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

Size: px
Start display at page:

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

Transcription

1 1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2. Find the Macaulay duration of a -year 00 par value bond with 8% annual coupons and an effective annual interest rate of 6.5%. A) 7.2 B) 7.4 C) 7.6 D) 7.8 E) At an effective annual rate of interest i, a person can pay off a loan of K in two ways: 1) 475 now and 475 in 1 year, or 2) 570 in 2 years and 570 in 3 years. Calculate K. A) 893 B) 901 C) 909 D) 917 E) A -year annuity-immediate pays 0 quarterly for the first year. In each subsequent year, each payment is increased by 5% over the payment for the previous year. There is a nominal annual interest of 8% convertible quarterly. Find the present value of this annuity. A) 2997 B) 3075 C) 38 D) 3225 E) 3333

2 2 Practice Exam 1 Exam FM / Exam 2 5. The present value of a -year annuity-immediate with level annual payments and interest rate i is X. The present value of a 20-year annuityimmediate with the same payments and interest rate is 1.5X. Find i. A) 7.2% B) 7.4% C) 7.6% D) 7.8% E) 8.0% For Problems 6 and 7 use the following account summary: Date Balance Before Deposits Withdrawals Activity January 1 0,000 March 1 5,000,000 September 1 112,000 30,000 December 31 95, Find the time-weighted yield for this account. A) 17.2% B) 17.5% C) 17.9% D) 18.1% E) 18.5% 7. Find the dollar-weighted yield for this account. A) 14.9% B) 15.3% C) 15.6% D) 16.1% E) 16.4% 8. An investor has 3000 worth of 5-year bonds with a modified duration of 4.615, 7000 worth of -year bonds with a modified duration of and,000 worth of 20-year bonds with a modified duration of What is the modified duration of this entire portfolio? A) 13.5 B) 13.7 C) 13.9 D) 14.1 E) A company has liabilities of 00, 3000 and 5000 payable at the end of years 1, 2 and 3 respectively. The investments available to the company are the following zero-coupon bonds: Maturity Effective Annual Par (years) Yield 1 7% % % 00 Determine the cost for matching these liabilities exactly. A) 6918 B) 7024 C) 7165 D) 7368 E) 7522

3 3. A man creates a retirement fund by depositing payments at the end of each month for 20 years. For the first years the deposits are 0 per month and for the last years the deposits are 200 per month. The fund earns interest at a nominal rate of 6% per year converted monthly. Upon retirement he uses the proceeds to purchase a 30-year annuity-immediate with monthly payments. The annuity earns at a nominal rate of 8% converted monthly. What are monthly payments from this annuity? A) 408 B) 425 C) 437 D) 441 E) An annuity pays annual payments at the beginning of each year for 20 years. For the first years the payments are 0. Starting with payment 11 each payment is increased by 6% over the previous payment. The annuity earns at an annual effective rate of 8%. Find the present value of this annuity. A) 1177 B) 1190 C) 1202 D) 1213 E) A corporate bond is priced to yield 7.2% and has a price of The Macaulay duration is D = Estimate the change in price if rates increase by 0.%. A) B) C) D) E) A 40-year loan is paid with level annual payments at the end of each year. The principal paid in the 20 th payment is and the principal paid in the 25 th payment is Find the interest rate for this loan. A) 7.7% B) 8.0% C) 8.2% D) 8.5% E) 8.8% 14. Linus deposits 0 into an account at the end of each year for 20 years. This account earns interest at an annual effective rate of 5%. Lucy deposits money into an account at the end of each year for 20 years. Her account also earns interest at an annual effective rate of 5%. Her deposits are: P, 2P,., 20P. At the end of 20 years the accumulated amounts are the same. Find P. A).93 B) C) D) E) Schroeder borrows money to buy a new piano. He agrees to pay back the loan with level annual payments at the end of each year for 30 years. The annual interest rate is 7%. The interest in his th payment is What is the interest in his 20 th payment? A) B) C) D) E)

