Time Value of Money, NPV and IRR equation solving with the TI86


 Alyson Tucker
 2 years ago
 Views:
Transcription
1 Time Value of Moey NPV ad IRR Equatio Solvig with the TI86 (may work with TI85) (similar process works with TI83, TI83 Plus ad may work with TI82) Time Value of Moey, NPV ad IRR equatio solvig with the TI Other TICalculators... 2 Mauals... 2 Trasfer of Formulas Usig Cable... 2 NPV ad IRR... 2 The formula... 2 Expressio of the NPV Formula i TI86 (ad possibly TI85)... 3 Expressio of the Formula i TI83, TI83Plus (ad possibly TI82)... 3 Usig the Equatio Solver i TI Solvig for NPV... 4 Solvig for IRR... 5 Time Value of Moey Calculatios... 6 The preset value of a auity formula... 6 The future value of a auity formula... 7 Future Value formula... 7 Future Value formula with cotiuous compoudig... 8 Effective Aual Rate... 8 Perpetuities ad Costat Growth Perpetuities... 9 EquatiosOTI86 1 of 9 Adrew Hall 2004
2 Time Value of Moey, NPV ad IRR equatio solvig with the TI86 Other TICalculators This approach may work for the TI85. You ca use a similar process with the TI83 ad TI83Plus, so it may help you with the TI82. O the TI82 ad TI83 variables i equatios appear to be limited to oe character; so you may eed to adjust the ames you use accordigly. Mauals Remember that pdf s of the relevat sectios of the mauals ca be dowloaded from the Course Web Page at Trasfer of Formulas Usig Cable Come to regular office hours with your calculator ad I will trasfer these equatios oto your TI86 (ad if it works your TI85!) NPV ad IRR The formula The formula which applies to both NPV ad IRR is { ( )} ( ) { } { ( ) }... { ( + ) } NPV C + 0 CF1 1 r + CF2 1 r + CF3 1 r + + CF = r Where C 0,CF 1,CF 2,CF 3...CF ca be positive or egative. For the IRR the formula assumes that NPV=0 ad looks as follows: { ( )} ( ) { } { ( ) } { ( ) } IRR IRR IRR IRR = C CF CF CF CF For coveiece, ad assumig problems o larger tha this o exams, let us work with the maximum umber of periods = 7 so =6: pv C1 C2 C3 C4 C5 C6 C = ( 1+r) ( 1+r) ( 1+r) ( 1+r) ( 1+r) ( 1+r) where r is either the Required Rate of Retur or the IRR (Iteral Rate of Retur); C0 is the iitial ivestmet; C1 is the cashflow at the ed of the first period; C2 is the cashflow at the ed of the secod period; NPV is either the value to be calculated for the et preset value or NPV is set to zero to calculate, r, the IRR. EquatiosOTI86 2 of 9 Adrew Hall 2004
3 Expressio of the NPV Formula i TI86 (ad possibly TI85) pv=c0+(c1/(1+r)^1)+(c2/(1+r)^2) +(C3/(1+r)^3) +(C4/(1+r)^4) +(C5/(1+r)^5) +(C6/(1+r)^6) O the mai scree: use 2 d ad ALPHA to eter the letter use 2 d ad ALPHA to eter the letters pv use ALPHA ad STO=> to eter a equals sig ALPHA C0 + Repeat (ALPHA C1 ( d ALPHA r)^1 ) six times. use the ENTER KEY to store expressio to expressio variable. Expressio of the Formula i TI83, TI83Plus (ad possibly TI82) =i+(a/(1+r)^1)+(b/(1+r)^2) +(c/(1+r)^3) +(d/(1+r)^4) +(e/(1+r)^5) +(f/(1+r)^6) I have ot worked out how to use variable ames loger tha a sigle character i these calculators. It will oly really be relevat to the TI82 users because TI83 ad TI83Plus already have the TVM_Solver fuctioality. Refer to the sectio above this oe o the Expressio of the NPV Formula i TI86. For pv substitute ; for C0 substitute i ; for C1 a ; for C2 b,, for C6 f. Usig the Equatio Solver i TI86 Oce the equatio has bee etered as a expressio i the TI86, typig 2 d GRAPH will take you ito the equatio solver. Use CLEAR to clear ay text to the right of eq:. At the bottom of your scree are 5 fuctio ames each associated with oe of the fuctio keys. The MORE key brigs up the ext five fuctios ad aother MORE will brig up the ext five fuctios util it loops back to the first 5 fuctios. Use MORE to avigate util pv is oe of the fuctios offered. Use the fuctio key below pv to select the equatio you etered as pv= The lie should ow read eq:pv Hit the ENTER key. EquatiosOTI86 3 of 9 Adrew Hall 2004
