Regular Annuities: Determining Present Value

Size: px
Start display at page:

Transcription

1 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 annually. One year from now he will go to college. While Harry attends college, the annuity must provide him with 4 equal annual payments of \$ for tuition. YOU WILL NEED graphing calculator with TVM Solver spreadsheet software? How much must be in Harry s account now if the first payment starts in a year? EXAMPLE 1 Selecting a strategy to determine the present value of an annuity Determine the present value of Harry s annuity. Rahiv s Solution: Using a Timeline Present Value of Annuity at 9%/a Compounded Annually Present value Year P = (1.09) 1 = \$ \$ \$ \$ \$ Deposit P = (1.09) 2 = \$ P = (1.09) 3 = \$ P = (1.09) 4 = \$ I used a timeline to organize the solution. The annual interest rate is 9%, or At the end of 1 year, the first payment s present value will have earned interest for 1 year: n 5 1. The second payment s present value will have earned interest for 2 years: n 5 2. The third payment s present value will have earned interest for 3 years: n 5 3. The fourth payment s present value will have earned interest for 4 years: n 5 4. NEL Solving Financial Problems Involving Exponential Functions 501

2 PV 5 (1.09) 1 1 (1.09) 2 1 (1.09) 3 1 (1.09) To have four equal annual payments of \$ starting 1 year from now, Harry needs \$ in his account now. The present value is the total of the present values of all the payments. Tamika s Solution: Use a Spreadsheet Formulas (as entered) A 1 End of Year Present Value ( )^A2 3 5 A ( )^A3 4 5 A ( )^A4 5 5 A ( )^A5 6 Total PV 5 SUM(B2:B5) B Values (as displayed) A B 1 End of Year Present Value Total PV The annual interest rate is 9%, or The formulas I used in the spreadsheet are in columns A and B. I knew that the amount paid at the end of each year had earned interest from the beginning of the annuity. So I used the year number, located in column A, in the formula to calculate the present value of each payment. I read the total present value of the annuity from cell B6. Reflecting A. In calculating the present value of an annuity, the amount of each payment is divided by a factor of (1 1 i) for each additional compounding period. Why does this factor increase the distance in the future the payment is made? B. Compare the methods used in the two solutions. What are the advantages and disadvantages of each? C. If Harry were to receive payments every month instead of every year, which method would you use? Explain. 502 Chapter 8 NEL

3 APPLY the Math If technology is not available to help you calculate the present value of an annuity, then you can also use a formula. 8.6 EXAMPLE 2 Using a formula to determine the present value of an annuity Roshan has set up an annuity to help his son pay living expenses over the next 5 years. The annuity will pay \$50 a month. The first payment will be made 1 month from now. The annuity earns 7.75%/a compounded monthly. a) How much money did Roshan put in the annuity? b) How much interest will the annuity earn over its term? c) Verify your results using the TVM solver. Tim s Solution a) b) c) PV 5 R 5 50 R 31 2 (1 1 i)2n i i n PV ( ) PV Roshan put \$ in the annuity The annuity earned \$ in interest over its term. I wrote the formula for calculating the present value of an annuity, where PV is the present value, in dollars R is the regular payment, in dollars i is the interest rate per compounding period, expressed as a decimal n is the total number of payments 3 7 The annual interest rate is. The monthly interest rate is 1 12 of the annual rate, so I divided it by 12. I multiplied the number of years by 12 to determine the number of compounding periods. 4 % I substituted the values for R, i, and n, and calculated PV. I determined the total interest earned over the term of the annuity by subtracting the present value of the annuity from the total value of payments. I entered 60 beside N for the 60 compounding periods. I entered 7.75 beside I% for 7.75% annual interest. The regular payment of \$50 means that Roshan has paid this amount out to his son, so I entered 250 beside PMT. FV is not required, so I entered a value of 0. I entered 12 for both P/Y and C/Y because the payments are made and compounded monthly. NEL Solving Financial Problems Involving Exponential Functions 503

4 I placed the cursor beside PV because I was solving for the present value. I solved for PV. The present value is positive because it is money that is deposited into the bank at the beginning of the annuity to provide for the monthly withdrawls. Roshan put \$ in the annuity. I could have also used PMT 5150, and the PV would have been I used the TVM Solver s interest function and entered 1 for the starting payment number and 60 for the ending payment number. The annuity earned \$ in interest. Support Tech Before using the SInt function, make sure that values have been entered into the TVM Solver for N, I%, PV, PMT, P/Y, C/Y, and PMT:END. For more help with using the TVM Solver to solve problems involving compound interest, see Technical Appendix, B-15. EXAMPLE 3 Selecting a strategy that uses present value to calculate the payment of an annuity Robin bought a bicycle for \$1500. She arranged to make a payment to the store at the end of every month for 1 year. The store is charging 11%/a interest compounded monthly. a) How much is each monthly payment? b) How much interest is Robin paying? Leshawn s Solution: Using a Formula a) PV 5 R 31 2 (1 1 i)2n 4 i PV i % n 5 12 I used the formula for present value so that I could solve for the payment. The present value is PV 5 \$1500. The annual interest rate is 11%, so the 1 monthly interest rate is as much. 12 She makes 12 payments in a year. 504 Chapter 8 NEL