4 4 Practice Exam 1 Exam FM / Exam A woman makes a deposit into an account. For the first 5 years the account accumulates with a force of interest of For the next years the fund accumulates with an annual nominal discount rate of 6% convertible quarterly. For the 15 year period, what is the annual nominal interest rate convertible monthly? A) 5.59% B) 5.71% C) 5.83% D) 5.96% E) 6.04% 17. Violet purchases a -year 00 par bond with 8% semiannual coupons. The bond is priced to yield 7.5% convertible semiannually. She reinvests the coupon payments in a fund that pays a nominal rate of 7% convertible semiannually. What is her nominal annual yield convertible semiannually? A) 7.36% B) 7.41% C) 7.48% D) 7.56% E) 7.63% 18. You are given the following yield curve: If i 4,5 = 6.1%, find s 4. Year Spot Rate 1 4.0% 2 4.2% 3 4.6% % A) 4.81% B) 4.83 C) 4.85% D) 4.87% E) 4.89% 19. A 20-year annuity-immediate has annual payments. The first payment is 0 and subsequent payments are increase by 0 until they reach 00. The remaining payments stay at 00. The annual effective interest rate is 7.5%. What is the cost of this annuity? A) 6201 B) 6372 C) 6413 D) 6584 E) A woman buys a 00 par 5-year zero coupon priced to yield 6%. At the same time she buys a 5-year 00 par bond with 8% semiannual coupons which is priced to yield 7%. The coupon payments are reinvested at 6.5% convertible semiannually. What is her annual effective yield for the combined investment? A) 6.0% B) 6.2% C) 6.4% D) 6.6% E) 6.8%

5 5 21. The S&R index currently has a price of The price of a six month forward contract is What annual interest rate (compounded continuously) is implied by this forward price? Note that the S&R has no dividend. A) B) C).0305 D).0355 E) The S&R index currently has a price of The price of a three month 1320-strike put is The annual interest rate is 4% compounded continuously. A buys this put, and B enters into a long forward contract. In three months A and B have the same profit. What is the price of the index in three months? A) 13 B) 1297 C) 1289 D) 1291 E) The current value of the a stock is S 0 = 25, and the continuously compounded risk free rate is r =.04. The price of a six month ( T =.5 ) 26-strike call is and the price of a six month ( T =.5 ) 26-strike put is Find the continuously compounded dividend yield δ. A) 1% B) 2% C) 3% D) 4% E) 5% 24. Investor C buys the S&R index at time 0 for 10 and buys an 10-strike put with T =.25 for a price of If the interest rate is r=.04, what is his minimum profit (loss)? A) B) C) D) E) There is no minimum 25. The current (spot) rate for corn is 1.60 per bushel. The 6 month forward price is \$1.50 per bushel. The continuously compounded annual rate is r =.035. Farmer Brown, has total fixed and variable costs of 1.44 per bushel, and plans to produce 0,000 bushels for \$144,000. A six month ( T =.5 ) put with a strike price of 1.52 per bushel is available at a price of What are the minimum and maximum profits for Farmer Brown in six months if he is hedged with a purchase of this put? A) minimum = -4,212, maximum = 19,678 B) minimum =-6222, maximum = 19,678 C) minimum= -4,212, no maximum D) minimum = -6,242, no maximum E) none of the above