4 The scree should cotai somethig like Exp=pv exp= C0= C1= r= C2= C3= C4= C5= C6= Boud=(1E99,1E99) Up to C3 should be visible. Use the cursor up ad dow keys to look at the full set of values. If you cursor oto the top lie, the variables will disappear. Cursorig dow will make them reappear. Solvig for NPV If solvig for NPV eter the values of the variables C0, C1, r, C2, C3, C4, C5, C6. Use the () for egative values. Fill i somethig for each variable i.e. use zeros for values for which there is o data, for example Exp=pv exp= C0=100 C1=0 r= 0.1 C2=0 C3=150 C4=0 C5=0 C6=0 Boud=(1E99,1E99) Cursor to the secod lie exp= ad use the F5 key to ivoke SOLVE from the fuctios list. EquatiosOTI86 4 of 9 Adrew Hall 2004
5 The Net Preset Value will be calculated ad etered ito the secod lie as Exp=pv exp= C0=100 C1=0 r= 0.1 C2=0 C3=150 Solvig for IRR If solvig for IRR eter the values of the variables exp (equals zero for the IRR), C0, C1, C2, C3, C4, C5, C6. Use the () for egative values. Fill i somethig for each variable i.e. use zeros for values for which there is o data, for example Exp=pv exp=0 C0=100 C1=0 r= C2=0 C3=150 C4=0 C5=0 C6=0 Boud=(1E99,1E99) Cursor to the fifth lie r= ad use the F5 key to ivoke SOLVE from the fuctios list. EquatiosOTI86 5 of 9 Adrew Hall 2004
6 The Iteral Rate of Retur will be calculated ad etered ito the fifth lie as Exp=pv exp=0 C0=100 C1=0 r= C2=0 C3=150 Time Value of Moey Calculatios The preset value of a auity formula PVA PVA DUE A { 1 r} 1 r ( 1+ r) { 1 r } r( 1+ r) = A = ca be expressed to the calculator as: 1 *(1 + r) pva=(pmt*((1/(r/m)(1/((r/m)*(1+(r/m))^(yrs*m))))*(1+(r/m)*beg) m is the umber of periods i a year yrs is the umber of years r is the aual iterest rate where (r/m) is the periodic iterest rate (yrs*m) is the umber of periods beg = 1 if the questio asks for a auity due beg = 0 if the questio asks for a auity I the solver, as with the NPV ad IRR, exp refers to the left had side of the equatio or the PVA i this case. As before you ca eter a value for exp ad calculate oe of the other variables: so if you wat to calculate the paymet give the PVA, yrs, m, r ad kowig the mode (beg/ed) you fill i exp=pva, yrs =umber, m= umber, r = decimal expressio of rate, ad beg =1 or beg=0. The go to the pmt lie ad hit F5 to solve. EquatiosOTI86 6 of 9 Adrew Hall 2004
7 The future value of a auity formula FVA FVA DUE A {( 1+ r) 1} ( 1+ r) = A { } = r ca be expressed to the calculator as: 1 r *(1 + r) fva=(pmt*((1+(r/m))^(yrs*m))1)/(r/m)))*(1+(r/m)*beg) Where m is the umber of periods i a year yrs is the umber of years r is the aual iterest rate where (r/m) is the periodic iterest rate (yrs*m) is the umber of periods beg = 1 if the questio asks for a auity due beg = 0 if the questio asks for a auity I the solver exp refers to the left had side of the equatio or the FVA i this case. As before you ca eter a value for exp ad calculate oe of the other variables: so if you wat to calculate the paymet give the FVA, yrs, m, r ad kowig the mode (beg/ed) you fill i exp=fva, yrs =umber, m= umber, r = decimal expressio of rate, ad beg =1 or beg=0. The go to the pmt lie ad hit F5 to solve. Future Value formula FV = PV 1 + { rm} m ca be expressed to the calculator as: fv=pv*((1/(r/m)) ^(yrs*m) where fv is the future value pv is the preset value m is the umber of periods i a year yrs is the umber of years r is the aual iterest rate where (r/m) is the periodic iterest rate (yrs*m) is the umber of periods EquatiosOTI86 7 of 9 Adrew Hall 2004
8 I the solver exp refers to the left had side of the equatio or the FV i this case. As before you ca eter a value for the FV beside exp= ad calculate oe of the other variables. Eter values for the kow variables (if aual the let m=1). The go to the lie with the variable for which you wat to solve ad hit F5 to solve. Future Value formula with cotiuous compoudig * FV = PV r e ca be expressed to the calculator as: fvc=pvc*e^(r*yrs) where fvc is the future value uder cotiuous compoudig pv is the preset value uder cotiuous compoudig yrs is the umber of years r is the aual iterest rate e^ is obtaied usig 2 d ad LN keys. I the solver exp refers to the left had side of the equatio or the FVC (uder cotious compoudig) i this case. As before you ca eter a value for the FVC beside exp= ad calculate oe of the other variables. Eter values for the kow variables. The go to the lie with the variable for which you wat to solve ad hit F5 to solve. Effective Aual Rate Effective Aual Rate 1 + ca be expressed to the calculator as: ear=((1+(r/m))^m) 1 where ear is the effective aual rate yrs is the umber of years m { rm} 1 = m is the umber of periods i a year r is the aual iterest rate I the solver exp refers to the left had side of the equatio or the EAR i this case. Eter values for the kow variables. The go to the exp= lie ad hit F5 to solve. EquatiosOTI86 8 of 9 Adrew Hall 2004
