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

Size: px
Start display at page:

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

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 perpetuty-due 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: () Annuty-due 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 0-year decreasng annuty-mmedate wth annual payments of 0, 9, 8,,. On the same date, Elzabeth buys a perpetuty-mmedate 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 perpetuty-mmedate 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: 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 information

Level Annuities with Payments Less Frequent than Each Interest Period

Level Annuities with Payments Less Frequent than Each Interest Period Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annuty-mmedate 2 Annuty-due Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annuty-mmedate 2 Annuty-due Symoblc approach

More information

On some special nonlevel annuities and yield rates for annuities

On 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 information

10. (# 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

10. (# 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 information

0.02t if 0 t 3 δ t = 0.045 if 3 < t

0.02t 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 information

Solution: 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.

Solution: 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 information

Lecture 3: Force of Interest, Real Interest Rate, Annuity

Lecture 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 annuty-mmedate, and ts present value Study annuty-due, and

More information

Time 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

Time 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 information

Section 2.3 Present Value of an Annuity; Amortization

Section 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 information

FINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals

FINANCIAL 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 information

10.2 Future Value and Present Value of an Ordinary Simple Annuity

10.2 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 information

Section 5.3 Annuities, Future Value, and Sinking Funds

Section 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 information

In 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

In 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 information

Using Series to Analyze Financial Situations: Present Value

Using 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 information

An Overview of Financial Mathematics

An 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 information

Time Value of Money Module

Time 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 information

Simple Interest Loans (Section 5.1) :

Simple 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 information

Section 2.2 Future Value of an Annuity

Section 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 information

Finite Math Chapter 10: Study Guide and Solution to Problems

Finite 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 information

7.5. Present Value of an Annuity. Investigate

7.5. 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 information

Section 5.4 Annuities, Present Value, and Amortization

Section 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 information

3. Present value of Annuity Problems

3. 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 information

EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A CALCULATOR

EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A CALCULATOR EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A 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 information

8.4. Annuities: Future Value. INVESTIGATE the Math. 504 8.4 Annuities: Future Value

8.4. 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 information

FINANCIAL MATHEMATICS

FINANCIAL 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 information

An Alternative Way to Measure Private Equity Performance

An 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 information

Mathematics of Finance

Mathematics 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 information

Mathematics of Finance

Mathematics 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 information

AS 2553a Mathematics of finance

AS 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 information

Mathematics of Finance

Mathematics 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 information

Problem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.

Problem 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 information

Chapter 15 Debt and Taxes

Chapter 15 Debt and Taxes hapter 15 Debt and Taxes 15-1. 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 information

Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error

Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error Intra-year 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 information

1. Math 210 Finite Mathematics

1. 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 information

Thursday, December 10, 2009 Noon - 1:50 pm Faraday 143

Thursday, 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 information

IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS

IDENTIFICATION 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 information

ANALYSIS OF FINANCIAL FLOWS

ANALYSIS 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 information

Answer: 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

Answer: 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 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.

More information

= i δ δ s n and PV = a n = 1 v n = 1 e nδ

= 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 information

Recurrence. 1 Definitions and main statements

Recurrence. 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 information

Present Values and Accumulations

Present Values and Accumulations Present Values an Accumulatons ANGUS S. MACDONALD Volume 3, pp. 1331 1336 In Encyclopea Of Actuaral Scence (ISBN -47-84676-3) Ete by Jozef L. Teugels an Bjørn Sunt John Wley & Sons, Lt, Chchester, 24 Present

More information

Interest Rate Futures

Interest 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 information

Number 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

Number 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

Addendum to: Importing Skill-Biased Technology

Addendum to: Importing Skill-Biased Technology Addendum to: Importng Skll-Based 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 information

Interest Rate Forwards and Swaps

Interest 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 (n-m) months, startng n m months: Example: Depostor wants to fx rate

More information

On the Optimal Control of a Cascade of Hydro-Electric Power Stations

On the Optimal Control of a Cascade of Hydro-Electric Power Stations On the Optmal Control of a Cascade of Hydro-Electrc 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 information

SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.

