Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = for six months.


 Bruce Ball
 6 years ago
 Views:
Transcription
1 Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at prices of 0.7P and 0.75P by cash and credit respectively. The interest rate over the six months is given by 0.7P 1 + i) = 0.75P i = for six months..7 We convert this to an effective rate of interest by the equation ) r e = 1 + i) 2 1 = 1 = 0.148, so 14.8%.7 b) As in a), the interest rate over three months is given by i) = and r e = 1+i) 4 1 so 1+i) = r e +1) 1 4 and 0.7r e +1) 1 4 =.725, r e = ) = , so 15.07% which is a slightly higher effective rate of interest than a). 2. a) The monthly interest rate r is given by 1.09 = 1 + r) 12 So the initial monthly payment X is given by r = 1.09) = = Xa 240 r X = 19750[1.09) ] ) = $ The present value of the 153 remaining payments immediately after the 87 th payment is [ ] ) a 153 r = ) = $16, An effective rate of 10% corresponds to a monthly rate of i = 1.10) = Thus the value of the revised payments would be Y where = Y a 153 i 1
2 Y = [ 1.10) ) ] = $ which is an increase of = $8.45. b) Given the present value of $16, of the remaining 153 payments immediately after payment 87, we wish to solve for n where [ ] ) n = )a n i = ) [1.10) ] = 1.10 n 12 n { 12 ln 1.10 = ln } [1.10) ] n = 12 ln = { } [1.10) ] ln 1.10 Since n must be an integer, there remain 169 payments. The final payment is given by = a 168 i + X1 + i) 169 where 1 + i) 12 = 1.10 X = a 168 i )1.10) = $ This annuity may be considered as the sum of 20 annuities of equal payments each year. The first one is payments of $2, 000 for 20 years, the second one is payments of $100 for 19 years, beginning one year after the first,..., the k th annuity is payments of $100 for 20 k + 1 years beginning k 1 years after the first annuity. The purchase price P of the original annuity is the sum of the present values of the 2
3 20 annuities at the time of purchase. 20 P a 20 k ) k+1 k=2 19 a 20 k ) k k= ) k k=1 19 k= ) ) ) 1.04) k 1.04) k 1.04) 20) k= ) k ) k= )1.04) k=1 ) k 1 19)100) )1.04) 20 ) ) )1.04) 20 by the formula for the sum of a geometric series 1.04) ) ) 0.04)1.04) ) ) = )1.04) )1.04)19 1) ) ) 19 = $38, The purchase price of the original annuity is $38, Interest rates corresponding to 8% compounded annually are: monthly: 1.08) = quarterly: 1.08) = semiannually: 1.08) = If X is the amount of the semiannual payments of the revised annuity, the equation of value at the time of the request on November 1, 1985 is: Xa ) 3 = 200a ) a ) + 15a
4 i.e. the annual annuity has a present value of 200a nine months before November 1, 1985, and so on. Solving for X, we get X = $ to the nearest half dollar. Your answer may vary by a few pennies depending on rounding errors.) The revised annuity has semiannual payments of $ The interest payments on the loan form an annuity of equal payments of ) = $550 at semiannual periods. With a nominal interest rate of 6% compounded semiannually, the equation of value at the beginning of the seven years is ) n = 550a ) 14 where n is the number of half years before the repayment of $23, is made. 1.03) n = n ln1.03) = ln n = 550a ) a ) 14 ) ln ) ln550a ) 14 ) n = 4 half years = 2 years ln1.03) 6. Interest rates corresponding to an effective rate of 10% are: monthly: 1.1) = quarterly: 1.1) = semiannually: 1.1) = If the initial payments are X dollars, the equation of value when the man receives the annuity is 2049 = Xa Xa ) 5 + 4Xa ) 10 ] 2049 = X [a ) 5 a ) 10 a ] 1 X = 2049 [a ) 5 a ) 10 a [ ) 10 X = ) ) 60 ) X = ) ) 20 ) ] 1
5 7. a) We have $16, 000 = Ra R = 16, ) ) = $2, b) The loan outstanding just after the fourth payment is: $2, a 6.08 ) ) 6 = $2, = $11, since there are still six annual payments of $2, to be made that is, before the change in interest. So the revised installment R is R = 11, a 6.10 = 11, ) = $2, ) 6.10 c) The loan outstanding just after the seventh payment is made is ) ) 3 $2, a 3.10 = $2, So the revised installment R is R = 6, a 3.09 = = $6, , ) = $2, ) 3 We now find the effective rate of interest r paid by the borrower on the completed transaction: The present value of the first four installments is $2, a 4 r. Also, the value at year four of the next three installments is $2, a 3 r. Hence the present value of this is $2, a 3 r 1 + r) 4. And the value at year seven of the final three installments is $2, a 3 r. Hence the present value of this is $2, a 3 r 1 + r) 7. A The sum of these is of course $16, 000: ) r) r) 3 16, 000 = 2, , r r ) r) 3 + 2, r) 7 r 5.09 ) 1 + r) 4