9 Perpetuities ad Costat Growth Perpetuities PVP PVCGP CF 1 = A r is equivalet to if A= ad g=0 { CF ( r g) 1 } = IF we express the Preset Value Costat Growth Perpetuity to the calculator as cgp=pmt/((r/m)(grw/m)) where pmt is either A or CF1 m is the umber of periods i a year r is the aual iterest rate grw is the aual growth rate I the solver exp refers to the left had side of the equatio or the PVCGP i this case. Eter values for the kow variables. The go to the exp= lie ad hit F5 to solve. To solve for the growth rate or the iterest rate or the paymet eter the kow variables go to the lie for the variable you wat to calculate ad hit F5 to solve. m should be equal to oe uless the paymet is occurrig more frequetly tha aually. grw should equal zero if the calculatio is for the simple perpetuity. EquatiosOTI86 9 of 9 Adrew Hall 2004
CHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
More informationMMQ Problems Solutions with Calculators. Managerial Finance
MMQ Problems Solutios with Calculators Maagerial Fiace 2008 Adrew Hall. MMQ Solutios With Calculators. Page 1 MMQ 1: Suppose Newma s spi lads o the prize of $100 to be collected i exactly 2 years, but
More information.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth
Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,
More informationChapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions
Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig
More informationBENEFITCOST ANALYSIS Financial and Economic Appraisal using Spreadsheets
BENEITCST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal  Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts
More informationTerminology for Bonds and Loans
³ ² ± Termiology for Bods ad Loas Pricipal give to borrower whe loa is made Simple loa: pricipal plus iterest repaid at oe date Fixedpaymet loa: series of (ofte equal) repaymets Bod is issued at some
More informationSimple Annuities Present Value.
Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX9850GB PLUS to efficietly compute values associated with preset value auities.
More informationPresent Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value
Cocept 9: Preset Value Is the value of a dollar received today the same as received a year from today? A dollar today is worth more tha a dollar tomorrow because of iflatio, opportuity cost, ad risk Brigig
More informationLearning objectives. Duc K. Nguyen  Corporate Finance 21/10/2014
1 Lecture 3 Time Value of Moey ad Project Valuatio The timelie Three rules of time travels NPV of a stream of cash flows Perpetuities, auities ad other special cases Learig objectives 2 Uderstad the timevalue
More informationTime Value of Money. First some technical stuff. HP10B II users
Time Value of Moey Basis for the course Power of compoud iterest $3,600 each year ito a 401(k) pla yields $2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle
More information5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?
5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso
More informationI. Why is there a time value to money (TVM)?
Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios
More informationCDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest
CDs Bought at a Bak verses CD s Bought from a Brokerage Floyd Vest CDs bought at a bak. CD stads for Certificate of Deposit with the CD origiatig i a FDIC isured bak so that the CD is isured by the Uited
More informationSolving Logarithms and Exponential Equations
Solvig Logarithms ad Epoetial Equatios Logarithmic Equatios There are two major ideas required whe solvig Logarithmic Equatios. The first is the Defiitio of a Logarithm. You may recall from a earlier topic:
More informationQuestion 2: How is a loan amortized?
