# Solutions to Time value of money practice problems

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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, compounded annually? quarterly? Annual compounding: FV = \$2,500 ( ) 10 = \$2,500 (1.4802) = \$3, Quarterly compounding: FV = \$2,500 ( ) 40 = \$2,500 (1.4889) = \$3, If you deposit \$10 in an account that pays 5% interest, compounded annually, how much will you have at the end of 10 years? 50 years? 100 years? 10 years: FV = \$10 (1+0.05) 10 = \$10 (1.6289) = \$ years: FV = \$10 ( ) 50 = \$10 ( ) = \$ years: FV = \$10 ( ) 100 = \$10 (131.50) = \$1, How much interest on interest is earned in an account by the end of 5 years if \$100,000 is deposited and interest is 4% per year, compounded continuously? Note: Interest on interest is the difference between the future value calculated using compounded interest and the future value calculated using simple interest, because simple interest includes only interest on the principal amount, not the interest-oninterest. Continuously compounded: FV = \$100,000 e 0.04(5) = \$100,000 (1.2214) = \$122, Simple interest: FV = \$100,000 + [\$100,000(0.04)(5)] = \$100, ,000 = \$120,000 Interest on interest = \$122, = \$120,000 = \$2, How much will be in an account at the end of five years the amount deposited today is \$10,000 and interest is 8% per year, compounded semi-annually? FV = \$10,000 (1+0.04)10 = \$10,000 (1.4802) = \$14, Complete the following, solving for the present value, PV: Case Future value Interest rate Number of periods Present value A \$10,000 5% 5 \$7, B \$563,000 4% 20 \$256, C \$5, % 3 \$4, Suppose you want to have \$0.5 million saved by the time you reach age 30 and suppose that you are 20 years old today. If you can earn 5% on your funds, how much would you have to invest today to reach your goal? Solutions to Time Value of Money Practice Problems 1

2 Given: FV = \$500,000; i = 5%; n = 10 PV = \$500,000 (1 / ( ) 10 ) = \$500,000 (0.6139) = \$306, How much would I have to deposit in an account today that pays 12% interest, compounded quarterly, so that I have a balance of \$20,000 in the account at the end of 10 years? Given: FV = \$20,000; i = 12%/4 = 3%; n = 10 x 4 = 40 quarters PV = \$6, Suppose I want to be able to withdraw \$5,000 at the end of five years and withdraw \$6,000 at the end of six years, leaving a zero balance in the account after the last withdrawal. If I can earn 5% on my balances, how much must I deposit today to satisfy my withdrawals needs? Given: Hint -- There are two different future values. Treat as two separate present values, then combine. FV = \$5,000; n = 5, i = 5% PV = \$3, FV = \$6,000; n = 6, i = 5% PV = \$4, PV of the two future values = \$3, , = \$8, Or, can use the NPV function in a financial calculator: In the TI-83/84, the cash flows are {0,0,0,0,5000,5000} In the HP10B, the cash flows are 0,0,0,0,0,5000, Consider a loan of \$1 million that is paid off quarterly over a period of nine years. Calculate the dollar amount of interest and loan principle repaid corresponding to each payment if the interest rate is 6% per year, compounded quarterly. Year Quarter Beginning balance Payment Interest Principal repayment Remaining principal 0 \$ 1,000, \$ 1,000, \$ 36, \$ 15, \$ 21, \$ 978, \$ 978, \$ 36, \$ 14, \$ 21, \$ 957, \$ 957, \$ 36, \$ 14, \$ 21, \$ 935, \$ 935, \$ 36, \$ 14, \$ 22, \$ 913, \$ 913, \$ 36, \$ 13, \$ 22, \$ 891, \$ 891, \$ 36, \$ 13, \$ 22, \$ 868, \$ 868, \$ 36, \$ 13, \$ 23, \$ 845, \$ 845, \$ 36, \$ 12, \$ 23, \$ 821, \$ 821, \$ 36, \$ 12, \$ 23, \$ 797, \$ 797, \$ 36, \$ 11, \$ 24, \$ 773, \$ 773, \$ 36, \$ 11, \$ 24, \$ 749, \$ 749, \$ 36, \$ 11, \$ 24, \$ 724, \$ 724, \$ 36, \$ 10, \$ 25, \$ 698, \$ 698, \$ 36, \$ 10, \$ 25, \$ 673, \$ 673, \$ 36, \$ 10, \$ 26, \$ 647, \$ 647, \$ 36, \$ 9, \$ 26, \$ 620, \$ 620, \$ 36, \$ 9, \$ 26, \$ 593, \$ 593, \$ 36, \$ 8, \$ 27, \$ 566, Solutions to Time Value of Money Practice Problems 2

