Chapter F: Finance. Section F.1F.4


 Drusilla Wood
 1 years ago
 Views:
Transcription
1 Chapter F: Finance Section F.1F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given as a decimal. Then the interest I at the end of t years is given by The future value F at the end of t years is Example 1 You borrow $300 on a credit card that charges simple interest at an annual rate of 12%. What is your interest for 9 months? Example 2 An account with an initial amount of $5000 earns simple interest at a rate of 6% annually. How much is in the account after 4 years? Example 3 Belinda takes out a loan earning simple interest for $1000. a) What simple interest rate is being obtained if the amount F at the end of 8 months is $1050? 1
2 b) After how many months from the beginning of the loan will you owe $1215? Example 4 How much should be placed into an account paying simple interest of 4% so that after 6 months, the future value of the account will be $2500? Round your answer to the nearest cent. F.2 Compound Interest Usually, interest is not calculated (only) from the original sum of money. A more common situation is one in which interest is calculated, or compounded, periodically and each time interest is calculated, the accumulated amount becomes the new principal. In other words, the interest earns interest. Suppose a principal P earns interest at an annual interest rate of r and interest is compounded m times a year. Then, after t years, the accumulated amount or future value F is Example 5 You put $500 into a savings account that earns 2% interest compounded monthly. How much is in the account after 1 month? 2 months? To calculate compound interest, we will use TVM Solver (we can t use this for simple interest). 2
3 Compound Interest with TVM Solver on the Calculator: 1. Press APPS. 2. Select Finance... (Option 1) 3. Select TVM Solver (Option 1) total number of compoundings during the time period interest rate (as a percent) initial amount in the account regularly occuring payments future value of the account the number of payments/compoundings per year END/BEGIN (Note: END should be highlighted) 4. Enter the known information. 5. Scroll to the line representing the unknown data. 6. Press SOLVE (ALPHA ENTER) TINspire: 1. Press MENU. 2. Select Finance (Option 8) 3. Select Finance Solver... (Option 1) 4. Enter the known information. 5. Scroll to the line representing the unknown data. 6. Press ENTER Important Note: In the TVM Solver, the values for PV, PMT, and FV will sometimes be negative. This is done to represent the transfer or flow of money. We will usually look at these problems from the standpoint of the investor or borrower. A negative number represents an of money away from the investor or borrower, i.e., when money is leaving your pocket. Use a negative number when: Making payments Depositing money in a bank 3
4 A positive number represents an of money to the investor or borrower, i.e., when you put money in your pocket. Use a positive number when: You receive a loan from a bank or lender. You receive money from a bank account. Example 6 An account with an initial amount of $5000 earns interest of 6% compounded monthly. How much is in the account after 4 years? How much interest is earned? Example 7 How much should be placed into an account paying interest of 4% compounded quarterly so that after 6 years, the future value of the account will be $2500? How much interest is earned? 4
5 Example 8 Find the time for an investment of $1000 compounding monthly at an interest rate of 3% per year to double. How much interest is earned? Example 9 Suppose that 4 years ago, I invested $2500 in an account that compounds interest weekly. Right now I have $3625 in the account. What is the interest rate for this account (rounded to 4 decimal places)? Example 10 Suppose $1000 is left for 3 years in an account that earns interest at a rate of 5% per year compounded monthly. How much interest is earned during the third month of the second year? 5
6 Example 11 Suppose $500 is invested in an account that earns %9 interest compounded monthly. How much interest is earned in 1 year? What percent of the original amount is this? Suppose a sum of money is invested at an annual rate of r expressed as a decimal and is compounded m times a year. The effective yield r eff is Effective Yield with Your Calculator: 1. Press APPS. 2. Select Finance... (Option 1) 3. Select Eff (Option C) 4. Give the arguments as follows: Eff(r, m). Example 12 What is the effective annual yield on an account paying 9% interest per year, compounded monthly? Example 13 Compare the following situations. Which would be the better choice for an investment? Which would be the better choice for a credit card? A: 8% compounded semiannually B: 7.9% compounded daily 6