6 6 Practice Exam 1 Exam FM / Exam Company XYZ makes an aircraft which costs 80,000,000 to manufacture. It will be completed in six months. At that time it will sell either for 90,000,000 with probability.5 or 74,000,000 with probability.5. The company decides to enter into a forward contract to sell the unit for 85,000,000 in six months The company has a 40% tax rate, and has no tax benefit for losses. What is the company s expected profit after tax? A) -1,000,000 B) 0 C) 1,000,000 D) 2,000,000 E) 3,000, A stock has current price. S 0 = 25 The annual continuous interest rate is r =.03. If the expiration time for a forward contract is T =.25 and the forward price is 25.15, what is the continuous dividend yield δ? A) B) C) 0.0 D) E) The S&R index has a spot price of S 0 = 10. The continuous interest rate is r =.03 and the continuous dividend yield is δ = 0 The one year forward price is Which of the following positions results in a synthetic long forward contract? A) Sell the index short for 10 and lend the proceeds at r =.03 B) Sell the index short for 10 and borrow 00 at r =.03 C) Borrow 00 at r =.03 and buy the index. D) Borrow 00 at r =.03 and sell the index short E) None of these. In Problems 29-30, use the following table of quarterly oil forward prices and zero-coupon bond prices. Quarter Oil Forward Price Zero-coupon bond price Find the price of a four quarter oil swap. A) B) C) D) E) Suppose you enter a three quarter interest rate swap. What net interest payment will be made to you in the second quarter if the spot interest rate for the second quarter is.018? A).00 B).0012 C).0016 D).0018 E).002

7 7 Solutions 1. The four year forward rate i 4,5 is given by 1 + i 4,5 = (1 + s 5 ) 5 /(1 + s 4 ) 4 = / = i 4,5 = ( Ia) ( Ia) ( Ia) 80 + (00) v D = Bond Price v a&& ( a&& v ) = i = = = (be sure calculator is in BGN mode) = Bond price = 1,7.83 (Reset calculator to END mode. N =, PMT = 80, I/Y =6.5, FV = 00. CPT PV = ) D = [80( ) + 5,327.26]/1,7.83 = Answer B 3. K = v = 570v v 2 = [475(1 + v)]/[570(1 + v)] = v = K = 475( ) =

8 8 Practice Exam 1 Exam FM / Exam 2 4. The accumulated amount at the end of year one is (N = 4, I/Y = 2, PMT = 0, PV =0. CPT FV = ) We can view the annuity as a -year annuity-immediate with annual payments, the first being and subsequent payments are increase by 5% each year. The effective annual rate is i = (1.02) 4 1 = The present value of this annuity is (412.16)[1 + (1.05/ ) + + (1.05/ ) 9 ] = [1 (1.05/ ) ]/( ) = X = (1 v )/i, 1.5X = (1 v 20 )/i Hence 1 + v = 1.5, v = 0.5, i = Answer A 6. For the time-weighted yield 1 + j = (5,000/0,000)(112,000/115,000)(95,000/82,000) = j = For the dollar-weighted yield, I = 95,000 0,000 (,000 30,000) = 15,000 i = 15,000/[0,000 + (1 1/6)(,000) (1 2/3)(30,000)] = Answer B 8. The weights are 3/20, 7/20 and 1/2 respectively for the 5-year, -year and the 20-year bonds. The modified duration is DM = (3/20)(4.615) + (7/20)(9.323) + (1/2)(19.085) = Answer A 9. The company must invest the present values of 00 in one year at 7%, 3000 in 2 years at 8% and 5000 in 3 years at 9%. The cost is 00/ / / = Answer D

9 9. The deposits can be viewed as payments of 0 into a 20-year annuityimmediate and 0 into a -year deferred -year annuity-immediate. The accumulated amount in the first annuity is 46, (N = 240, I/Y = 0.5, PMT = -0, PV = 0. CPT FV = 46,204.09) The accumulated amount in the second annuity is 16, (Reset N = 120. CPT FV = 16,387.94) Total accumulation is 62, The monthly payments from the 30-year annuity are (N = 360, I/Y =0.6667, PV = - 62,592.02, FV = 0. CPT PMT = ) 11. The present value of this annuity is 9 0 a && + (6 / 1.08 )[1 + (1.06 / 1.08) + K + (1.06 / 1.08) ] To get the value of the first term set the BA II Plus to BGN mode. Set N =, I/Y = 8, PMT = -0, and FV = 0. CPT PV = The value of the second expression is (6/1.08 )[1 (1.06/1.08) ]/[1- (1.06/1.08)] = Present value is = 1, Answer A 12. The change is ΔP = (D)P(i)Δi/(1 + i) = (7.1245)(972.48)(0.001)/(1.072) = Answer A 13. PRin k is the amount of principal repaid in the k th period. Prin k+n = (1 + i) n PRin k. Let k = 20 and n = = (1 + i) 5 (166.59). i = (244.78/166.59) 1/5 1 i =.08 Answer B

