# Ordinary Annuities Chapter 10

Size: px
Start display at page:

Transcription

1

2 Ordinary Annuities Chapter 10

3 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate the future value and present value of ordinary simple annuities. > Calculate the fair market value of a cash flow stream that includes an annuity. > Calculate the principal balance owed on a loan immediately after any payment. > Calculate the present value and period of deferral of a deferred annuity > Calculate the interest rate per payment interval in a general annuity. 10-3

4 10-4 Annuity - A series of equal payments at regular intervals Term of the annuity - the time from the beginning of the first payment period to the end of the last payment period. Future value of annuity - the future dollar amount of a series of payments plus interest Present value of an annuity - the amount of money needed to invest today in order to receive a stream of payments for a given number of years in the future

5 10-5 Terminology > PMT = Amount of each payment in an annuity > n = Number of payments in the annuity > payment interval is the time between successive payments in an annuity. > ordinary annuities are ones in which payments are made at the end of each payment interval.

6 10-6 Terminology Suppose you obtain a personal loan to be repaid by 48 equal monthly payments. > The payment interval is 1 month > the term of the annuity is 48 months or 4years. > The first payment will be due 1 month after you receive the loan i.e.., at the end of the first payment interval. > the payments form an ordinary annuity.

7 10-7 Figure 10.1 Time Diagram for an n-payment Ordinary Annuity Payment interval n-1 n PMT PMT PMT PMT PMT Interval number Term of the annuity

8 10-8 Ordinary Annuities Ordinary Simple Annuities: The payment interval equals the compounding interval. Eg. Monthly payments and interest is compounded monthly Ordinary General Annuities: The payment interval differs from the compounding interval. Eg. Monthly payments, but interest is compounded semi-annually.

9 10-9 Future Value of an Ordinary Simple Annuity the sum of the future values of all the payments FV= PMT [(1+ i) n - 1 i [

10 10-10 Future Value of an Ordinary Simple Annuity \$1000 \$1000 \$1000 n = 3 n = 2 n = 1 \$1000 \$1000 (1.04) Interval number \$1000 (1.04) 2 \$1000 (1.04) 3 Sum = FV of annuity Just like compound interest! the sum of the future values of all the payments

11 10-11 Figure 10.2 The Future Value of an Ordinary Simple Annuity \$1000 \$1000 \$1000 n = 3 n = 2 n = 1 \$1000 \$1000 (1.04) Interval number \$1000 (1.04) 2 \$1000 (1.04) 3 Assume 4 \$1000 payments with interest at 4% Sum = FV of annuity

12 Figure 10.2 The Future Value of a Four-Payment Ordinary Simple Annuity \$1000 \$1000 \$1000 n = 1 n = 3 n = 2 \$1000 Interval number \$1000 (1.04) \$1000 (1.04) 2 \$1000 (1.04) Assume 4 \$1000 payments with interest at 4% Sum = FV of annuity FV of annuity = \$ \$ ( ) + \$1000( 1.04) + \$1000( 1.04) = \$ \$ \$ \$ = \$

13 10-13 Suppose that you vow to save \$500/month for the next four months, with your first deposit one month from today. If your savings can earn 3% pa converted monthly, determine the total in your account four months from now. Result Month \$ Now \$500 \$500 \$500 \$500 \$500 (1 +.03/12) \$500 (1 +.03/12) 2 \$500 (1 +.03/12) 3 Sum = FV of annuity \$2,007.51

14 10-14 Now imagine that you save \$500 every month for the next three years. Although the same logic applies, I certainly don t want to do it this way! Let s start with the financial calculator method Since your account was empty when you began, PV = 0 n = 3 yrs * 12 pay ts per year = 36 FV = \$ Financial Calculator sol n: 3/12= I/Y 36 n 0 PV 500 +/- PMT comp FV

15 10-15 Cash Flow Sign Convention Keep in mind that when you are making payments, or even making deposits to savings, these are cash outflows, and therefore the values must be negative.

16 Suppose that you vow to save \$500/month for the next four months, with your first deposit one month from today. If your savings can earn 3% pa converted monthly, determine the total in your account four months from now. Financial Calculator sol n: Applying our new calculator solution... Since your account was empty when you began, PV = 0 n = 4 payments FV = \$ /12 = /- comp I/Y n PV PMT FV 10-16

17 10-17 Or, solving using the formula, FV = PMT[(1+ i) n - 1] i PMT = \$500 n = 4 i =.03/12.03/12 = sto + 1 = y x 4 = - 1 = / rcl * 500 = \$

18 10-18 Or, when investing for 3 full years: FV = PMT[(1+ i) n - 1 i PMT = \$500 n = 3 * 12 = 36 i =.03/12.03/12 = sto + 1 = y x 36= - 1 = / rcl * 500 = \$