7 Continuous Compound of Interest Example 14 An account with an initial amount of $100 earns 5% interest. How much is in the account after 1 year is interest is compounded a) annually? b) quarterly? c) monthly? d) daily? e) every hour? f) 1 million times per year? Suppose a principal P earns interest at an annual rate of r per year (as a decimal) and interest is compounded continuously. Then, after t years, the accumulated amount (or future value), F, is Example 15 Consider the previous problem. How much interest is in the account after 1 year if interest is compounded continuously? Example 16 If you invest $5000 at 8% per year with interest compounded continuously, how much would you have in your account after 7 months? How much interest is earned during this time? 7
8 F.3 Annuities and Sinking Funds An time periods. is a sequence of equal payments made at equal An are made at the end of the time periods compounding. is one in which the payments The of an annuity is the time from the beginning of the first period to the end of the last period. The is the total amount in the account, including interest, at the end of the term of an annuity. Example 17 Some examples of annuities are: regular deposits into a savings account, monthly home mortgage payments, monthly insurance payments The future value F V of an ordinary annuity of n payments of P MT dollars paid at the end of each period into an account that earns interest at the rate of i per period is We will use TVM Solver. Example 18 Suppose a person opens up a retirement account in which he/she places $750 each month into an account that earns interest at a rate of 8%/year compounded monthly. a) How much will be in the account when this person retires in 25 years? 8
9 b) How much interest is earned in total? A to meet a future need. is an account established for accumulating funds Example 19 You find a retirement account that earns interest at a rate of 4% per year compounded monthly. How much should you deposit into your account every month if you want to have $500,000 in the account when you retire in 40 years? Example 20 Dane s parents anticipate that his first year of college will cost $15,000. Knowing Dane s first year of college is 15 years away, determine the amount of money they should deposit into an account each year making 6.25% per year compounded annually if they intend on having the money ready to pay for his first year when he starts college. 9
10 How much would they have to deposit monthly over the same time period to reach the desired goal if they found an account paying interest at a rate of 6.25%/yr compounded monthly? Example 21 A family wants to save up some money to make a $25,000 down payment on a house in 6 years. a) How much should they deposit each month into an account if the account earns interest at the rate of 2.75%/year compunded monthly? b) How much is in the account after 3 years? How much of this is due to interest? 10
11 c) If they can afford $500 a month instead, when can they afford the down payment for the house? F.4 Present Value of Annuities and Amortization The present value of an ordinary annuity of n payments of P M T dollars with interest compounded at the rate of i per period is We will use TVM Solver. Example 22 Suppose you win a lottery worth $4,250,000 which is paid out with $170,000 payments for the next 25 years. In order to make these payments to you, how much money must the lottery commission have in an account now if the account earns interest at a rate of 3.25%/year compounded annually? 11
12 If you are given the option of taking a lump sum of $3,000,000 now or of accepting the payments, which should you take? Assume you are also able to invest the money at an interest rate of 3.25%. Option A: Take the lump sum Option B: Accept the payments is the process of paying off a debt. The periodic payment P MT to be made at the end of each period on a loan of P V dollars that is to be amortized over n periods with interest at the rate of i per period is Example 23 What monthly payment is required to amortize a loan of $75,000 over 10 years if interest at the rate of 5.25% per year, compounded monthly, is charged on the unpaid balance at the end of each month? 12
13 Example 24 Thaddeus made a down payment of $5000 towards the purchase of a new car. To pay the balance, he secured a loan at the rate of 1.9% per year compounded monthly. Under the terms of his finance agreement, he is required to make payments of $144/month for 36 months. a) What is the cash price of the car? b) How much total interest did Thaddeus pay on the loan? Example 25 A family secured a 15year bank loan of $162,600 to purchase a house. The bank charges interest at a rate of 2.6% per year, compounded monthly. a) What is their monthly payment? b) How much total interest will they end up paying? 13