10 Practice Exam 1 Exam FM / Exam The accumulation in Linus s account is 0s 20 = 3, (N = 20, I/Y = 5, PV = 0, PMT = -0. CPT FV = 3,306.60) The accumulation is Lucy s account is P( Is ) 20. (&& s20 20) ( Is) = = , P = = Answer D 15. Let P be the annual payment. The interest paid in the th payment is P(1 v ) = P(1 v 21 ) = P( ) = P = For the 20 th payment the interest is (1 v 11 ) = ( )= If Y is the amount deposited, then the accumulation is A = Ye 0.05(5) ( ) 40 = Y. There are 180 months in the 15 year period. If j is the monthly interest then j = /180 1 = i = 12( ) = Answer B 17. The price of the bond is (N = 20, I/Y = 0.375, PMT = 40 and FV = 00. CPT PMT = ) The accumulated amount of reinvested coupon payments is 40s 20 = The total accumulation is The semiannual yield on the investment is j = ( /34.74) 1/20 1 = The annual yield is 2(.0368) = Answer A

11 i 4,5 = (1 + s 5 ) 5 /(1 + s 4 ) 4 (1 + s 4 ) 4 = (1 + s 5 ) 5 /(1 + i 4,5 ) = (1.051) 5 /(1.061) = s 4 = , s 4 = This can be viewed as a -year increasing annuity and a -year deferred -year annuity. The present value of the -year deferred annuity is 00v a = = 3, ( )( ) The present value of the increasing annuity is 0( Ia ). ( Ia) ( a&& v ) = = = i Total cost is 3, , = 6, The price of the zero-coupon bond is 00/ = To find the price of the second bond with the BA II Plus set N =, I/Y = 3.5, PMT = - 40 and FV = -00. CPT PV = The accumulation of the reinvested coupon payments is (N =, I/Y =3.25, PMT = -40 and PV =0. CPT FV = ) Total investment is = Total accumulation is = Annual effective yield is ( / ) 1 = Answer D 21. F S e e r rt.5r 0, T = = 1300 =.0305

12 12 Practice Exam 1 Exam FM / Exam 2 rt 22. The forward price is F0, T = S0e = 1300e = The long forward profit is S F0, = S T T T The put profit is ( T) ( ) ( ) ( T) max 0,1320 S 81.41e max 0,1320 S =. Assume that S T < Then the equality of prices implies that S = 1320 S S = T T T 23. By put-call parity T C P = S e δ Ke 0 rt e δ = 26 e r =.03 ( ) 24. Buying the index and buying a put with strike 10 creates a floor. The floor has the same profit function as a long call with strike 10. The minimum profit on the floor is the (negative) loss of the future value of the call premium when the call expires unexercised. By parity the value of the call premium is The minimum profit is e = Answer A 25. The profit from the put option is.035(.5) 0,000 max(0,1.52 x).12e = 0,000max(0,1.52 x) 12, The total profit for the hedged position is ( x ) 0,000x 144, ,000max(0,1.52 ) 12, ,211.85, x < 1.52 = 0,000x 156,211.85, x 1.5

13 The calculations are in the table below. Values are given in millions. With Short Forward at 85 Price Price Pre-tax op income -6 Income from Forward Taxable Income % 2 2 After Tax Income ( r δ) T ( δ) F0, T = S0e = 25e ln δ 25 = δ =.006 Answer B STOCK - ZERO COUPON BOND = LONG FORWARD Thus you buy the index for 00 and sell a zero coupon bond for 00 (borrow the money to buy the stock.). 29. We will use the general formula P n ( 0, i) 0 ( i) P t f t ( 0, ti ) ( ) + ( ) + ( ) + ( ) i= 1 = = = n i= 1 P The guaranteed interest rate is the three year par coupon bond rate. 1 P ( 0,3) c = = =.0162 P 0,1 + P 0,2 + P 0, ( ) ( ) ( ) The net rate paid to you will be =.0018 Answer D