SUPPLIER 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: 976-76-10-00

More information

Texas Instruments 30X IIS Calculator

Texas Instruments 30X IIS Calculator Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X 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 information

ADVERSE 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 * 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, Perre-Andre

More information

Financial Mathemetics

Financial 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 information

The Application of Fractional Brownian Motion in Option Pricing

The Application of Fractional Brownian Motion in Option Pricing Vol. 0, No. (05), pp. 73-8 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qng-xn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com

More information

A Master Time Value of Money Formula. Floyd Vest

A 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 information

Laddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems

Laddered 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 information

Documentation about calculation methods used for the electricity supply price index (SPIN 35.1),

Documentation about calculation methods used for the electricity supply price index (SPIN 35.1), STATISTICS SWEDEN Documentaton (6) ES/PR-S 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 information

Professor Iordanis Karagiannidis. 2010 Iordanis Karagiannidis

Professor 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 information

Effective December 2015

Effective 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 information

Interchangeability of the median operator with the present value operator

Interchangeability 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 information

Effective September 2015

Effective 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 information

Fast degree elevation and knot insertion for B-spline curves

Fast degree elevation and knot insertion for B-spline curves Computer Aded Geometrc Desgn 22 (2005) 183 197 www.elsever.com/locate/cagd Fast degree elevaton and knot nserton for B-splne curves Q-Xng Huang a,sh-mnhu a,, Ralph R. Martn b a Department of Computer Scence

More information

Uncrystallised funds pension lump sum payment instruction

Uncrystallised 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 information

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol

CHOLESTEROL 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 information

Small pots lump sum payment instruction

Small 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 information

Traffic-light a stress test for life insurance provisions

Traffic-light a stress test for life insurance provisions MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax

More information

Applied Research Laboratory. Decision Theory and Receiver Design

Applied 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 information

YIELD CURVE FITTING 2.0 Constructing Bond and Money Market Yield Curves using Cubic B-Spline and Natural Cubic Spline Methodology.

YIELD CURVE FITTING 2.0 Constructing Bond and Money Market Yield Curves using Cubic B-Spline and Natural Cubic Spline Methodology. YIELD CURVE FITTING 2.0 Constructng Bond and Money Market Yeld Curves usng Cubc B-Splne and Natural Cubc Splne Methodology Users Manual YIELD CURVE FITTING 2.0 Users Manual Authors: Zhuosh Lu, Moorad Choudhry

More information

Joe Pimbley, unpublished, 2005. Yield Curve Calculations

Joe 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 information

17 Capital tax competition

17 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

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit 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 information

Chapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT

Chapter 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 information

Chapter 15: Debt and Taxes

Chapter 15: Debt and Taxes Chapter 15: Debt and Taxes-1 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 information

Application of Quasi Monte Carlo methods and Global Sensitivity Analysis in finance

Application 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 information

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS 21 22 September 2007, BULGARIA 119 Proceedngs of the Internatonal Conference on Informaton Technologes (InfoTech-2007) 21 st 22 nd September 2007, Bulgara vol. 2 INVESTIGATION OF VEHICULAR USERS FAIRNESS

More information

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12 14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) 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 information

ADVERSE 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 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 information

Luby s Alg. for Maximal Independent Sets using Pairwise Independence

Luby 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 information

CHAPTER 2. Time Value of Money 6-1

CHAPTER 2. Time Value of Money 6-1 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 6-2 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show

More information

Stock Profit Patterns

Stock 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 information

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:

SPEE 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 information

Hedging Interest-Rate Risk with Duration

Hedging Interest-Rate Risk with Duration FIXED-INCOME SECURITIES Chapter 5 Hedgng Interest-Rate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cash-flows Interest rate rsk Hedgng prncples Duraton-Based Hedgng Technques Defnton of duraton

More information

10/19/2011. Financial Mathematics. Lecture 24 Annuities. Ana NoraEvans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.

10/19/2011. 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 information

An Analysis of Pricing Methods for Baskets Options

An Analysis of Pricing Methods for Baskets Options An Analyss of Prcng Methods for Baskets Optons Martn Krekel, Johan de Kock, Ralf Korn, Tn-Kwa Man Fraunhofer ITWM, Department of Fnancal Mathematcs, 67653 Kaserslautern, Germany, emal: krekel@twm.fhg.de

More information

PAS: A Packet Accounting System to Limit the Effects of DoS & DDoS. Debish Fesehaye & Klara Naherstedt University of Illinois-Urbana Champaign

PAS: A Packet Accounting System to Limit the Effects of DoS & DDoS. Debish Fesehaye & Klara Naherstedt University of Illinois-Urbana Champaign PAS: A Packet Accountng System to Lmt the Effects of DoS & DDoS Debsh Fesehaye & Klara Naherstedt Unversty of Illnos-Urbana Champagn DoS and DDoS DDoS attacks are ncreasng threats to our dgtal world. Exstng

More information

1. The Time Value of Money

1. The Time Value of Money Corporate Face [00-0345]. 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 information

ADVA FINAN QUAN ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS VAULT GUIDE TO. Customized for: Jason (jason.barquero@cgu.edu) 2002 Vault Inc.