19 10-19 Figure 10.3 Contribution of Each Payment to an Annuity s Future Value 4 Years \$ Years \$ Years \$12.10 \$ Year \$11.00 \$ st 2nd 3rd 4th 5th Future Payment Payment Payment Payment Payment Values

20 Suppose you decide to save \$75/month for the next three years. If you invest all of these savings in an account which will pay you 7% pa compounded monthly, determine: a) the total in the account after 3 years b) the amount you deposited Financial Calculator sol n: c) the amount of interest earned PMT = - 75 I/Y = 7/12 n = 3*12 = 36 PV = 0 FV =? FV = \$ /12 = Total deposits = 75 * 36 = \$ Interest earned = = \$ /- comp I/Y n PV PMT FV

21 10-21 Present Value of an Ordinary Simple Annuity the sum of the present values of all the payments PV = PMT[1 - (1+ i)- n ] i

22 10-22 Figure 10.4 The Present Value of a Four-Payment Ordinary Simple Annuity Interval number \$1000 (1.04) -1 n = 1 \$1000 \$1000 \$1000 \$1000 n = 2 \$1000 (1.04) -2 n = 3 \$1000 (1.04) -3 \$1000 (1.04) -4 n = 4 Sum = PV of annuity

23 10-23 Figure 10.4 The Present Value of an Ordinary Simple Annuity Interval number \$1000 (1.04) -1 n = 1 \$1000 \$1000 \$1000 \$1000 n = 2 \$1000 (1.04) -2 n = 3 \$1000 (1.04) -3 \$1000 (1.04) -4 n = 4 Sum = PV of annuity PV = \$1000 (1.04) -1 + \$1000 (1.04) -2 + \$1000 (1.04) -3 + \$1000 (1.04) -4 = \$ \$ \$ \$ = \$

24 You overhear your buddy saying the he is repaying a loan at \$500 every month for the next four months. The interest rate he has been charged is 12%pa compounded monthly. Figure out the size of the loan, and the amount of interest involved. Interest: use 12, not.12 when using financial calculator n = 4 payments Since you are making payments, not receiving them, PMT = -500 at the end of the loan, you don t owe any money, so FV = 0 PV = \$ Interest charged = 12/12= /- comp I/Y n FV PMT PV Financial Calculator sol n: = \$49.02

25 You overhear your buddy saying the he is repaying a loan at \$500 every month for the next four months. The interest rate he has been charged is 12%pa compounded monthly. Figure out the size of the loan, and the amount of interest involved Solving the same question using the formula: PV = PMT[1 - (1+ i)- n ] i PV = \$ Interest charged = = \$ / 12 = sto + 1 = y x 4 +/- = - 1 = +/- / rcl * 500 =

26 10-26 Figure 10.5 Contribution of Each Payment to an Annuity s Present Value \$ years \$ years \$37.91 \$ years \$ years \$9.09 \$10.00 Present values 1 st 2 nd 3 rd 4 th 5 th payment payment payment payment payment

27 10-27 Deferred Annuities A deferred annuity may be viewed as an ordinary annuity that does not begin until a time interval (named the period of deferral) has passed. d = Number of payment intervals in the period of deferral Two-step procedure to find PV: > Calculate the present value, PV 1, of the payments at the end of the period of deferral this is just the PV of an ordinary annuity. > Calculate the present value, PV 2, of the step 1 amount at the beginning of the period of deferral.

28 If this same buddy doesn t begin to repay his loan for another 11 months, at a rate \$500 every month for four months. The interest rate is still 12%pa compounded monthly. Determine the size of the loan. Financial Calculator sol n: The deferral period is 10 months PV = \$ This is the value 10 months from now Today s value: \$ /- FV 0 PMT 10 n comp PV 12/12= /- comp I/Y n FV PMT PV 10-28

29 10-29 General Annuities number of compoundings per year > c = number of payments per year > Use i 2 = (1+i) c - 1 to calculate the equivalent periodic rate that matches the payment interval. > Use this equivalent periodic rate as the value for i in the appropriate simple annuity formula, or as the value entered into the i memory of the financial calculator.

30 Suppose you decide to save \$50/month for the next three years. If you invest all of these savings in an account which will pay you 7% pa compounded semi-annually, determine the total in the account after 3 years

31 Suppose you decide to save \$50/month for the next three years. If you invest all of these savings in an account which will pay you 7% pa compounded semi-annually,, determine the total in the account after 3 years Note the differing compounding frequency and payment intervals This is a GENERAL annuity and so we need to calculate c number of compoundings per year c = number of payments per year = Store it!

