A) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.


 Shanon Richard
 3 years ago
 Views:
Transcription
1 ACTS 408 Instructor: Natala A. Humphreys SOLUTION TO HOMEWOR 4 Secton 7: Annutes whose payments follow a geometrc progresson. Secton 8: Annutes whose payments follow an arthmetc progresson. Problem Suppose you buy a perpetutydue wth varyng annual payments. The frst 5 payments are constant and equal to. Startng the sxth payment, the payments start to ncrease so that each year s payment s % larger than the prevous years payment. At an annual effectve nterest rate of 7%, the perpetuty has a present value of 05. Calculate, gven < 7. A). B). C).5 D).7 E).9 Soluton. 0 4 ( + ) 5 ( + ) 6 Ths perpetuty conssts of two cash flows: () Annutydue of for 4 years () Annuty whose payments follow a geometrc progresson startng wth payment of at the begnnng of the 5th year Hence, P V = ä = = 05 = = = % B Problem The prce of a stock s $ per share. Annual dvdends are pad at the end of each year forever; the frst dvdend s $ and the expected growth rate for the dvdends s % per year. The annual effectve nterest rate s 5%. Calculate. Soluton. = = 0.0 = Problem Morrs makes a seres of payments at the end of each year for 9 years. The frst payment s. Each subsequent payment through the tenth year ncreases by 5% from the prevous payment. After the tenth payment, each payment decreases by 5% from the prevous payment. Calculate the present value of these payments usng an annual effectve rate of 7%. Soluton We splt our cash flow nto two cash flows:
2 ACTS 408. AU 04. SOLUTION TO HOMEWOR 4. () Annuty whose payments follow a geometrc progresson startng wth payment of at tme, wth multpler q =.05 for 0 years; () Annuty whose payments follow a geometrc progresson startng wth payment of.05 8 at tme, wth multpler q =.05 for 9 years, dscounted for 0 years. The present value of the frst cash flow s: P V = ( = Let us now calculate the present value of the second cash flow. Let =.05 8, q = /.05, v = /.07. Then, Hence, P V = v 0 ( v + qv + q v + + q n v n = v 0 v( + qv + (qv) + + (qv) n ) ) = ( = v 0 v ) (qv)n, qv P V = (.07) ( Alternatvely, ) 9 ) 0 = (.07) = P V = P V + P V = = Agan, We splt our cash flow nto two cash flows: () Annuty whose payments follow a geometrc progresson startng wth payment of at tme, wth multpler q =.05 for 0 years; () Annuty whose payments follow a geometrc progresson startng wth payment of at tme, wth multpler q = 0.95 for 9 years, dscounted for 0 years. The present value of the frst cash flow s: P V = ( = Let us now calculate the present value of the second cash flow. Let = , q = /.05, v = /.07. Then, Hence, P V = v 0 ( v + qv + q v + + q n v n = v 0 v( + qv + (qv) + + (qv) n ) ) = ( = v 0 v ) (qv)n, qv P V = (.07) ( 0.95 ) = ) 0 P V = P V + P V = = Problem 4 Common stock S pays a dvdend of 5 at the end of the frst year, wth each subsequent annual dvdend beng 4% greater than the precedng one. Mary purchases the stock at a theoretcal prce Copyrght Natala A. Humphreys, 04 Page of 5
3 ACTS 408. AU 04. SOLUTION TO HOMEWOR 4. to earn an expected annual effectve yeld of 8%. Immedately after recevng the th dvdend, Mary sells the stock for a prce of P. Her annual effectve yeld over the year perod was 6.75%. Calculate P. Soluton. The ntal prce of the stock s Therefore, 5 ) P ( S = = = P = 875 P = Problem 5 Vernon buys a 0year decreasng annutymmedate wth annual payments of 0, 9, 8,,. On the same date, Elzabeth buys a perpetutymmedate wth annual payments. For the frst years, payments are,,,,. Thereafter, payments reman constant at. At an annual effectve nterest rate of, both annutes have a present