6 We now guess by interpolation. r should be somewhat less than 9%, say 8.8%? With r =.088, the RHS of A is $15, , so our guess for r was too large... With r =.086, the RHS of A is $15, With r =.0859, the RHS of A is $15, With r =.08586, the RHS of A is $16, Thus, to within one Hence, the actual correct r lies between 8.59% and 8.586%. hundredth of a percentage point, r is 8.59%. 8. a) The annuity payments are shown as follows: September 1, 1990 September 1, January 1, ) May 1, ) 2.. May 1, ) 14 We calculate the present value of the annuity on September 1, Summing up the present values of the payments, we have 1000) 3 [ )) ) 2 ) ) 14 ) 14] [ = 1000) ) 2 ) ] [ = ) 15 ] ) 3 1 ) 1.05 by the formula for the sum of a geometric series = The purchase price was $17,
7 b) The present value of the remaining payments just after the sixth payment is )) 9 } {{ } The present value of all payments at this time 1000[) )) ) 4 ) ) 5 ] } {{ } the present value of payments 1,2,...,6 at this time [ = )) )) = )) )) 5 1 ) 1.05 by the formula for the sum of a geometric series = 13, ) 6 ) ) ] Therefore the interest content of the seventh installment was 0.02)13, ) = $ a) First, convert to annual interest compounded monthly: n = = 300. So, 1 + r m 12 ) 12 = 1 + re = r m 12 = r m = ) , % $9, 880 = Ra R = $9, ) ) = $ b) The March 10 th payment is the 1312) + 8 = 164 th payment. So there are 136 payments remaining. The principal outstanding is 68.48a = $ c) The October 10 th, 1989 payment is the 1112) + 3 = 135 th payment. So, the principal contained is k = 135) ] R [1 ra n k+1, = $68.48[ ) 166 ] = $ ) = $
8 d) April 10 th, 1996 is the 1712) + 9 = 213 th payment. March 10 th, 1997 is the = 224 th payment. i) We look for the loan outstanding at the beginning of the 213 th period and subtract the loan outstanding at the end of the 224 th, or beginning of the 225 th, period. { [ ] [ ] } ) ) 76 = $ [ ) ) 88 ] = $ = $68.48[ ] = $ ii) The total interest in these installments is just, by part i) 12$68.48) $ = $ a) We determine the contributions needed from i) and ii) individually and then sum them. i) There is a.05751, 000, 000) = $57, 500 payment halfway through the year and another $57, 500 payment at the end of the year. We calculate the sum of the present values of these two payments i.e., this is an annuity with two payments of $57, 500 semiannually with 5% interest during each payment period). ) ) 2 P V = $57, 500a 2.05 = 57, 500 = $106, So $106, should be deposited at the start of the year to cover part i). ii) We determine the effective annual rate compounded annually) of 10% compounded semiannually 1 + r a = 1 + r s 2 ) 2 = 1.05) 2 = So the effective annual rate compounded annually) is 10.25%. Now we consider the amount R of yearly payments needed so that the future value of a 20 year annuity due at 10 1 % is $1, 000, 000 notice the payments of R are at the start 4 of the year). R = 1, 000, 000 s = 1, 000, 000 ) ) = $15, So $15, should be deposited at the start of the year to cover part ii). The sum of the payments for i) and ii) is $122, , and this is the amount deposited by the company at the start of the year. 8
9 Note: a trickier method for solving a): We first pretend that, instead of making one payment at the start of the year, the company makes equal payments at months six and twelve in the year. Each payment will just be $57, $1, 000, 000 = $57, s $1, 000, 000 ) 1.05) = $57, , = $65, paid semiannually. But now, instead of $65, paid at months six and twelve of the year, we calculate the equivalent lump sum payment at the beginning of the year: ) ) 2 $65, a 2.05 = $65, = $122, b) We answer ii) first. Since the coupon payments and the face value payment at redemption do not change, then neither does the corporation change how much they deposit at the start of the year. They still must cover the same amount. Rather, the company is going to sell the bonds at a discount in order to make the purchase of the bonds worthwhile for those investors who want a yield of 12% payable semiannually). Now, the yield rate i desired is 6% per period halfyear). The coupon rate r is 5.75% per period. n = 20 2 = 40; and the face value is $1, 000, 000. We calculate the price P of the bond: P = V 1 + i) n + rv a n i ) ) = $1, 000, ) $1, 000, 000).06 = 97, , = $962, First, we look for the quarterly yield rate. Using the formula of the bond salesman s method, we guess i r p V nv 1+ p V 2V. Here, n = 80, V = 100, P = 49.50, r = Note: for the bond salesman s method see Supplementary Notes, Prob. 7 on page 10.) ) = Substituting i =.0268 in i) i) 80 i we get P = $57.18 awful estimate!), so we guess i =.03. Now, we get P = $50.92 Setting i =.0307, P = $49.70 Setting i =.03083, P = $