14 on a loan at a given point in time. is the amount you still owe To find the outstanding principal, find the remaining payments. of the Example 26 Consider the scenario from the previous example. a) What is the outstanding principal after 10 years? In other words, how much do they still owe after 10 years? b) How much thave they actually paid in these 10 years? Why couldn t we subtract this from $162,600 to find the outstanding principal? in a loan scenario is how much of the item you actually OWN. It is how much principal you have paid on the original loan plus any down payment (what belongs to you). The interest you pay does NOT count towards your equity. At any moment in time the following is true: 14
15 Example 27 We again consider the problem from the last two examples. What is their equity after 10 years? Example 28 Five years ago, Janella got a bank loan for the purchase of a home. The home was worth $245,546 and she made a 20% down payment. The interest on the loan was 5.35%/year compounded monthly and the term of the loan was 30 years. a) What is Janella s current monthly mortgage payment? b) After these first 5 years, Janella decides to refinance her home. What is her outstanding principal at this point? Equity? 15
16 c) Janella refinanced her home by securing a new 20year loan for the outstanding principal at a new rate of 4%/year compounded monthly. What will her new monthly mortgage payment now? d) How much money will Janella save by refinancing the loan? Example 29 Suppose I take out a 2year loan in the amount of $5000 at an interest rate of 6.5%/year compounded quarterly in order to buy a used car. a) What is my current quarterly payment? b) How much of the first payment goes toward interest? c) How much goes toward the principal? 16
17 d) What is the outstanding principal now? Equity? e) How much of the second payment goes toward interest and how much goes toward principal? What is the outstanding principal now? Equity? f) Finish the amortization table for the next two periods: Period Payment Towards Interest Towards Principal Outstanding Principal Equity Earned ,
18 Example 30 A boat costs $65,000. You make a down payment of $10,000 and finance the remaining balance with a 10year loan at an interest rate of 5.1%/year compounded monthly. You find that your monthly payment is $ (Check this on your own). a) Fill in the amortization table for the first two monthly payments. Period Payment Towards Interest Towards Principal Outstanding Principal Equity Earned b) What are the outstanding principal and equity after 7 years? (Hint: Don t analyze all 84 payments that have been made.) 18
19 Example 31 You have a $3000 credit card bill on a card that charges interest at a rate of 12% per year, compounded monthly, on the unpaid balance. a) If you do not make any additional purchases on the card and make a $71 payment each month, how long will it take you to pay off your bill? How much total interest do you end up paying? b) If you instead plan to pay off this credit card at the end of 3 years, how much will you have to pay each month? How much of your first payment goes toward interest? How much of your first payment goes toward principal (paying off your debt)? 19
2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationSection 5.1  Compound Interest
Section 5.1  Compound Interest Simple Interest Formulas If I denotes the interest on a principal P (in dollars) at an interest rate of r (as a decimal) per year for t years, then we have: Interest: Accumulated
More informationThe values in the TVM Solver are quantities involved in compound interest and annuities.
Texas Instruments Graphing Calculators have a built in app that may be used to compute quantities involved in compound interest, annuities, and amortization. For the examples below, we ll utilize the screens
More informationfirst complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest.
ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular
More information1. Annuity a sequence of payments, each made at equally spaced time intervals.
Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More informationUsing the Finance Menu of the TI83/84/Plus calculators KEY
Using the Finance Menu of the TI83/84/Plus calculators KEY To get to the FINANCE menu On the TI83 press 2 nd x 1 On the TI83, TI83 Plus, TI84, or TI84 Plus press APPS and then select 1:FINANCE The
More informationMain TVM functions of a BAII Plus Financial Calculator
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More information1. % of workers age 55 and up have saved less than $50,000 for retirement (not including the value of a primary residence).