ADVA FINAN QUAN ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS VAULT GUIDE TO. Customized for: Jason (jason.barquero@cgu.edu) 2002 Vault Inc. ADVA FINAN QUAN 00 Vault Inc. VAULT GUIDE TO ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS Copyrght 00 by Vault Inc. All rghts reserved. All nformaton n ths book s subject to change wthout notce. Vault

More information

VRT012 User s guide V0.1. Address: Žirmūnų g. 27, Vilnius LT-09105, Phone: (370-5) 2127472, Fax: (370-5) 276 1380, Email: info@teltonika.

VRT012 User s guide V0.1. Address: Žirmūnų g. 27, Vilnius LT-09105, Phone: (370-5) 2127472, Fax: (370-5) 276 1380, Email: info@teltonika. VRT012 User s gude V0.1 Thank you for purchasng our product. We hope ths user-frendly devce wll be helpful n realsng your deas and brngng comfort to your lfe. Please take few mnutes to read ths manual

More information

Trivial lump sum R5.0

Trivial 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 information

Pricing Overage and Underage Penalties for Inventory with Continuous Replenishment and Compound Renewal Demand via Martingale Methods

Pricing Overage and Underage Penalties for Inventory with Continuous Replenishment and Compound Renewal Demand via Martingale Methods Prcng Overage and Underage Penaltes for Inventory wth Contnuous Replenshment and Compound Renewal emand va Martngale Methods RAF -Jun-3 - comments welcome, do not cte or dstrbute wthout permsson Junmn

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.

More information

Adverse selection in the annuity market with sequential and simultaneous insurance demand. Johann K. Brunner and Susanne Pech *) January 2005

Adverse selection in the annuity market with sequential and simultaneous insurance demand. Johann K. Brunner and Susanne Pech *) January 2005 Adverse selecton n the annuty market wth sequental and smultaneous nsurance demand Johann K. Brunner and Susanne Pech *) January 005 Revsed Verson of Workng Paper 004, Department of Economcs, Unversty

More information

RISK PREMIUM IN MOTOR VEHICLE INSURANCE. Banu ÖZGÜREL * ABSTRACT

RISK PREMIUM IN MOTOR VEHICLE INSURANCE. Banu ÖZGÜREL * ABSTRACT D.E.Ü.İİ.B.F. Dergs Clt: 0 Sayı:, Yıl: 005, ss:47-60 RISK PREMIUM IN MOTOR VEHICLE INSURANCE Banu ÖZGÜREL * ABSTRACT The pure premum or rsk premum s the premum that would exactly meet the expected cost

More information

Interest Rate Fundamentals

Interest Rate Fundamentals Lecture Part II Interest Rate Fundamentals Topcs n Quanttatve Fnance: Inflaton Dervatves Instructor: Iraj Kan Fundamentals of Interest Rates In part II of ths lecture we wll consder fundamental concepts

More information

Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid

Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid J. Non-Newtonan Flud Mech., 72 (1997) 31 53 Effect of a spectrum of relaxaton tmes on the capllary thnnng of a flament of elastc lqud V.M. Entov a, E.J. Hnch b, * a Laboratory of Appled Contnuum Mechancs,

More information

The Cox-Ross-Rubinstein Option Pricing Model

The Cox-Ross-Rubinstein Option Pricing Model Fnance 400 A. Penat - G. Pennacc Te Cox-Ross-Rubnsten 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 no-arbtrage

More information

Variable Payout Annuities with Downside Protection: How to Replace the Lost Longevity Insurance in DC Plans

Variable 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 information

FINANCIAL MATHEMATICS 12 MARCH 2014

FINANCIAL MATHEMATICS 12 MARCH 2014 FINNCIL MTHEMTICS 12 MRCH 2014 I ths lesso we: Lesso Descrpto Make use of logarthms to calculate the value of, the tme perod, the equato P1 or P1. Solve problems volvg preset value ad future value autes.

More information

Depreciation of Business R&D Capital

Depreciation of Business R&D Capital Deprecaton of Busness R&D Captal U.S. Bureau of Economc Analyss Abstract R&D deprecaton rates are crtcal to calculatng the rates of return to R&D nvestments and captal servce costs, whch are mportant for

More information

Gaining Insights to the Tea Industry of Sri Lanka using Data Mining

Gaining Insights to the Tea Industry of Sri Lanka using Data Mining Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 2008 Vol I Ganng Insghts to the Tea Industry of Sr Lanka usng Data Mnng H.C. Fernando, W. M. R Tssera, and R. I. Athauda

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange

More information

The Stock Market Game and the Kelly-Nash Equilibrium

The Stock Market Game and the Kelly-Nash Equilibrium The Stock Market Game and the Kelly-Nash Equlbrum Carlos Alós-Ferrer, Ana B. Ana Department of Economcs, Unversty of Venna. Hohenstaufengasse 9, A-1010 Venna, Austra. July 2003 Abstract We formulate the

More information