value of. Calculate. A) 7 B) 8 C) 88 D) 9 E) 98 Soluton. Vernon: Elzabeth: P V V = (Da) 0 = 0 a = 0 0 P V E = (Ia) 0 + ( + ) 0 ä0 0v0 = + v0 Equatng these two values, we obtan: 0 a 0 = ä 0 + v 0. Recall that: ä n = a n + v n. Hence, = ä0 + v0 ä 0 = a 0 + v 0 0 a 0 = a 0 + v 0 + v 0 a 0 = 9 a 0 = 4.5 = 5.5% = = ä0 + v0 = B = Problem 6 You are gven two seres of payments. Seres A s a perpetuty wth payments of at the end of each of the frst years, at the end of each of the next years, at the end of each of the next years, and so on. Seres B s a perpetuty wth payments of at the end of each of the frst years, at the end of each of the next years, at the end of each of the next years, and so on. The present values of the two seres of payments are equal. Calculate. A) B) d C) a a D) a ä E) s s Soluton. Seres A: Copyrght Natala A. Humphreys, 04 Page of 5
4 ACTS 408. AU 04. SOLUTION TO HOMEWOR P V A = (Ia) j + ( + ) (Ia) j, where j = (0.5) 0.5 (Ia) j = j + j = + j ( + ) ( + ) j = (( + ) = ) ( + ) ( + j) 0.5 = + j = ( + ) = ( + )( + + ) = ( + ) ( + ) ( + ) P V A = ( + ) (Ia) j = ( + ) ( + ) = ( + ) Seres B can be thought as a payment of s, s, s, at the end of years, 6, 9, etc Therefore, ( P V B = s j + ) j, where j = ( ), ( + j) = +, + j = ( + ), j = ( + ) s = ( + ), j + j = + j j = P V B = ( + ) ( + ) (( + ) ) ( + ) ( + ) (( + ) = ) (( + ) ) Snce the present values of the two seres of payments are equal P V A = P V B ( + ) ( + ) = ( + ) (( + ) ) ( + ) = + ( + ) = ( + ) ( + )( + ) ( + ) ( + ) = ( + ) = (( + ) )( + ) = ( + ) (( + ) )( + ) = s s ( + ) = (( + ) )( + ) = (( + ) )v (( + ) )( + )v = v (( + ) )v = v v = a C a Problem 7 At an annual effectve nterest rate of, the present value of a perpetutymmedate startng wth a payment of 500 n the frst year and ncreasng by 0 each year thereafter s Calculate. A).5% B) 5.0% C) 7.5% D) 40.0% E) 4.5% Soluton. Ths perpetuty can be represented as the sum of two perpetutes: a level perpetutymmedate of 500, plus an ncreasng perpetuty wth the frst payment of 0 at the end of the second year ncreasng by 0 n each subsequent year: = Copyrght Natala A. Humphreys, 04 Page 4 of 5
5 ACTS 408. AU 04. SOLUTION TO HOMEWOR 4. Therefore, Problem 8 P V = ( + ) 0 (Ia) = ( + + ) = = = = = 0 D = = 90. = , = = 0.75 = 7.5% C Payments of are made at the end of each month for a year. These payments earn nterest at a nomnal rate of j% convertble monthly. The nterest s mmedately renvested at a nomnal rate of % convertble monthly. At the end of the year, the accumulated value of the payments and the renvested nterest s Calculate j. Soluton. Interest payments are: I = j I I 4I 4 I + I (Is) % = I s % 68.50I = I =.4 j = = 0.68 = 95.55, s % =.685 Problem 9 Payments of are made at the begnnng of each year for 5 years. These payments earn nterest at the end of each year at an annual effectve rate of 8%. The nterest s mmedately renvested at an annual effectve rate of 5%. At the end of 5 years, the accumulated value of the 5 payments and the renvested nterest s Calculate. A) 47 B) 5 C) 57 D) 6 E) 67 Soluton. I I 4 4I 4 5 5I 5 I = 0.08, 5 + I (Is) 5 5% = s6 5% = 4000 = A 0.05 = 4000, s 6 5% =.6575 Problem 0 Mke receves a cash flow of today, 00 n two years, and n four years. The present value of ths cash flow s 78 at an annual effectve rate of nterest. Calculate. A).9% B).9% C) 4.9% D) 5.9% E) 6.9% Soluton. Copyrght Natala A. Humphreys, 04 Page 5 of 5
6 ACTS 408. AU 04. SOLUTION TO HOMEWOR v + v 4 = 78, x = v x + x + =.78 ( + x) =.78, x = v = =.9% A Copyrght Natala A. Humphreys, 04 Page 6 of 5
Lecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationLevel Annuities with Payments Less Frequent than Each Interest Period
Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Symoblc approach
More informationOn some special nonlevel annuities and yield rates for annuities
On some specal nonlevel annutes and yeld rates for annutes 1 Annutes wth payments n geometrc progresson 2 Annutes wth payments n Arthmetc Progresson 1 Annutes wth payments n geometrc progresson 2 Annutes
More information10. (# 45, May 2001). At time t = 0, 1 is deposited into each of Fund X and Fund Y. Fund X accumulates at a force of interest
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual e ectve
More information0.02t if 0 t 3 δ t = 0.045 if 3 < t
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual effectve
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationSection 2.3 Present Value of an Annuity; Amortization
Secton 2.3 Present Value of an Annuty; Amortzaton Prncpal Intal Value PV s the present value or present sum of the payments. PMT s the perodc payments. Gven r = 6% semannually, n order to wthdraw $1,000.00
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount in the account, the balance, is
Payout annutes: Start wth P dollars, e.g., P = 100, 000. Over a 30 year perod you receve equal payments of A dollars at the end of each month. The amount of money left n the account, the balance, earns
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationSection 2.2 Future Value of an Annuity
Secton 2.2 Future Value of an Annuty Annuty s any sequence of equal perodc payments. Depost s equal payment each nterval There are two basc types of annutes. An annuty due requres that the frst payment
More informationAn Overview of Financial Mathematics
An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationSolutions to First Midterm
rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e.
More information3. Present value of Annuity Problems
Mathematcs of Fnance The formulae 1. A = P(1 +.n) smple nterest 2. A = P(1 + ) n compound nterest formula 3. A = P(1.n) deprecaton straght lne 4. A = P(1 ) n compound decrease dmshng balance 5. P = 
More informationEXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR
EXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR 8S CHAPTER 8 EXAMPLES EXAMPLE 8.4A THE INVESTMENT NEEDED TO REACH A PARTICULAR FUTURE VALUE What amount must you nvest now at 4% compoune monthly
More information8.4. Annuities: Future Value. INVESTIGATE the Math. 504 8.4 Annuities: Future Value
8. Annutes: Future Value YOU WILL NEED graphng calculator spreadsheet software GOAL Determne the future value of an annuty earnng compound nterest. INVESTIGATE the Math Chrstne decdes to nvest $000 at
More informationCompound Interest: Further Topics and Applications. Chapter 9
92 Compound Interest: Further Topcs and Applcatons Chapter 9 93 Learnng Objectves After letng ths chapter, you wll be able to:? Calculate the nterest rate and term n ound nterest applcatons? Gven a nomnal
More informationFINANCIAL MATHEMATICS
3 LESSON FINANCIAL MATHEMATICS Annutes What s an annuty? The term annuty s used n fnancal mathematcs to refer to any termnatng sequence of regular fxed payments over a specfed perod of tme. Loans are usually
More informationAS 2553a Mathematics of finance
AS 2553a Mathematcs of fnance Formula sheet November 29, 2010 Ths ocument contans some of the most frequently use formulae that are scusse n the course As a general rule, stuents are responsble for all
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount owed is. P (1 + i) A
Amortzed loans: Suppose you borrow P dollars, e.g., P = 100, 000 for a house wth a 30 year mortgage wth an nterest rate of 8.25% (compounded monthly). In ths type of loan you make equal payments of A dollars
