c  1 = ( ) (4/12)  1 = per month Using Formula 10.2(a) and substituting i 2 for i, n ^1+ h  1 FV = PMT ; E 48 ^ h  1 = 100 ; E = 100 [ ] = = $ Therefore, the accumulated value of her investments at the end of four years would be $ (ii) Interest Earned = FV  n(pmt) = $ (100) = = $ Enter payment periods per year first Next, Enter compoundings per year Therefore, the amount of interest earned over the time period would be $
3 362 Chapter 10 Annuities Example 10.3(c) Calculating the Present Value of an Ordinary General Annuity Joseph borrowed money from a bank at 6% compounded annually. He settled the loan by repaying $500 at the end of every month for six years. (i) What was the loan amount received? (ii) What was the amount of interest charged? Solution This is an ordinary general annuity as: Payments are made at the end of each payment period (monthly) Compounding period (annually) payment period (monthly) (i) Using Formula 10.3(a), Number of compounding periods per year 1 c = = Number of payments per year 12 Using Formula 10.3(b), i 2 = (1 + i) c  1 = ( ) (1/12)  1 = per month Using Formula 10.2(b) and substituting i 2 for i,  n 1 ^1+ h PV = PMT ; E ^ h = 500 ; E = 500[ ] = 30, Therefore, the loan amount received was $30, (ii) Interest Charged = n(pmt)  PV = 72(500)  30, = = $ Therefore, the amount of interest charged was $ Exercises Answers to the oddnumbered problems are available at the end of the textbook 1. Calculate the number of compounding periods per payment period (expressed as a fraction, wherever applicable) and the equivalent periodic interest rate per payment period (rounded to six decimal places, wherever applicable) that matches the payment period for each of the following: a. Interest rate is 5% compounded quarterly. Payment period is semiannually. b. Interest rate is 4.2% compounded daily. Payment period is monthly. c. Interest rate is 4.8% compounded monthly. Payment period is semiannually. d. Interest rate is 4.9% compounded semiannually. Payment period is quarterly.
4 Chapter 10 Annuities Calculate the number of compounding periods per payment period (expressed as a fraction, wherever applicable) and the equivalent periodic interest rate per payment period (rounded to six decimal places, wherever applicable) that matches the payment period for each of the following: a. Interest rate is 4% compounded daily. Payment period is quarterly. b. Interest rate is 3.9% compounded quarterly. Payment period is monthly. c. Interest rate is 5% compounded semiannually. Payment period is monthly. d. Interest rate is 4.9% compounded monthly. Payment period is quarterly. 3. Calculate the future value of each of the following ordinary general annuities: Periodic Payment Payment Period Term of Annuity Interest Rate Compounding Frequency a. $2200 Every year 15 years 4.80% Quarterly b. $1400 Every 6 months 16.5 years 4.00% Monthly c. $1000 Every 3 months 11 years and 3 months 3.75% Semiannually d. $750 Every month 5 years 2 months 3.90% Daily 4. Calculate the future value of each of the following ordinary general annuities: Periodic Payment Payment Period Term of Annuity Interest Rate Compounding Frequency a. $1200 Every 3 months 8 years and 6 months 3.20% Monthly b. $400 Every month 15 years and 9 months 3.60% Semiannually c. $1850 Every 6 months 7.5 years 4.40% Quarterly d. $3000 Every year 12 years 4.70% Daily 5. Calculate the present value of each of the ordinary general annuities in Problem Calculate the present value of each of the ordinary general annuities in Problem Adrian invested $100 at the end of every month into an RRSP for five years. If the RRSP was providing an interest rate of 5% compounded quarterly, how much did he have in the RRSP at the end of the five years? 8. Bina saved $250 at the end of every month for two years in a savings account that earns 5% compounded quarterly. How much would she have in the account at the end of two years and how much of this is the interest earned? 9. Calculate the accumulated value of endofquarter payments of $800 made at the following interest rates for five years: a. 6.23% compounded quarterly. b. 6.24% compounded semiannually. 10. Calculate the future value of monthend payments of $180 made at the following interest rates for ten years: a. 7.8% compounded monthly. b. 8% compounded quarterly. 11. Barry has been contributing $1000 at the end of every three months into a retirement fund for the past 10 years. He decided to stop making payments and to allow his investment to grow for another 5 years. If money could earn 8% compounded semiannually, how much interest would he have earned over the 15year period? 12. Toby deposited $300 in a savings account at the end of every three months for five years. If the amount earned 5% compounded monthly, and if he left the accumulated money in the account to grow for another three years, calculate the balance in his savings account at the end of the period. What was his total deposit and total earnings?