10 Setting i =.03081, P = $ Setting i = , P = $ So the quarterly yield is between % and 3.082%. b) The investor sold the bonds for $12, Moreover, the investor had already received four bond payments of $275. The present value of these payments is 275s = $1, So, overall, the investor receives $1, $12, = $13, from the bonds. For the mortgage, we first calculate the periodic monthly rate 1 + r m = 1.06) 1 6 = rm.9759% Now, the mortgage will give, after one year $1, 100s = ) = $13, This is more than the money made from the bonds, so the bonds were not the right choice. 10
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
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 information, plus the present value of the $1,000 received in 15 years, which is 1, 000(1 + i) 30. Hence the present value of the bond is = 1000 ;
2 Bond Prices A bond is a security which offers semiannual* interest payments, at a rate r, for a fixed period of time, followed by a return of capital Suppose you purchase a $,000 utility bond, freshly
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More 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 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 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 information1 Cashflows, discounting, interest rate models
Assignment 1 BS4a Actuarial Science Oxford MT 2014 1 1 Cashflows, discounting, interest rate models Please hand in your answers to questions 3, 4, 5 and 8 for marking. The rest are for further practice.
More informationModule 1: Corporate Finance and the Role of Venture Capital Financing TABLE OF CONTENTS
1.0 ALTERNATIVE SOURCES OF FINANCE Module 1: Corporate Finance and the Role of Venture Capital Financing Alternative Sources of Finance TABLE OF CONTENTS 1.1 ShortTerm Debt (ShortTerm Loans, Line of
More informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin534/fin534week4quiz3 str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More information1 (1 + i) 12 = ( 1 + r 2 1 + i = ( 1 + r 2 i = ( 1 + r 2
1. Mortgages Mortage loans are commonly quoted with a nominal rate compounded semiannually; but the payments are monthly. To find the monthly payments in this case one finds the effective monthly rate
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 informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM0905. January 14, 2014: Questions and solutions 58 60 were
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 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 informationHow to calculate present values
How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance
More informationPresent Value (PV) Tutorial
EYK 151 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,
More 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 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 informationLevel Annuities with Payments More Frequent than Each Interest Period
Level Annuities with Payments More Frequent than Each Interest Period 1 Examples 2 Annuityimmediate 3 Annuitydue Level Annuities with Payments More Frequent than Each Interest Period 1 Examples 2 Annuityimmediate
More informationINSTITUTE OF ACTUARIES OF INDIA
INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 15 th November 2010 Subject CT1 Financial Mathematics Time allowed: Three Hours (15.00 18.00 Hrs) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1. Please
More informationChapter 03  Basic Annuities
31 Chapter 03  Basic Annuities Section 7.0  Sum of a Geometric Sequence The form for the sum of a geometric sequence is: Sum(n) a + ar + ar 2 + ar 3 + + ar n 1 Here a = (the first term) n = (the number
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 informationFin 3312 Sample Exam 1 Questions
Fin 3312 Sample Exam 1 Questions Here are some representative type questions. This review is intended to give you an idea of the types of questions that may appear on the exam, and how the questions might
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More informationIntroduction to Real Estate Investment Appraisal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
More informationPRESENT 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
More informationST334 ACTUARIAL METHODS
ST334 ACTUARIAL METHODS version 214/3 These notes are for ST334 Actuarial Methods. The course covers Actuarial CT1 and some related financial topics. Actuarial CT1 which is called Financial Mathematics
More informationChapter 7 Internal Rate of Return
Chapter 7 Internal Rate of Return 71 Andrew T. invested $15,000 in a high yield account. At the end of 30 years he closed the account and received $539,250. Compute the effective interest rate he received
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 informationPercent, Sales Tax, & Discounts