3 19 \$ 566, \$ 36, \$ 8, \$ 27, \$ 538, \$ 538, \$ 36, \$ 8, \$ 28, \$ 510, \$ 510, \$ 36, \$ 7, \$ 28, \$ 482, \$ 482, \$ 36, \$ 7, \$ 28, \$ 453, \$ 453, \$ 36, \$ 6, \$ 29, \$ 424, \$ 424, \$ 36, \$ 6, \$ 29, \$ 394, \$ 394, \$ 36, \$ 5, \$ 30, \$ 364, \$ 364, \$ 36, \$ 5, \$ 30, \$ 333, \$ 333, \$ 36, \$ 5, \$ 31, \$ 302, \$ 302, \$ 36, \$ 4, \$ 31, \$ 270, \$ 270, \$ 36, \$ 4, \$ 32, \$ 238, \$ 238, \$ 36, \$ 3, \$ 32, \$ 205, \$ 205, \$ 36, \$ 3, \$ 33, \$ 172, \$ 172, \$ 36, \$ 2, \$ 33, \$ 139, \$ 139, \$ 36, \$ 2, \$ 34, \$ 105, \$ 105, \$ 36, \$ 1, \$ 34, \$ 70, \$ 70, \$ 36, \$ 1, \$ 35, \$ 35, \$ 35, \$ 36, \$ \$ 35, \$ (0.00) 10. Suppose you deposit \$100,000 in an account today that pays 6% interest, compounded annually. How long does it take before the balance in your account is \$500,000? Given: I = 6%; PV = \$100,000; FV = \$500,000 Solution: N = The Lucky Loan Company will lend you \$10,000 today with terms that require you to pay off the loan in thirty-six monthly installments of \$500 each. What is the effective annual rate of interest that the Lucky Loan Company is charging you? Given: PV = \$10,000; N = 36; PMT = 500 Solve for i: i = % EAR = ( ) 12 1 = % 12. How long does it take for your money to grow to ten times its original value if the interest rate of 5% per year? Given: PV = 1; FV = 10; I = 5% Solution: 48 years 13. Under what conditions does the effective annual rate of interest (EAR) differ from the annual percentage rate (APR)? If interest is compounded more frequently than once a year, the EAR will be different than the APR; the EAR will be greater than the APR except in the case in which there is annual compounding (in which case the EAR will be equal to the APR) 14. As the frequency of compounding increases within the annual period, what happens to the relation between the EAR and the APR? The EAR will become larger than the APR as the frequency of compounding increases. The largest difference between the two is in the case in which interest is compounded continuously. 15. If interest is paid at a rate of 5% per year, compounded quarterly, what is the: a) annual percentage rate? Solutions to Time Value of Money Practice Problems 3

4 APR = 5% b) effective annual rate? EAR = ( ) 4-1 = % 16. L. Shark is willing to lend you \$10,000 for three months. At the end of six months, L. Shark requires you to repay the \$10,000, plus 50%. a) What is the length of the compounding period? Six months b) What is the rate of interest per compounding period? 50% c) What is the annual percentage rate associated with L. Shark's lending activities? APR = 50% x 2 = 100% d) What is the effective annual rate of interest associated with L. Shark's lending activities? EAR = ( ) 2-1 = 125% 17. The Consistent Savings and Loan is designing a new account that pays interest quarterly. They wish to pay, effectively, 16% per year on this account. Consistent desires to advertise the annual percentage rate on this new account, instead of the effective rate, since its competitors state their interest on an annualized basis. What is the APR that corresponds to an effective rate of 16% for this new account? EAR = 16% APR = this takes the fourth root of 1 + EAR i = 3.78% APR = 3.78% x 4 = % 18. Consider an annuity consisting of three cash flows of \$2,000 each. Assume a 4% interest rate. What is the present value of the annuity if the first cash flow occurs: a) today. PV of annuity due = \$5, b) one year from today. PV of ordinary annuity = \$5, c) two years from today. PV of a deferred annuity = \$5, / 1.04 = \$5, d) three years from today. PV of a deferred annuity = \$5, / = \$5, e) four years from today. PV of a deferred annuity = \$5, / = \$4, Solutions to Time Value of Money Practice Problems 4