5 364 Chapter 10 Annuities 13. Becca can afford to invest $400 at the end of every month in an RRSP for five years. By calculating the accumulated value of the payments in each of the following two investment options, identify the one that will give her the best return on her investment: RRSP 1: 3.55% compounded annually. RRSP 2: 3.50% compounded semiannually. 14. If an annuity payment for five years is $200 at the end of every month, compare the future values if the investment earns 4% compounded monthly, 4% compounded quarterly, and 4% compounded semiannually. 15. A credit union offers an interest rate of 4.5% compounded monthly for all investments. Which of the following would result in a higher future value and by how much more, when invested at the credit union? a. $18,250 invested for ten years. b. Annuity payments of $475 at the end of every quarter for ten years. 16. Calculate the accumulated value of the following investment options if the bank offers an interest rate of 5% compounded semiannually: a. A single amount of $5000 saved for five years. b. A series of payments of $100 at the end of every month for five years. 17. Alejandro has $25,000 in a savings account that yields 5.75% compounded quarterly. He intends to use these savings for his retirement in five years. In addition to these savings, he intends to deposit $1250 at the end of every month in a mutual fund that yields the same return. How much money will he have available for his retirement in five years? 18. Lily has accumulated $90,000 in a mutual fund. If she continues to deposit $500 at the end of every month from her salary into the fund for the next ten years, how much money will she have at the end of ten years if the fund earns interest at 3.75% compounded quarterly? 19. Amanda invested $500 at the end of every month into an RRSP that had an interest rate of 3% compounded quarterly. Two years later, the interest rate on her RRSP increased to 3.25% compounded quarterly and remained the same, thereafter. What is the accumulated value of the RRSP in six years? 20. What will be the future value of a series of $1000 deposits made at the end of each quarter for ten years, if the interest rate is 5% compounded monthly for the first five years and 4% compounded annually for the next five years? 21. What is the discounted value of annuity payments of $2000 made at the end of every year for five years at 6% compounded semiannually? 22. How much should Gilbert pay for a tenyear annuity that provides monthend payments of $1800 at 4.5% compounded quarterly? 23. A lottery winner is offered a choice between $100,000 now and another $100,000 in five years or monthend payments of $2300 for eight years. If money can earn 3.75% compounded semiannually, which alternative is economically better (in current value) for her and by how much more? 24. If you win a lottery that entitles you to receive $250,000 now and another $125,000 in three years or monthend payments of $8300 for five years, which offer is economically better (in current value) for you and by how much more, if money can earn 3.65% compounded daily? 25. Calculate the price of Troy's car if he has to make a down payment of $1000 at the time of purchase and payments of $330 at the end of every month for 3 years and 3 months at an interest rate of 6% compounded semiannually. What is the total interest he would pay for the car? 26. Byron Manufacturing Inc. paid $30,000 as a down payment to purchase a machine. It received a loan for the remaining amount at 4.5% compounded quarterly. What is the purchase price of the machine and the total amount of interest paid if it settled the loan with payments of $4500 made at the end of every month for five years?