Percent, Sales Tax, & Discounts Many applications involving percent are based on the following formula: Note that of implies multiplication. Suppose that the local sales tax rate is 7.5% and you purchase
More informationChapter 2 The Time Value of Money
Chapter 2 The Time Value of Money 21 The effective interest rate is 19.56%. If there are 12 compounding periods per year, what is the nominal interest rate? i eff = (1 + (r/m)) m 1 r/m = (1 + i eff )
More informationVilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis
Vilnius University Faculty of Mathematics and Informatics Gintautas Bareikis CONTENT Chapter 1. SIMPLE AND COMPOUND INTEREST 1.1 Simple interest......................................................................
More informationLoans Practice. Math 107 Worksheet #23
Math 107 Worksheet #23 Loans Practice M P r ( 1 + r) n ( 1 + r) n =, M = the monthly payment; P = the original loan amount; r = the monthly interest rate; n = number of payments 1 For each of the following,
More informationAnnuities Certain. 1 Introduction. 2 Annuitiesimmediate. 3 Annuitiesdue
Annuities Certain 1 Introduction 2 Annuitiesimmediate 3 Annuitiesdue Annuities Certain 1 Introduction 2 Annuitiesimmediate 3 Annuitiesdue General terminology An annuity is a series of payments made
More informationThe Time Value of Money (contd.)
The Time Value of Money (contd.) February 11, 2004 Time Value Equivalence Factors (Discrete compounding, discrete payments) Factor Name Factor Notation Formula Cash Flow Diagram Future worth factor (compound
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 informationMATHEMATICS OF FINANCE AND INVESTMENT
MATHEMATICS OF FINANCE AND INVESTMENT G. I. FALIN Department of Probability Theory Faculty of Mechanics & Mathematics Moscow State Lomonosov University Moscow 119992 g.falin@mail.ru 2 G.I.Falin. Mathematics
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 informationChapter 16. Debentures: An Introduction. Noncurrent Liabilities. Horngren, Best, Fraser, Willett: Accounting 6e 2010 Pearson Australia.
PowerPoint to accompany Noncurrent Liabilities Chapter 16 Learning Objectives 1. Account for debentures payable transactions 2. Measure interest expense by the straight line interest method 3. Account
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 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 informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM0905. April 28, 2014: Question and solutions 61 were added. January 14, 2014:
More informationBond Price Arithmetic
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
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 informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
Chapter  The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
More informationSample Examination Questions CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY MULTIPLE CHOICE Conceptual Answer No. Description d 1. Definition of present value. c 2. Understanding compound interest tables.
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
More informationFinance 350: Problem Set 6 Alternative Solutions
Finance 350: Problem Set 6 Alternative Solutions Note: Where appropriate, the final answer for each problem is given in bold italics for those not interested in the discussion of the solution. I. Formulas
More informationExcel Financial Functions
Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint() Future Value How much will your money
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 21: Savings Models
October 16, 2013 Last time Arithmetic Growth Simple Interest Geometric Growth Compound Interest A limit to Compounding Problems Question: I put $1,000 dollars in a savings account with 2% nominal interest
More information2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationNominal rates of interest and discount
1 Nominal rates of interest and discount i (m) : The nominal rate of interest payable m times per period, where m is a positive integer > 1. By a nominal rate of interest i (m), we mean a rate payable
More informationINSTITUTE AND FACULTY OF ACTUARIES EXAMINATION
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 12 April 2016 (am) Subject CT1 Financial Mathematics Core
More informationThe Basics of Interest Theory
Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest
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 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 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 informationPowerPoint. 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
More informationWarmup: Compound vs. Annuity!