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

SOCIETY 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 FM-09-05. April 28, 2014: Question and solutions 61 were added. January 14, 2014:

Fixed Income: Practice Problems with Solutions

Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.

n(n + 1) 2 1 + 2 + + n = 1 r (iii) infinite geometric series: if r < 1 then 1 + 2r + 3r 2 1 e x = 1 + x + x2 3! + for x < 1 ln(1 + x) = x x2 2 + x3 3

ACTS 4308 FORMULA SUMMARY Section 1: Calculus review and effective rates of interest and discount 1 Some useful finite and infinite series: (i) sum of the first n positive integers: (ii) finite geometric

SOCIETY 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 FM-09-05. January 14, 2014: Questions and solutions 58 60 were

Practice Questions for Midterm II

Finance 333 Investments Practice Questions for Midterm II Winter 2004 Professor Yan 1. The market portfolio has a beta of a. 0. *b. 1. c. -1. d. 0.5. By definition, the beta of the market portfolio is

Manual 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,

2015 Exam 2 Syllabus Financial Mathematics Exam

2015 Exam 2 Syllabus Financial Mathematics Exam The syllabus for this exam is defined in the form of learning objectives that set forth, usually in broad terms, what the candidate should be able to do

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

Mathematics. 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

Financial Mathematics Exam

2014 Exam 2 Syllabus Financial Mathematics Exam The purpose of the syllabus for this examination is to develop knowledge of the fundamental concepts of financial mathematics and how those concepts are

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 defined-contribution

SOCIETY 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

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 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.

Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10-year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity

FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin-534/fin-534-week-4-quiz-3- str/ For more course tutorials visit www.tutorialoutlet.com Which of the following

I. Readings and Suggested Practice Problems. II. Risks Associated with Default-Free Bonds

Prof. Alex Shapiro Lecture Notes 13 Bond Portfolio Management I. Readings and Suggested Practice Problems II. Risks Associated with Default-Free Bonds III. Duration: Details and Examples IV. Immunization

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

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Financial Economics

SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Financial Economics June 2014 changes Questions 1-30 are from the prior version of this document. They have been edited to conform

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is

Practice Set #2 and Solutions.

FIN-672 Securities Analysis & Portfolio Management Professor Michel A. Robe Practice Set #2 and Solutions. What to do with this practice set? To help MBA students prepare for the assignment and the exams,

The explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.

USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas

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

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

You just paid \$350,000 for a policy that will pay you and your heirs \$12,000 a year forever. What rate of return are you earning on this policy?

1 You estimate that you will have \$24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each

Manual for SOA Exam FM/CAS Exam 2.

Manual for SOA Exam FM/CAS Exam 2. Chapter 7. Derivatives markets. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics. Fall

Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition

C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future

Chapter 6. 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

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

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,

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.

Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter

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

CHAPTER 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

CHAPTER 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

Study 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

How To Read The Book \"Financial Planning\"

Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value

Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator

University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights

We first solve for the present value of the cost per two barrels: (1.065) 2 = 41.033 (1.07) 3 = 55.341. x = 20.9519

Chapter 8 Swaps Question 8.1. We first solve for the present value of the cost per two barrels: \$22 1.06 + \$23 (1.065) 2 = 41.033. We then obtain the swap price per barrel by solving: which was to be shown.

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.

1. The Purdue Life Insurance Company has two assets and two liabilities.

Chapter 9, Section 1 1. The Purdue Life Insurance Company has two assets and two liabilities. The assets are: a. A 5 year par value bond with a maturity value of 100,000. The bond pays annual coupons at

Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs. Binomial Option Pricing: Basics (Chapter 10 of McDonald)

Copyright 2003 Pearson Education, Inc. Slide 08-1 Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs Binomial Option Pricing: Basics (Chapter 10 of McDonald) Originally prepared

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

TVM Applications Chapter

Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (long-term receivables) 7 Long-term assets 10

HANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR

HANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR This document is designed to provide you with (1) the basics of how your TI BA II Plus financial calculator operates, and (2) the typical keystrokes that

2. Determine the appropriate discount rate based on the risk of the security

Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the

3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.

Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the

FINANCIAL MATHEMATICS FIXED INCOME

FINANCIAL MATHEMATICS FIXED INCOME 1. Converting from Money Market Basis to Bond Basis and vice versa 2 2. Calculating the Effective Interest Rate (Non-annual Payments)... 4 3. Conversion of Annual into

VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below

VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below 1. Determine the value of the following risk-free debt instrument, which promises to make the respective

Lecture 7: Bounds on Options Prices Steven Skiena. http://www.cs.sunysb.edu/ skiena

Lecture 7: Bounds on Options Prices Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena Option Price Quotes Reading the

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

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

Interest Rate and Currency Swaps

Interest Rate and Currency Swaps Eiteman et al., Chapter 14 Winter 2004 Bond Basics Consider the following: Zero-Coupon Zero-Coupon One-Year Implied Maturity Bond Yield Bond Price Forward Rate t r 0 (0,t)

Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The

Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

TIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction

TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 1-5, which are prerequisites. In this

Time Value of Money Problems

Time Value of Money Problems 1. What will a deposit of \$4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. \$8,020.22 b. \$7,959.55 c. \$8,081.55 d. \$8,181.55 2. What will

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 14: BOND PRICES AND YIELDS

CHAPTER 14: BOND PRICES AND YIELDS PROBLEM SETS 1. The bond callable at 105 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should

FinQuiz Notes 2 0 1 4

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

Manual for SOA Exam FM/CAS Exam 2.

Manual for SOA Exam FM/CAS Exam 2. Chapter 6. Variable interest rates and portfolio insurance. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam

LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.

LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely

Notes for Lecture 2 (February 7)

CONTINUOUS COMPOUNDING Invest \$1 for one year at interest rate r. Annual compounding: you get \$(1+r). Semi-annual compounding: you get \$(1 + (r/2)) 2. Continuous compounding: you get \$e r. Invest \$1 for

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

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

Compounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions.

Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has built-in preset assumptions

Option Values. Determinants of Call Option Values. CHAPTER 16 Option Valuation. Figure 16.1 Call Option Value Before Expiration

CHAPTER 16 Option Valuation 16.1 OPTION VALUATION: INTRODUCTION Option Values Intrinsic value - profit that could be made if the option was immediately exercised Call: stock price - exercise price Put:

Prepared by: Dalia A. Marafi Version 2.0

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

EC372 Bond and Derivatives Markets Topic #5: Options Markets I: fundamentals

EC372 Bond and Derivatives Markets Topic #5: Options Markets I: fundamentals R. E. Bailey Department of Economics University of Essex Outline Contents 1 Call options and put options 1 2 Payoffs on options

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

LOS 56.a: Explain steps in the bond valuation process.

The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction

Chapter 21: Options and Corporate Finance

Chapter 21: Options and Corporate Finance 21.1 a. An option is a contract which gives its owner the right to buy or sell an underlying asset at a fixed price on or before a given date. b. Exercise is the

Math Workshop Algebra (Time Value of Money; TVM)

Math Workshop Algebra (Time Value of Money; TVM) FV 1 = PV+INT 1 = PV+PV*I = PV(1+I) = \$100(1+10%) = \$110.00 FV 2 = FV 1 (1+I) = PV(1+I)(1+I) = PV(1+I) 2 =\$100(1.10) 2 = \$121.00 FV 3 = FV 2 (1+I) = PV(1

Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices

196 Part Interest Rates and Valuing Cash Flows Chapter 6 APPENDIX B The Yield Curve and the Law of One Price Thus far, we have focused on the relationship between the price of an individual bond and its

Lecture 12. Options Strategies

Lecture 12. Options Strategies Introduction to Options Strategies Options, Futures, Derivatives 10/15/07 back to start 1 Solutions Problem 6:23: Assume that a bank can borrow or lend money at the same