6 Chapter 10 Annuities Two annuities that provide endofquarter payments of $850 for a period of five years have the following interest rates: Annuity A: 9.45% compounded monthly. Annuity B: 9.50% compounded semiannually. Which one would have a cheaper purchase price and by how much? 28. Ellen wants to receive a retirement income of $3000 every month for 20 years from her savings. If a bank in London was offering 6% compounded semiannually, how much would she have to invest to get her planned retirement income? If a bank in Toronto was offering 5.98% compounded quarterly, by how much would it be cheaper for Ellen to invest in this bank instead of investing in the bank in London? 29. What is the purchase price of an annuity that provides monthend payments of $500 for the first two years and $1000 for the next three years? Assume that the interest rate is 3% compounded quarterly throughout the time period. 30. How much should Emma pay for an annuity that would give her $5000 at the end of every year for the first seven years and $8000 at the end of every year for the next four years, if the interest rate is 6% compounded semiannually throughout the time period? 31. Starting at age 35, Gabriella invested $400 into an RRSP at the end of every month until her 45 th birthday and left the fund to grow under compound interest until her 65 th birthday. Starting at age 50, Gerard deposited $800 into a similar fund at the end of each month until his 65 th birthday. Assuming that both funds earned 6.4% compounded quarterly, who had more money and how much more in his or her fund at age 65? 32. Harry deposited $1000 in a retirement account at the end of each quarter for 20 years until he reached the age of 55, and then made no further deposits. His wife deposited $1000 in a retirement fund at the end of each quarter for 30 years until she reached the age of 65. Assuming that both funds earned 4.65% compounded monthly, who had more money and how much more in his or her fund at age 65? 33. A loan is settled by making payments of $2000 at the end of every three months for four years and then $500 at the end of every month for the next six years. What was the loan amount if the interest rate was 4.5% compounded monthly? 34. Georgia borrowed money from a bank at 6% compounded quarterly. She settled the loan by repaying $500 at the end of every month for the first two years and $2000 at the end of every three months for the next two years. What was the loan amount received? Future Value and Present Value of a Simple Annuity Due In a simple annuity due, payments are made at the beginning of each payment period, and the compounding period is equal to the payment period. In this section, you will learn how to calculate the future value and present value of a simple annuity due. Future Value of a Simple Annuity Due In an annuity due, as each payment is made at the beginning of the payment period, you will notice that the future value (accumulated value) of each payment is a multiple of the future value (accumulated value) of each payment in an ordinary annuity by a factor of (1+i). Let us compare two examples of an annuity with five annual payments, where in the first example, payments are made at the beginning of each year (annuity due) and in the second example, payments are made at the end of each year (ordinary annuity).
Problem Set: Annuities and Perpetuities (Solutions Below)
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
More information1. 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 informationChapter 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 informationChapter 4: Time Value of Money
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)
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
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
More informationSolutions to Time value of money practice problems
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,
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationChapter 3 Mathematics of Finance
Chapter 3 Mathematics of Finance Section 3 Future Value of an Annuity; Sinking Funds Learning Objectives for Section 3.3 Future Value of an Annuity; Sinking Funds The student will be able to compute the
More informationAppendix 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 informationDiscounted 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 informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.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 informationfirst complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest.
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
More information132. Annuities Due. Chapter 13. MH Ryerson
132 Annuities Due Chapter 13 133 Learning Objectives After completing this chapter, you will be able to: > Calculate the future value and present value of annuities due. > Calculate the payment size,
More informationSample problems from Chapter 10.1
Sample problems from Chapter 10.1 This is the annuities sinking funds formula. This formula is used in most cases for annuities. The payments for this formula are made at the end of a period. Your book
More informationTIME VALUE OF MONEY (TVM)
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
More informationMain TVM functions of a BAII Plus Financial Calculator
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
More informationAppendix. 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 informationFIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1
FIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems  Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 31 a) Future Value = FV(n,i,PV,PMT)
More informationA = P (1 + r / n) n t
Finance Formulas for College Algebra (LCU  Fall 2013)  Formula 1: Amount
More informationChapter 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 informationReview Page 468 #1,3,5,7,9,10
MAP4C Financial Student Checklist Topic/Goal Task Prerequisite Skills Simple & Compound Interest Video Lesson Part Video Lesson Part Worksheet (pages) Present Value Goal: I will use the present value formula
More informationInternational Financial Strategies Time Value of Money
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
More informationActivity 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 informationSolutions to Problems: Chapter 5
Solutions to Problems: Chapter 5 P51. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start
More informationRegular Annuities: Determining Present Value
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
More informationMAT116 Project 2 Chapters 8 & 9
MAT116 Project 2 Chapters 8 & 9 1 81: 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
More informationCHAPTER 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 informationDiscounted Cash Flow Valuation
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?