5 f) five years from today. PV of a deferred annuity = \$5, / = \$4, Suppose you wish to retire forty years from today. You determine that you need \$50,000 per year once you retire, with the first retirement funds withdrawn one year from the day you retire. You estimate that you will earn 6% per year on your retirement funds and that you will need funds up to and including your 25th birthday after retirement. a) How much must you deposit in an account today so that you have enough funds for retirement? PV retire = \$50,000 (PV annuity factor, N=25 and i=6%) Given: PMT = \$50,000; N = 25; I = 6%; Solve for PV PV retire = \$ Given: FV = \$639,167.81; N = 40; I = 6%; Solve for PV PV today = \$639, / ( ) 40 = \$62, b) How much must you deposit each year in an account, starting one year from today, so that you have enough funds for retirement? PV retire = \$50,000 (PV annuity factor, N=25 and i=6%) Given: PMT = \$50,000; N = 25; I = 6%; Solve for PV PV retire = \$ Given: FV = \$639,167.81; N = 40; I = 6%; Solve for PMT PMT = \$4, Using an interest rate of 5% per year, what is the value today of the following cash flows: Years from today Cash flow , ,000 FV = \$8, , = \$16, Note: Cash flow list: {0,0,10000,10000} Solutions to Time Value of Money Practice Problems 5

### 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

### 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

### 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

### 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

### Calculating interest rates

Calculating interest rates A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction 2. Annual percentage rate 3. Effective annual rate 1. Introduction The basis of the time value of money

### 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.

### 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

### 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)

### 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

### 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

### 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

### 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

### Ordinary 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

### 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

### 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?

### 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

### 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

### Finance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.

Chapter 1 Finance 331 What is finance? - Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: -

### 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

### HOW TO CALCULATE PRESENT VALUES

Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

### Time 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

### 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

### 2. 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 equal-sized

### 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. If you deposit \$100 in an account that pays 6% annual interest, what amount will you expect to have in

Time Value of Money Future value Present value Rates of return 1 If you deposit \$100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.

### 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

### FIN 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 3-1 a) Future Value = FV(n,i,PV,PMT)

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

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

### 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 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

### 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

### 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.

### CHAPTER 6 Accounting and the Time Value of Money

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

### How 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

### 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

### 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

### 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

### Chapter 28 Time Value of Money

Chapter 28 Time Value of Money Lump sum cash flows 1. For example, how much would I get if I deposit \$100 in a bank account for 5 years at an annual interest rate of 10%? Let s try using our calculator:

### 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

### 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

### 1.3.2015 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

### 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

### Prepared by: Dalia A. Marafi Version 2.0

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

### 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

### Statistical Models for Forecasting and Planning

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

### 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

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

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

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

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

### Chapter. Discounted Cash Flow Valuation. CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG.

Chapter 6 Discounted Cash Flow Valuation CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG. Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute

### Time Value of Money. Background

Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple

### 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

### 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

### 5. Time value of money

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

### 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

### hp calculators HP 20b Time value of money basics The time value of money The time value of money application Special settings

The time value of money The time value of money application Special settings Clearing the time value of money registers Begin / End mode Periods per year Cash flow diagrams and sign conventions Practice

### How 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

### 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

### Solutions to Problems: Chapter 5

Solutions to Problems: Chapter 5 P5-1. 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

### 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

### Chapter 02 How to Calculate Present Values

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

### 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,

### 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,

### 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 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

### 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

### 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

### Chapter 4. The Time Value of Money

Chapter 4 The Time Value of Money 4-2 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest

### Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is \$75. You will receive \$100 five years later.

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

### Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e

Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,

### 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

### CHAPTER 9 Time Value Analysis

Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams

### 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

### 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

### 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

### Compound Interest Formula

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

### 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,

### Time Value of Money, Part 5 Present Value aueof An Annuity. Learning Outcomes. Present Value

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

### 13-2. Annuities Due. Chapter 13. MH Ryerson

13-2 Annuities Due Chapter 13 13-3 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,

### Week 4. Chonga Zangpo, DFB

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

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

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

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

### Chapter 3 Present Value

Chapter 3 Present Value MULTIPLE CHOICE 1. Which of the following cannot be calculated? a. Present value of an annuity. b. Future value of an annuity. c. Present value of a perpetuity. d. Future value

### 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

### CHAPTER 5. Interest Rates. Chapter Synopsis

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

### CALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time

CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses

### 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

### Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value

Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations

### F V P V = F V = P (1 + r) n. n 1. FV n = C (1 + r) i. i=0. = C 1 r. (1 + r) n 1 ]

1 Week 2 1.1 Recap Week 1 P V = F V (1 + r) n F V = P (1 + r) n 1.2 FV of Annuity: oncept 1.2.1 Multiple Payments: Annuities Multiple payments over time. A special case of multiple payments: annuities

### Financial Management Spring 2012

3-1 Financial Management Spring 2012 Week 4 How to Calculate Present Values III 4-1 3-2 Topics Covered More Shortcuts Growing Perpetuities and Annuities How Interest Is Paid and Quoted 4-2 Example 3-3

### Chapter 4 Discounted Cash Flow Valuation

University of Science and Technology Beijing Dongling School of Economics and management Chapter 4 Discounted Cash Flow Valuation Sep. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Be able to compute

### 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

### 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

### 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

### 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

### 9. Time Value of Money 1: Present and Future Value

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