32 Suppose you decide to save \$50/month for the next three years. If you invest all of these savings in an account which will pay you 7% pa compounded semi-annually, determine the total in the account after 3 years PMT = -50 PV = 0 FV =? n = 3*12 = 36 i =.07/2 c = 2/12 = i 2 = Once we have c, we need to determine i 2. i 2 = (1 + i) c / 12 = sto.07 / 2 = + 1 = y x rcl = - 1 = * 100 = FV = \$ /- comp I/Y n FV PMT PV

33 Tip: Improving the Accuracy of Calculated Results > the value for c can be a repeating decimal > when this happens, save c in memory > your calculator then retains at least two more digits than you see in the display. > when you need the exponent for the y x function, recall the value for c from the memory > the value for i 2 should be saved in memory as soon you calculate it. Whenever i 2 is needed in a subsequent calculation, recall it from the memory.

34 10-34 Reid David made annual deposits of \$1,000 to Fleet Bank, which pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit? /- comp I/Y n PV PMT FV FV = \$ Future value of an annuity Future value of a lump sum /- PV 10 n 0 PMT comp FV \$7,834.03

35 10-35

### 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

### 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,

### 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 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

### 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,

### 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

### 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

### 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

### 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

### 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

### 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

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

### 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

### PV Tutorial Using Calculator (Sharp EL-738)

EYK 15-2 PV Tutorial Using Calculator (Sharp EL-738) TABLE OF CONTENTS Calculator Configuration and Abbreviations Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise

### 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

### USING 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

### Present Value Concepts

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

### 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

### 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

### 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

### 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

### 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

### Module 5: Interest concepts of future and present value

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

### 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 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

### 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.

### Course FM / Exam 2. Calculator advice

Course FM / Exam 2 Introduction It wasn t very long ago that the square root key was the most advanced function of the only calculator approved by the SOA/CAS for use during an actuarial exam. Now students

### Continue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.

Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two

### 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

### BUSI 121 Foundations of Real Estate Mathematics

Real Estate Division BUSI 121 Foundations of Real Estate Mathematics SESSION 2 By Graham McIntosh Sauder School of Business University of British Columbia Outline Introduction Cash Flow Problems Cash Flow

### Module 5: Interest concepts of future and present value

file:///f /Courses/2010-11/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present

### 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

### 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

### 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

### 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

### NPV calculation. Academic Resource Center

NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year

### 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.

### Hewlett-Packard 10BII Tutorial

This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,

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

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

### 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,

### Time Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology

Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations

### 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

### 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,

### 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

### 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

### 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 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

### 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

### 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

### Value of Money Concept\$

Value of Money Concept\$ Time, not timing is the key to investing 2 Introduction Time Value of Money Application of TVM in financial planning : - determine capital needs for retirement plan - determine

### THE TIME VALUE OF MONEY

QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost

### 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

### 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

### Foundation review. Introduction. Learning objectives

Foundation review: Introduction Foundation review Introduction Throughout FN1, you will be expected to apply techniques and concepts that you learned in prerequisite courses. The purpose of this foundation

### 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)

### Notes on the SHARP EL-738 calculator

Chapter 1 Notes on the SHARP EL-738 calculator General The SHARP EL-738 calculator is recommended for this module. The advantage of this calculator is that it can do basic calculations, financial calculations

### 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 5 & 6 Financial Calculator and Examples

Chapter 5 & 6 Financial Calculator and Examples Konan Chan Financial Management, Spring 2016 Five Factors in TVM Present value: PV Future value: FV Discount rate: r Payment: PMT Number of periods: N Get

### The Time Value of Money

The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time

### 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

### 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

### Basic financial arithmetic

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

### Future 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

### 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

### 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

### 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

### 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

### 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

### Introduction. Turning the Calculator On and Off

Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction

### Chapter 4: Time Value of Money

Chapter 4: Time Value of Money BASIC KEYS USED IN FINANCE PROBLEMS The following two key sequences should be done before starting any "new" problem: ~ is used to separate key strokes (3~N: enter 3 then

### 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

### Hewlett Packard (HP) 10BII

Hewlett Packard (HP) 10BII The HP10BII is programmed to perform two basic types of operations: statistical operations and financial operations. Various types of computations are activated by depressing

### The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-738 Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### Sharp EL-733A Tutorial

To begin, look at the face of the calculator. Almost every key on the EL-733A has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in

### 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.

### 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

### 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,

### 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

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

for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society

### 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

### 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 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

### 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

### 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 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6

CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use

### Hewlett-Packard 10B Tutorial

To begin, look at the face of the calculator. Every key (except one, the gold shift key) on the 10B has two functions: each key's primary function is noted in white on the key itself, while each key's

### 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

### 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

### 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

### 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

### 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.

### 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

### 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

### Real estate investment & Appraisal Dr. Ahmed Y. Dashti. Sample Exam Questions

Real estate investment & Appraisal Dr. Ahmed Y. Dashti Sample Exam Questions Problem 3-1 a) Future Value = \$12,000 (FVIF, 9%, 7 years) = \$12,000 (1.82804) = \$21,936 (annual compounding) b) Future Value