More informationSection 5.1  Compound Interest
Section 5.1  Compound Interest Simple Interest Formulas If I denotes the interest on a principal P (in dollars) at an interest rate of r (as a decimal) per year for t years, then we have: Interest: Accumulated
More informationHow To Calculate A Pension
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
More informationKey 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 information1. 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 information2 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 definedcontribution
More informationPresent Value (PV) Tutorial
EYK 151 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,
More informationUsing the Finance Menu of the TI83/84/Plus calculators KEY
Using the Finance Menu of the TI83/84/Plus calculators KEY To get to the FINANCE menu On the TI83 press 2 nd x 1 On the TI83, TI83 Plus, TI84, or TI84 Plus press APPS and then select 1:FINANCE The
More informationE 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 informationThe values in the TVM Solver are quantities involved in compound interest and annuities.
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
More informationFinding 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 informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 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
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationANNUITIES. Ordinary Simple Annuities
An annuity is a series of payments or withdrawals. ANNUITIES An Annuity can be either Simple or General Simple Annuities  Compounding periods and payment periods coincide. General Annuities  Compounding
More informationTime Value of Money. Nature of Interest. appendix. study objectives
2918T_appC_C01C20.qxd 8/28/08 9:57 PM Page C1 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 informationLesson 1. Key Financial Concepts INTRODUCTION
Key Financial Concepts INTRODUCTION Welcome to Financial Management! One of the most important components of every business operation is financial decision making. Business decisions at all levels have
More informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case  single cash flow Multiperiod case  single cash flow Multiperiod case  compounding periods Multiperiod case  multiple
More informationBusiness 2019. Fundamentals of Finance, Chapter 6 Solution to Selected Problems
Business 209 Fundamentals of Finance, Chapter 6 Solution to Selected Problems 8. Calculating Annuity Values You want to have $50,000 in your savings account five years from now, and you re prepared to
More information2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?
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 equalsized
More informationReal estate investment & Appraisal Dr. Ahmed Y. Dashti. Sample Exam Questions
Real estate investment & Appraisal Dr. Ahmed Y. Dashti Sample Exam Questions Problem 31 a) Future Value = $12,000 (FVIF, 9%, 7 years) = $12,000 (1.82804) = $21,936 (annual compounding) b) Future Value
More informationSection 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 informationTIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY
TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value
More informationPresent 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 informationThe 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 informationApplying Time Value Concepts
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
More informationIn Section 5.3, we ll modify the worksheet shown above. This will allow us to use Excel to calculate the different amounts in the annuity formula,
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
More informationAnnuities: Present Value
8.5 nnuities: Present Value GOL Determine the present value of an annuity earning compound interest. INVESTIGTE the Math Kew wants to invest some money at 5.5%/a compounded annually. He would like the
More informationHow to calculate present values
How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
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
More informationTIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!