5 8.6 b) R31 2 ( ) (1500) 1 2 ( ) R R Robin makes monthly payments of \$ The interest paid to the store is \$ I multiplied both sides of the equation by , then I divided both sides by 1 2 ( ) 212 to solve for R. To calculate the interest paid, I found the total of the payments and subtracted the cost of the bicycle. The difference was the interest paid to the store. Henrique s Solution: Using the TVM Solver a) I entered 12 beside N for the 12 compounding periods and 11 beside I% for 11% annual interest. The bicycle cost \$1500, so I entered beside PV, because this is what she paid for the bike out of her bank account. FV is not required, so I entered 0. I entered 12 for both P/Y and C/Y because the payments are made and compounded monthly. I placed the cursor beside PMT because I was solving for the payment. I solved for PMT. The payment is positive because the money is paid into the account. b) Robin makes monthly payments of \$ I used the TVM Solver s interest function and entered 1 for the starting payment number and 12 for the ending payment number. The interest paid to the store is \$ NEL Solving Financial Problems Involving Exponential Functions 505

6 In Summary Key Ideas The present value of an annuity is (1) the amount that must be invested now to provide payments of a specific amount at regular intervals over a certain term or (2) the amount borrowed or financed now that must be paid for by deposits of a specific amount at regular intervals over a certain term. The present value of an annuity is the sum of the present values of all of the regular payments. The formula for calculating the present value of an annuity is PV 5 R31 2 (1 1 i)2n 4 i where PV is the present value, in dollars R is the regular payment, in dollars i is the interest rate per compounding period, expressed as a decimal n is the number of payments or withdrawals Need to Know Problems involving annuities can be solved with a formula, spreadsheet software, or financial software such as the TVM Solver. CHECK Your Understanding 1. Draw a timeline to represent an annuity of semi-annual payments of \$300 for 3 years at 8%/a compounded semi-annually. Use the timeline to organize a solution that shows how the present value of each payment contributes toward the present value of the annuity. 2. For each situation, identify R, i, and n in the formula PV 5 R31 2 (1 1 i)2n 4. i Then determine the present value of the annuity. a) b) c) Annual Interest Compounding Term of Withdrawal (\$) Rate (%) Period Annuity annual 3 years 450 quarterly 8.5 years monthly 5 years 3. Solve for each unknown. a) b) R( ) PV 5 450( ) Chapter 8 NEL

8 12. René buys a computer system for \$80 down and 18 monthly payments of \$55 each. The first payment is due next month. a) The interest rate is 15%/a compounded monthly. What is the selling price of the computer system? b) What is the finance charge? 13. Betty is retiring. She has \$ in savings. She is concerned that she will not have enough money to live on. She would like to know how much an annuity, compounded monthly, will pay her each month for a variety of interest rates. She needs to know the monthly payments over the next 10 years, starting next month. Use a spreadsheet and different annual interest rates to prepare three different schedules of payments for Betty. 14. The present value of the last payment of an annuity is 2500(1.05) 236. T a) Describe two annuities, with different compounding periods, that can be represented by the present value of the last payment. b) Calculate the present values of the total payments for each annuity in part (a). 15. The screens shown were obtained from the TVM Solver. Write a C problem that corresponds to the information from each screen. a) b) 508 Chapter 8 Extending 16. Do the following situations double the amount of an annuity at maturity? a) Double the duration of the annuity. b) Double each payment made. Use examples to support your explanation. 17. Rudi deposited \$100 at the end of each month into an annuity that paid 7.5%/a compounded monthly. At the end of 6 years, the interest rate increased to 8.5%/a. The deposits were continued for another 5 years. a) What is the amount of the annuity on the date of the last deposit? b) What is the interest rate earned on the annuity over the 11 years? 18. Kyla must repay her \$ student loan. She can afford to make monthly payments of \$325. The bank s interest rate is 7.2%/a compounded monthly. Determine how long it will take Kyla to repay her loan. NEL

first 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

TIME 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

Review 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

TIME 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

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.

The 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

Annuities: 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

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

THE 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

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

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

DISCOUNTED 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

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

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.

Section 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

Compounding 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,

Main 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

Using the Finance Menu of the TI-83/84/Plus calculators KEY

Using the Finance Menu of the TI-83/84/Plus calculators KEY To get to the FINANCE menu On the TI-83 press 2 nd x -1 On the TI-83, TI-83 Plus, TI-84, or TI-84 Plus press APPS and then select 1:FINANCE The

In 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

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

Reducing balance loans

Reducing balance loans 5 VCEcoverage Area of study Units 3 & 4 Business related mathematics In this chapter 5A Loan schedules 5B The annuities formula 5C Number of repayments 5D Effects of changing the

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

Finance 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

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

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

1.6. Solving Investment Portfolio Problems. INVESTIGATE the Math

1.6 Solving Investment Portfolio Problems YOU WILL NEED spreadsheet software financial application on a graphing calculator EXPLORE Describe three different investments that would result in \$30 000 in

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

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

Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest \$1,000 at 6% simple interest for 3 years.