Warmup: Compound vs. Annuity! 1) How much will you have after 5 years if you deposit $500 twice a year into an account yielding 3% compounded semiannually? 2) How much money is in the bank after 3 years
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 informationKENT FAMILY FINANCES
FACTS KENT FAMILY FINANCES Ken and Kendra Kent have been married twelve years and have twin 4yearold sons. Kendra earns $78,000 as a Walmart assistant manager and Ken is a stayathome dad. They give
More informationChapter 2. CASH FLOW Objectives: To calculate the values of cash flows using the standard methods.. To evaluate alternatives and make reasonable
Chapter 2 CASH FLOW Objectives: To calculate the values of cash flows using the standard methods To evaluate alternatives and make reasonable suggestions To simulate mathematical and real content situations
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 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 informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
More informationANALYSIS OF FIXED INCOME SECURITIES
ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its
More information2. Annuities. 1. Basic Annuities 1.1 Introduction. Annuity: A series of payments made at equal intervals of time.
2. Annuities 1. Basic Annuities 1.1 Introduction Annuity: A series of payments made at equal intervals of time. Examples: House rents, mortgage payments, installment payments on automobiles, and interest
More informationChapter 4: Time Value of Money
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
More informationTVM 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 (longterm receivables) 7 Longterm assets 10
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on longterm bonds are geometric averages of present and expected future short rates. An upward sloping curve is
More informationLesson 4 Annuities: The Mathematics of Regular Payments
Lesson 4 Annuities: The Mathematics of Regular Payments Introduction An annuity is a sequence of equal, periodic payments where each payment receives compound interest. One example of an annuity is a Christmas
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 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 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationCourse 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
More informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given
More informationStudy Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010
P a g e 1 Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010 P a g e 2 Background The purpose of my senior project is to prepare myself, as well as other students who may read my senior
More informationCalculations for Time Value of Money
KEATMX01_p001008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with
More informationUndergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics
Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics A Semester Course in Finite Mathematics for Business and Economics Marcel B. Finan c All Rights Reserved August 10,
More informationEC3070 FINANCIAL DERIVATIVES. Exercise 1
EC3070 FINANCIAL DERIVATIVES Exercise 1 1. A credit card company charges an annual interest rate of 15%, which is effective only if the interest on the outstanding debts is paid in monthly instalments.
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 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 informationMatt 109 Business Mathematics Notes. Spring 2013
1 To be used with: Title: Business Math (Without MyMathLab) Edition: 8 th Author: Cleaves and Hobbs Publisher: Pearson/Prentice Hall Copyright: 2009 ISBN #: 9780135136874 Matt 109 Business Mathematics
More informationChapter 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 informationManual for SOA Exam FM/CAS Exam 2.
Manual for SOA Exam FM/CAS Exam 2. Chapter 5. Bonds. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics. Fall 2009 Edition,
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 informationApplications of Geometric Se to Financ Content Course 4.3 & 4.4
pplications of Geometric Se to Financ Content Course 4.3 & 4.4 Name: School: pplications of Geometric Series to Finance Question 1 ER before DIRT Using one of the brochures for NTM State Savings products,
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 informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
More information5. 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
More informationFinancial Mathematics for Actuaries. Chapter 2 Annuities
Financial Mathematics for Actuaries Chapter 2 Annuities Learning Objectives 1. Annuityimmediate and annuitydue 2. Present and future values of annuities 3. Perpetuities and deferred annuities 4. Other
More informationHow To Value A Bond In Excel
Financial Modeling Templates http://spreadsheetml.com/finance/bondvaluationyieldtomaturity.shtml Copyright (c) 20092014, ConnectCode All Rights Reserved. ConnectCode accepts no responsibility for any
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 informationFinancial Math on Spreadsheet and Calculator Version 4.0
Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS
More informationSOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM SAMPLE QUESTIONS
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Copyright 2005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions
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 informationCompound Interest. Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate:
Compound Interest Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate: Table 1 Development of Nominal Payments and the Terminal Value, S.
More information