More informationProperties of American Derivative Securities
Capter 6 Propertes of Amercan Dervatve Securtes 6.1 Te propertes Defnton 6.1 An Amercan dervatve securty s a sequence of nonnegatve random varables fg k g n k= suc tat eac G k s F k measurable. Te owner
More informationChapter 15 Debt and Taxes
hapter 15 Debt and Taxes 151. Pelamed Pharmaceutcals has EBIT of $325 mllon n 2006. In addton, Pelamed has nterest expenses of $125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More informationMathematics of Finance
CHAPTER 5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty; Amortzaton Revew Exercses Extended Applcaton: Tme, Money, and Polynomals Buyng
More informationMathematics of Finance
5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty;Amortzaton Chapter 5 Revew Extended Applcaton:Tme, Money, and Polynomals Buyng a car
More informationMathematics of Finance
Mathematcs of Fnance 5 C H A P T E R CHAPTER OUTLINE 5.1 Smple Interest and Dscount 5.2 Compound Interest 5.3 Annutes, Future Value, and Snkng Funds 5.4 Annutes, Present Value, and Amortzaton CASE STUDY
More informationChapter 4 Financial Markets
Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationThursday, December 10, 2009 Noon  1:50 pm Faraday 143
1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationANALYSIS OF FINANCIAL FLOWS
ANALYSIS OF FINANCIAL FLOWS AND INVESTMENTS II 4 Annutes Only rarely wll one encounter an nvestment or loan where the underlyng fnancal arrangement s as smple as the lump sum, sngle cash flow problems
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationPresent Values and Accumulations
Present Values an Accumulatons ANGUS S. MACDONALD Volume 3, pp. 1331 1336 In Encyclopea Of Actuaral Scence (ISBN 47846763) Ete by Jozef L. Teugels an Bjørn Sunt John Wley & Sons, Lt, Chchester, 24 Present
More informationInterest Rate Futures
Interest Rate Futures Chapter 6 6.1 Day Count Conventons n the U.S. (Page 129) Treasury Bonds: Corporate Bonds: Money Market Instruments: Actual/Actual (n perod) 30/360 Actual/360 The day count conventon
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More information= i δ δ s n and PV = a n = 1 v n = 1 e nδ
Exam 2 s Th March 19 You are allowe 7 sheets of notes an a calculator 41) An mportant fact about smple nterest s that for smple nterest A(t) = K[1+t], the amount of nterest earne each year s constant =
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationTexas Instruments 30Xa Calculator
Teas Instruments 30Xa Calculator Keystrokes for the TI30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationAddendum to: Importing SkillBiased Technology
Addendum to: Importng SkllBased Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationInterest Rate Forwards and Swaps
Interest Rate Forwards and Swaps Forward rate agreement (FRA) mxn FRA = agreement that fxes desgnated nterest rate coverng a perod of (nm) months, startng n m months: Example: Depostor wants to fx rate
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationSUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.
SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976761000
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 738 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qngxn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More informationA Master Time Value of Money Formula. Floyd Vest
A Master Tme Value of Money Formula Floyd Vest For Fnancal Functons on a calculator or computer, Master Tme Value of Money (TVM) Formulas are usually used for the Compound Interest Formula and for Annutes.
More informationLaddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems
Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) Laddered Multlevel DC/AC Inverters used n Solar Panel Energy Systems Fang Ln Luo, Senor Member IEEE
More informationEffective December 2015
Annuty rates for all states EXCEPT: NY Prevous Index Annuty s effectve Wednesday, December 7 Global Multple Index Cap S&P Annual Pt to Pt Cap MLSB Annual Pt to Pt Spread MLSB 2Yr Pt to Pt Spread 3 (Annualzed)
More informationProfessor Iordanis Karagiannidis. 2010 Iordanis Karagiannidis
Fnancal Modelng Notes Basc Excel Fnancal Functons Professor Iordans Karagannds Excel Functons Excel Functons are preformatted formulas that allow you to perform arthmetc and other operatons very quckly
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, PerreAndre
More informationEffective September 2015
Annuty rates for all states EXCEPT: NY Lock Polces Prevous Prevous Sheet Feld Bulletns Index Annuty s effectve Monday, September 28 Global Multple Index Cap S&P Annual Pt to Pt Cap MLSB Annual Pt to Pt
More informationDocumentation about calculation methods used for the electricity supply price index (SPIN 35.1),
STATISTICS SWEDEN Documentaton (6) ES/PRS 0 artn Kullendorff arcus rdén Documentaton about calculaton methods used for the electrct suppl prce ndex (SPIN 35.), home sales (HPI) The ndex fgure for electrct
More informationFast degree elevation and knot insertion for Bspline curves
Computer Aded Geometrc Desgn 22 (2005) 183 197 www.elsever.com/locate/cagd Fast degree elevaton and knot nserton for Bsplne curves QXng Huang a,shmnhu a,, Ralph R. Martn b a Department of Computer Scence
More informationUncrystallised funds pension lump sum payment instruction
For customers Uncrystallsed funds penson lump sum payment nstructon Don t complete ths form f your wrapper s derved from a penson credt receved followng a dvorce where your ex spouse or cvl partner had
More informationChapter 15: Debt and Taxes
Chapter 15: Debt and Taxes1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationComplex Number Representation in RCBNS Form for Arithmetic Operations and Conversion of the Result into Standard Binary Form
Complex Number epresentaton n CBNS Form for Arthmetc Operatons and Converson of the esult nto Standard Bnary Form Hatm Zan and. G. Deshmukh Florda Insttute of Technology rgd@ee.ft.edu ABSTACT Ths paper
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationApplied Research Laboratory. Decision Theory and Receiver Design
Decson Theor and Recever Desgn Sgnal Detecton and Performance Estmaton Sgnal Processor Decde Sgnal s resent or Sgnal s not resent Nose Nose Sgnal? Problem: How should receved sgnals be rocessed n order
More informationInterchangeability of the median operator with the present value operator
Appled Economcs Letters, 20, 5, Frst Interchangeablty of the medan operator wth the present value operator Gary R. Skoog and James E. Cecka* Department of Economcs, DePaul Unversty, East Jackson Boulevard,
More informationCHAPTER 2. Time Value of Money 61
CHAPTER 2 Tme Value of Moey 6 Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 62 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationYIELD CURVE FITTING 2.0 Constructing Bond and Money Market Yield Curves using Cubic BSpline and Natural Cubic Spline Methodology.
YIELD CURVE FITTING 2.0 Constructng Bond and Money Market Yeld Curves usng Cubc BSplne and Natural Cubc Splne Methodology Users Manual YIELD CURVE FITTING 2.0 Users Manual Authors: Zhuosh Lu, Moorad Choudhry
More information17 Capital tax competition
17 Captal tax competton 17.1 Introducton Governments would lke to tax a varety of transactons that ncreasngly appear to be moble across jursdctonal boundares. Ths creates one obvous problem: tax base flght.