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

Chapter 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

Unit VI. Complete the table based on the following information:

Aqr Review Unit VI Name 1. You have just finished medical school and you have been offered two jobs at a local hospital. The first one is a physical therapist for the hospital with a salary of \$45,500.

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

Future Value. Basic TVM Concepts. Chapter 2 Time Value of Money. \$500 cash flow. On a time line for 3 years: \$100. FV 15%, 10 yr.

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

Calculations for Time Value of Money

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

TIME 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

What You ll Learn. And Why. Key Words. interest simple interest principal amount compound interest compounding period present value future value

What You ll Learn To solve problems involving compound interest and to research and compare various savings and investment options And Why Knowing how to save and invest the money you earn will help you

Chapter 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

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

Key Concepts and Skills

McGraw-Hill/Irwin Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash

Ing. Tomáš Rábek, PhD Department of finance

Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,

Lesson 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

10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans

10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans Introduction This chapter continues the discussion on the time value of money. In this chapter, you will learn how inflation

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

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

Week in Review #10. Section 5.2 and 5.3: Annuities, Sinking Funds, and Amortization

WIR Math 141-copyright Joe Kahlig, 10B Page 1 Week in Review #10 Section 5.2 and 5.3: Annuities, Sinking Funds, and Amortization an annuity is a sequence of payments made at a regular time intervals. For

Chapter 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)

Dick Schwanke Finite Math 111 Harford Community College Fall 2015

Using Technology to Assist in Financial Calculations Calculators: TI-83 and HP-12C Software: Microsoft Excel 2007/2010 Session #4 of Finite Mathematics 1 TI-83 / 84 Graphing Calculator Section 5.5 of textbook

How 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

International 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

Chapter 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

Key Concepts and Skills. Chapter Outline. Basic Definitions. Future Values. Future Values: General Formula 1-1. Chapter 4

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

The 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

10.3 Future Value and Present Value of an Ordinary General Annuity

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

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

Present Value (PV) Tutorial

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,

The time value of money: Part II

The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods

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.

Chapter 5 Discounted Cash Flow Valuation

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

BEST INTEREST RATE. To convert a nominal rate to an effective rate, press

FINANCIAL COMPUTATIONS George A. Jahn Chairman, Dept. of Mathematics Palm Beach Community College Palm Beach Gardens Location http://www.pbcc.edu/faculty/jahng/ The TI-83 Plus and TI-84 Plus have a wonderful

CALCULATOR 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 time-value-of-money

Sample 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

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

TIME 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 1-5, which are prerequisites. In this

Oklahoma State University Spears School of Business. Time Value of Money

Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a sign-in bonus for your new job? 1. \$15,000 cash upon signing the

Discounted 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?

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

Solutions 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,

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

Present 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

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS

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 PROBLEM #5: ZERO COUPON BOND

TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This assignment will focus on using the TI - 83 to calculate the price of a Zero

CHAPTER 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

ANNUITIES. 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

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

Exercise 1 for Time Value of Money

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

CHAPTER 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

PRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.

PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values

PV Tutorial Using Excel

EYK 15-3 PV Tutorial Using Excel TABLE OF CONTENTS Introduction Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise 8: Exercise 9: Exercise 10: Exercise 11: Exercise

Accounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money

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

Note: If you are not familiar with your calculator s functions, you may want to locate a copy of your manual.

Tab 1: Introduction and Objectives Tab Introduction This section contains basic TVOM practice problems. To complete this section, you must fully understand the basis of TVOM and be familiar with definitions

MAT116 Project 2 Chapters 8 & 9

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

rate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 \$100.00 \$112.00

In Excel language, if the initial cash flow is an inflow (positive), then the future value must be an outflow (negative). Therefore you must add a negative sign before the FV (and PV) function. The inputs

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

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

A = P (1 + r / n) n t

Finance Formulas for College Algebra (LCU - Fall 2013) ---------------------------------------------------------------------------------------------------------------------------------- Formula 1: Amount

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,

Corporate Finance Fundamentals [FN1]

Page 1 of 32 Foundation review Introduction Throughout FN1, you encounter important techniques and concepts that you learned in previous courses in the CGA program of professional studies. The purpose

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

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

Chapter 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

The Time Value of Money

C H A P T E R6 The Time Value of Money When plumbers or carpenters tackle a job, they begin by opening their toolboxes, which hold a variety of specialized tools to help them perform their jobs. The financial

Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation

Integrated Case. 5-42 First National Bank Time Value of Money Analysis

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 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

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

Using Financial Calculators

Chapter 4 Discounted Cash Flow Valuation 4B-1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your Hewlett-Packard or Texas Instruments BA II Plus financial calculator

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.

CHAPTER 2. Time Value of Money 2-1

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

TVM Appendix B: Using the TI-83/84. Time Value of Money Problems on a Texas Instruments TI-83 1

Before you start: Time Value of Money Problems on a Texas Instruments TI-83 1 To calculate problems on a TI-83, you have to go into the applications menu, the blue APPS key on the calculator. Several applications

CHAPTER 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