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
More informationCALCULATOR HINTS ANNUITIES
CALCULATOR HINTS ANNUITIES CALCULATING ANNUITIES WITH THE FINANCE APP: Select APPS and then press ENTER to open the Finance application. SELECT 1: TVM Solver The TVM Solver displays the timevalueofmoney
More informationOrdinary Annuities Chapter 10
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
More informationStatistical 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 informationPresent Value and Annuities. Chapter 3 Cont d
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
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
More informationCalculations for Time Value of Money
KEATMX01_p001008.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
More informationHow To Use Excel To Compute Compound Interest
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
More informationCompounding Quarterly, Monthly, and Daily
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,
More informationMatt 109 Business Mathematics Notes. Spring 2013
1 To be used with: Title: Business Math (Without MyMathLab) Edition: 8 th Author: Cleaves and Hobbs Publisher: Pearson/Prentice Hall Copyright: 2009 ISBN #: 9780135136874 Matt 109 Business Mathematics
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, 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 informationFinite 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 informationThe 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 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationT121 REVIEW EXERCISES CHAPTER 12 SECTION I
T121 REVIEW EXERCISES CHAPTER 12 SECTION I Use Table 121 to calculate the future value of the following ordinary annuities: Annuity Payment Time Nominal Interest Future Value Payment Frequency Period
More informationChapter 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 informationTHE VALUE OF MONEY PROBLEM #3: ANNUITY. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction
THE VALUE OF MONEY PROBLEM #3: ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction Earlier, we explained how to calculate the future value of a single sum placed on deposit
More informationSample 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.
More information5.1 Simple and Compound Interest
5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?
More informationHOW TO CALCULATE PRESENT VALUES
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGrawHill/Irwin Copyright 2014 by The McGrawHill Companies, Inc. All rights reserved.
More informationChapter 4. The Time Value of Money
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
More informationThe Time Value of Money
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
More informationTIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;
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.
More informationFinance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date
1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand
More informationUSING THE SHARP EL 738 FINANCIAL CALCULATOR
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
More informationUSING FINANCIAL CALCULATORS
lwww.wiley.com/col APPEDIX C USIG FIACIAL CALCULATORS OBJECTIVE 1 Use a financial calculator to solve time value of money problems. Illustration C1 Financial Calculator Keys Business professionals, once
More informationKENT FAMILY FINANCES
FACTS KENT FAMILY FINANCES Ken and Kendra Kent have been married twelve years and have twin 4yearold sons. Kendra earns $78,000 as a Walmart assistant manager and Ken is a stayathome dad. They give
More informationFuture Value of an Annuity Sinking Fund. MATH 1003 Calculus and Linear Algebra (Lecture 3)
MATH 1003 Calculus and Linear Algebra (Lecture 3) Future Value of an Annuity Definition An annuity is a sequence of equal periodic payments. We call it an ordinary annuity if the payments are made at the
More information1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000
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
More informationTime Value of Money Problems
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
More information300 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 informationFinance Notes ANNUITIES
Annuities Page 1 of 8 ANNUITIES Objectives: After completing this section, you should be able to do the following: Calculate the future value of an ordinary annuity. Calculate the amount of interest earned
More informationCHAPTER 6 Accounting and the Time Value of Money
CHAPTER 6 Accounting and the Time Value of Money 61 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
More informationTIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction
TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 15, which are prerequisites. In this
More informationSection 4.2 (Future Value of Annuities)
Math 34: Fall 2015 Section 4.2 (Future Value of Annuities) At the end of each year Bethany deposits $2, 000 into an investment account that earns 5% interest compounded annually. How much is in her account
More informationFinQuiz 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 informationPractice 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 informationChapter 2 Applying Time Value Concepts
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
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
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
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationFinancial Literacy in Grade 11 Mathematics Understanding Annuities
Grade 11 Mathematics Functions (MCR3U) Connections to Financial Literacy Students are building their understanding of financial literacy by solving problems related to annuities. Students set up a hypothetical
More informationTIME VALUE OF MONEY PROBLEM #7: MORTGAGE AMORTIZATION
TIME VALUE OF MONEY PROBLEM #7: MORTGAGE AMORTIZATION Professor Peter Harris Mathematics by Sharon Petrushka Introduction This problem will focus on calculating mortgage payments. Knowledge of Time Value
More information