Toward Quantitative Literacy: Interesting Problems in Finance 2008 AMATYC Conference, Washington, D.C., Saturday, November 22, 2008 http://www.delta.edu/jaham Fill in the blanks. 1. % of workers age 55
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationMAT116 Project 2 Chapters 8 & 9
MAT116 Project 2 Chapters 8 & 9 1 81: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the
More informationExample. L.N. Stout () Problems on annuities 1 / 14
Example A credit card charges an annual rate of 14% compounded monthly. This month s bill is $6000. The minimum payment is $5. Suppose I keep paying $5 each month. How long will it take to pay off the
More informationChapter 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
More informationFIN 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
More informationBEST 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 TI83 Plus and TI84 Plus have a wonderful
More informationE INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is
E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =
More informationIn Section 5.3, we ll modify the worksheet shown above. This will allow us to use Excel to calculate the different amounts in the annuity formula,
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
More informationCompound 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
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationMathematics. Rosella Castellano. Rome, University of Tor Vergata
and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings
More informationWeek in Review #10. Section 5.2 and 5.3: Annuities, Sinking Funds, and Amortization
WIR Math 141copyright 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
More informationREVIEW MATERIALS FOR REAL ESTATE ANALYSIS
REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS
More informationSample problems from Chapter 10.1
Sample problems from Chapter 10.1 This is the annuities sinking funds formula. This formula is used in most cases for annuities. The payments for this formula are made at the end of a period. Your book
More informationCALCULATOR HINTS ANNUITIES
CALCULATOR HINTS ANNUITIES CALCULATING ANNUITIES WITH THE FINANCE APP: Select APPS and then press ENTER to open the Finance application. SELECT 1: TVM Solver The TVM Solver displays the timevalueofmoney
More informationSection 8.1. I. Percent per hundred
1 Section 8.1 I. Percent per hundred a. Fractions to Percents: 1. Write the fraction as an improper fraction 2. Divide the numerator by the denominator 3. Multiply by 100 (Move the decimal two times Right)
More informationTIME VALUE OF MONEY (TVM)
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
More informationAnnuities and Sinking Funds
Annuities and Sinking Funds Sinking Fund A sinking fund is an account earning compound interest into which you make periodic deposits. Suppose that the account has an annual interest rate of compounded
More informationDiscounted Cash Flow Valuation
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationChapter 3 Mathematics of Finance
Chapter 3 Mathematics of Finance Section 3 Future Value of an Annuity; Sinking Funds Learning Objectives for Section 3.3 Future Value of an Annuity; Sinking Funds The student will be able to compute the
More informationFuture Value Sinking Fund Present Value Amortization. P V = P MT [1 (1 + i) n ] i
Math 141copyright Joe Kahlig, 15C Page 1 Section 5.2: Annuities Section 5.3: Amortization and Sinking Funds Definition: An annuity is an instrument that involves fixed payments be made/received at equal
More information300 Chapter 5 Finance
300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for $200,000 with a down payment of $40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which
More informationAppendix C 1. Time Value of Money. Appendix C 2. Financial Accounting, Fifth Edition
C 1 Time Value of Money C 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
More informationExercise 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
More informationFinite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan
Finite Mathematics Helene Payne CHAPTER 6 Finance 6.1. Interest savings account bond mortgage loan auto loan Lender Borrower Interest: Fee charged by the lender to the borrower. Principal or Present Value:
More informationFinance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date
1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand
More informationThe explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.
USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas
More informationDick 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
More informationActivity 3.1 Annuities & Installment Payments
Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.
More informationModule 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
More informationCHAPTER 2. Time Value of Money 21
CHAPTER 2 Time Value of Money 21 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 22 Time lines 0 1 2 3
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationMath 120 Basic finance percent problems from prior courses (amount = % X base)
Math 120 Basic finance percent problems from prior courses (amount = % X base) 1) Given a sales tax rate of 8%, a) find the tax on an item priced at $250, b) find the total amount due (which includes both
More informationReview Page 468 #1,3,5,7,9,10
MAP4C Financial Student Checklist Topic/Goal Task Prerequisite Skills Simple & Compound Interest Video Lesson Part Video Lesson Part Worksheet (pages) Present Value Goal: I will use the present value formula
More informationPractice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.
PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor
More informationIntroduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations
Introduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the HewlettPackard
More informationChapter 2 Applying Time Value Concepts
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
More informationValue of Money Concept$
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
More informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 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
More informationFIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1
FIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems  Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 31 a) Future Value = FV(n,i,PV,PMT)
More informationAppendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C 1
C Time Value of Money C 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.