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

CHAPTER 5. Interest Rates. Chapter Synopsis

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

Contents. Introduction 1

Contents Introduction 1 PART I FINANCIAL MATHEMATICS 7 SEC. 1 The Measurement of Interest 9 1a Basic Concepts 9 Calculator Notes 14 Calculator Notes #1: Formatting; Present Values and Future Values 15

ACI THE FINANCIAL MARKETS ASSOCIATION

ACI THE FINANCIAL MARKETS ASSOCIATION EXAMINATION FORMULAE 2009 VERSION page number INTEREST RATE..2 MONEY MARKET..... 3 FORWARD-FORWARDS & FORWARD RATE AGREEMENTS..4 FIXED INCOME.....5 FOREIGN EXCHANGE

Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk

Bond Valuation 1 Topics in Chapter Key features of bonds Bond valuation Measuring yield Assessing risk 2 Determinants of Intrinsic Value: The Cost of Debt Net operating profit after taxes Free cash flow

Name: 1 (5) a b c d e TRUE/FALSE 1 (2) TRUE FALSE. 2 (5) a b c d e. 3 (5) a b c d e 2 (2) TRUE FALSE. 4 (5) a b c d e.

Name: Thursday, February 28 th M375T=M396C Introduction to Actuarial Financial Mathematics Spring 2013, The University of Texas at Austin In-Term Exam I Instructor: Milica Čudina Notes: This is a closed

Overview. Option Basics. Options and Derivatives. Professor Lasse H. Pedersen. Option basics and option strategies

Options and Derivatives Professor Lasse H. Pedersen Prof. Lasse H. Pedersen 1 Overview Option basics and option strategies No-arbitrage bounds on option prices Binomial option pricing Black-Scholes-Merton

CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS

1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries

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

Review for Exam 1. Instructions: Please read carefully

Review for Exam 1 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems covering chapter 1, 2, 3, 4, 14, 16. Questions in the multiple choice section will

Exam 1 Morning Session

91. A high yield bond fund states that through active management, the fund s return has outperformed an index of Treasury securities by 4% on average over the past five years. As a performance benchmark

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 5: Valuing Bonds

FIN 302 Class Notes Chapter 5: Valuing Bonds What is a bond? A long-term debt instrument A contract where a borrower agrees to make interest and principal payments on specific dates Corporate Bond Quotations

Bonds. Describe Bonds. Define Key Words. Created 2007 By Michael Worthington Elizabeth City State University

Bonds OBJECTIVES Describe bonds Define key words Explain why bond prices fluctuate Compute interest payments Calculate the price of bonds Created 2007 By Michael Worthington Elizabeth City State University

CHAPTER 21: OPTION VALUATION

CHAPTER 21: OPTION VALUATION 1. Put values also must increase as the volatility of the underlying stock increases. We see this from the parity relation as follows: P = C + PV(X) S 0 + PV(Dividends). Given

CHAPTER 14: BOND PRICES AND YIELDS

CHAPTER 14: BOND PRICES AND YIELDS 1. a. Effective annual rate on 3-month T-bill: ( 100,000 97,645 )4 1 = 1.02412 4 1 =.10 or 10% b. Effective annual interest rate on coupon bond paying 5% semiannually:

Interest Rates and Bond Valuation

Interest Rates and Bond Valuation Chapter 6 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean

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

Chapter 2 An Introduction to Forwards and Options

Chapter 2 An Introduction to Forwards and Options Question 2.1. The payoff diagram of the stock is just a graph of the stock price as a function of the stock price: In order to obtain the profit diagram

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

Finance 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

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

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

Bond Valuation. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Bond Valuation: An Overview

Bond Valuation FINANCE 350 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University 1 Bond Valuation: An Overview Bond Markets What are they? How big? How important? Valuation

Time Value of Money. Nature of Interest. appendix. study objectives

2918T_appC_C01-C20.qxd 8/28/08 9:57 PM Page C-1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.

Chapter 03 - Basic Annuities

3-1 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