More information( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76
Homework Solutons Physcs 8B Sprng 09 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat = E. Please refer to Fgure EX32.5. We wll choose a clockwse
More informationHomework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76
Homework Solutons Physcs 8B Sprng 202 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat =. Please refer to Fgure EX32.5. We wll choose a clockwse
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationApplication of Quasi Monte Carlo methods and Global Sensitivity Analysis in finance
Applcaton of Quas Monte Carlo methods and Global Senstvty Analyss n fnance Serge Kucherenko, Nlay Shah Imperal College London, UK skucherenko@mperalacuk Daro Czraky Barclays Captal DaroCzraky@barclayscaptalcom
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationINVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMAHDR NETWORKS
21 22 September 2007, BULGARIA 119 Proceedngs of the Internatonal Conference on Informaton Technologes (InfoTech2007) 21 st 22 nd September 2007, Bulgara vol. 2 INVESTIGATION OF VEHICULAR USERS FAIRNESS
More informationThe CoxRossRubinstein Option Pricing Model
Fnance 400 A. Penat  G. Pennacc Te CoxRossRubnsten Opton Prcng Model Te prevous notes sowed tat te absence o arbtrage restrcts te prce o an opton n terms o ts underlyng asset. However, te noarbtrage
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER Revsed May 2003 ABSTRACT In ths paper, we nvestgate
More informationStock Profit Patterns
Stock Proft Patterns Suppose a share of Farsta Shppng stock n January 004 s prce n the market to 56. Assume that a September call opton at exercse prce 50 costs 8. A September put opton at exercse prce
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationVariable Payout Annuities with Downside Protection: How to Replace the Lost Longevity Insurance in DC Plans
Varable Payout Annutes wth Downsde Protecton: How to Replace the Lost Longevty Insurance n DC Plans By: Moshe A. Mlevsky 1 and Anna Abamova 2 Summary Abstract Date: 12 October 2005 Motvated by the rapd
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationHedging InterestRate Risk with Duration
FIXEDINCOME SECURITIES Chapter 5 Hedgng InterestRate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cashflows Interest rate rsk Hedgng prncples DuratonBased Hedgng Technques Defnton of duraton
More information10/19/2011. Financial Mathematics. Lecture 24 Annuities. Ana NoraEvans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.
Math 40 Lecture 24 Autes Facal Mathematcs How ready do you feel for the quz o Frday: A) Brg t o B) I wll be by Frday C) I eed aother week D) I eed aother moth Aa NoraEvas 403 Kerchof AaNEvas@vrga.edu http://people.vrga.edu/~as5k/
More informationSection B9: Zener Diodes
Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peaknverse
More information1. The Time Value of Money
Corporate Face [000345]. The Tme Value of Moey. Compoudg ad Dscoutg Captalzato (compoudg, fdg future values) s a process of movg a value forward tme. It yelds the future value gve the relevat compoudg
More informationAn Analysis of Pricing Methods for Baskets Options
An Analyss of Prcng Methods for Baskets Optons Martn Krekel, Johan de Kock, Ralf Korn, TnKwa Man Fraunhofer ITWM, Department of Fnancal Mathematcs, 67653 Kaserslautern, Germany, emal: krekel@twm.fhg.de
More informationPAS: A Packet Accounting System to Limit the Effects of DoS & DDoS. Debish Fesehaye & Klara Naherstedt University of IllinoisUrbana Champaign
PAS: A Packet Accountng System to Lmt the Effects of DoS & DDoS Debsh Fesehaye & Klara Naherstedt Unversty of IllnosUrbana Champagn DoS and DDoS DDoS attacks are ncreasng threats to our dgtal world. Exstng
More informationTrivial lump sum R5.0
Optons form Once you have flled n ths form, please return t wth your orgnal brth certfcate to: Premer PO Box 2067 Croydon CR90 9ND. Fll n ths form usng BLOCK CAPITALS and black nk. Mark all answers wth
More informationVRT012 User s guide V0.1. Address: Žirmūnų g. 27, Vilnius LT09105, Phone: (3705) 2127472, Fax: (3705) 276 1380, Email: info@teltonika.
VRT012 User s gude V0.1 Thank you for purchasng our product. We hope ths userfrendly devce wll be helpful n realsng your deas and brngng comfort to your lfe. Please take few mnutes to read ths manual
More information