More informationFinance 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
More informationFinance 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: 
More informationFind the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 2) 15% compounded semiannually
Exam Name Find the compound amount for the deposit. Round to the nearest cent. 1) $1200 at 4% compounded quarterly for 5 years Find the effective rate corresponding to the given nominal rate. Round results
More informationChapter 22: Borrowings Models
October 21, 2013 Last Time The Consumer Price Index Real Growth The Consumer Price index The official measure of inflation is the Consumer Price Index (CPI) which is the determined by the Bureau of Labor
More informationTime Value of Money. Nature of Interest. appendix. study objectives
2918T_appC_C01C20.qxd 8/28/08 9:57 PM Page C1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.
More informationFinance 197. Simple Onetime 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
More informationReview for Exam 1. Instructions: Please read carefully
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
More informationCompounding Quarterly, Monthly, and Daily
126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,
More informationModule 5: Interest concepts of future and present value
file:///f /Courses/201011/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
More informationKey Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationTIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY
TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value
More information10. 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
More informationSolutions to Problems: Chapter 5
Solutions to Problems: Chapter 5 P51. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More informationsubstantially 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
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationTIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!
TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest $1,000 it becomes $1,050 $1,000 return of $50 return on Factors to consider when assessing Return on
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective
More informationTVM Appendix B: Using the TI83/84. Time Value of Money Problems on a Texas Instruments TI83 1
Before you start: Time Value of Money Problems on a Texas Instruments TI83 1 To calculate problems on a TI83, you have to go into the applications menu, the blue APPS key on the calculator. Several applications
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More informationRegular Annuities: Determining Present Value
8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded
More informationDiscounted Cash Flow Valuation
BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?
More informationTopics. 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
More informationCHAPTER 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)
More informationCHAPTER 1. Compound Interest
CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.
More informationThe Time Value of Money
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
More informationCALCULATOR 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
More informationhp 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
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
More informationCheck off these skills when you feel that you have mastered them.
Chapter Objectives Check off these skills when you feel that you have mastered them. Know the basic loan terms principal and interest. Be able to solve the simple interest formula to find the amount of
More informationMath 1332 Test 5 Review
Name Find the simple interest. The rate is an annual rate unless otherwise noted. Assume 365 days in a year and 30 days per month. 1) $1660 at 6% for 4 months Find the future value of the deposit if the
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationTIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;
In following we will introduce one of the most important and powerful concepts you will learn in your study of finance; the time value of money. It is generally acknowledged that money has a time value.
More informationFuture Value of an Annuity Sinking Fund. MATH 1003 Calculus and Linear Algebra (Lecture 3)
MATH 1003 Calculus and Linear Algebra (Lecture 3) Future Value of an Annuity Definition An annuity is a sequence of equal periodic payments. We call it an ordinary annuity if the payments are made at the
More informationChapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS 41 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
More information10.3 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
More informationFuture 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
More informationFINANCIAL CALCULATIONS
FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N
More informationThe Institute of Chartered Accountants of India
CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2015
Using Technology to Assist in Financial Calculations Calculators: TI83 and HP12C Software: Microsoft Excel 2007/2010 Session #4 of Finite Mathematics 1 TI83 / 84 Graphing Calculator Section 5.5 of textbook
More informationUnit 4: Finance and Spreadsheets Applied Math 30. Unit 4: Finance and Spreadsheet
41A: Investing Money Unit 4: Finance and Spreadsheet Compound Interest:  interest is incurred on the existing balance.  usually interest incurs at each term. (A term can be annually, semiannually,
More informationPurpose EL773A HP10B BAII PLUS Clear memory 0 n registers
DHow to Use a Financial Calculator* Most personal finance decisions involve calculations of the time value of money. Three methods are used to compute this value: time value of money tables (such as those
More informationReal Estate. Refinancing
Introduction This Solutions Handbook has been designed to supplement the HP2C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or stepbystep keystroke procedures
More informationTexas 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,
More informationSolutions to Time value of money practice problems
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
More information1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000
D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of
More information