Questio 2: How is a loa amortized? Decreasig auities may be used i auto or home loas. I these types of loas, some amout of moey is borrowed. Fixed paymets are made to pay off the loa as well as ay accrued
More informationCHAPTER 4: NET PRESENT VALUE
EMBA 807 Corporate Fiace Dr. Rodey Boehe CHAPTER 4: NET PRESENT VALUE (Assiged probles are, 2, 7, 8,, 6, 23, 25, 28, 29, 3, 33, 36, 4, 42, 46, 50, ad 52) The title of this chapter ay be Net Preset Value,
More informationAnnuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.
Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio  Israel Istitute of Techology, 3000, Haifa, Israel I memory
More informationUnderstanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions
Udestadig Fiacial Maagemet: A Pactical Guide Guidelie Aswes to the Cocept Check Questios Chapte 4 The Time Value of Moey Cocept Check 4.. What is the meaig of the tems isketu tadeoff ad time value of
More informationFM4 CREDIT AND BORROWING
FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer
More informationINVESTMENT PERFORMANCE COUNCIL (IPC)
INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks
More informationTHE TIME VALUE OF MONEY
QRMC04 9/17/01 4:43 PM Page 51 CHAPTER FOUR THE TIME VALUE OF MONEY 4.1 INTRODUCTION AND FUTURE VALUE The perspective ad the orgaizatio of this chapter differs from that of chapters 2 ad 3 i that topics
More informationNow here is the important step
LINEST i Excel The Excel spreadsheet fuctio "liest" is a complete liear least squares curve fittig routie that produces ucertaity estimates for the fit values. There are two ways to access the "liest"
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationFI A CIAL MATHEMATICS
CHAPTER 7 FI A CIAL MATHEMATICS Page Cotets 7.1 Compoud Value 117 7.2 Compoud Value of a Auity 118 7.3 Sikig Fuds 119 7.4 Preset Value 122 7.5 Preset Value of a Auity 122 7.6 Term Loas ad Amortizatio 123
More information2 Time Value of Money
2 Time Value of Moey BASIC CONCEPTS AND FORMULAE 1. Time Value of Moey It meas moey has time value. A rupee today is more valuable tha a rupee a year hece. We use rate of iterest to express the time value
More informationwhere: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return
EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The
More informationFramingham State College Department of Economics and Business Managerial Finance Practice Final Exam Spring 2006
Name Framigham State College Departmet of Ecoomics ad Busiess Maagerial Fiace Practice Fial Exam Sprig 2006 This exam provides questios that are represetative of those cotaied o your exam. This test should
More informationDiscounting. Finance 100
Discoutig Fiace 100 Prof. Michael R. Roberts 1 Topic Overview The Timelie Compoudig & Future Value Discoutig & Preset Value Multiple Cash Flows Special Streams of Cash Flows» Perpetuities» Auities Iterest
More informationYour organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:
Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network
More informationTO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2
TO: Users of the ACTEX Review Semiar o DVD for SOA Exam FM/CAS Exam FROM: Richard L. (Dick) Lodo, FSA Dear Studets, Thak you for purchasig the DVD recordig of the ACTEX Review Semiar for SOA Exam FM (CAS
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 informationChecklist. Assignment
Checklist Part I Fid the simple iterest o a pricipal. Fid a compouded iterest o a pricipal. Part II Use the compoud iterest formula. Compare iterest growth rates. Cotiuous compoudig. (Math 1030) M 1030
More informationSubject CT5 Contingencies Core Technical Syllabus
Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value
More informationVALUATION OF FINANCIAL ASSETS
P A R T T W O As a parter for Erst & Youg, a atioal accoutig ad cosultig firm, Do Erickso is i charge of the busiess valuatio practice for the firm s Southwest regio. Erickso s sigle job for the firm is
More informationBond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond
What is a bod? Bod Valuatio I Bod is a I.O.U. Bod is a borrowig agreemet Bod issuers borrow moey from bod holders Bod is a fixedicome security that typically pays periodic coupo paymets, ad a pricipal
More informationINTRODUCTION TO ENGINEERING ECONOMICS. Types of Interest
INTRODUCTION TO ENGINEERING ECONOMICS A. J. Clark School of Egieerig Departmet of Civil ad Evirometal Egieerig by Dr. Ibrahim A. Assakkaf Sprig 2000 Departmet of Civil ad Evirometal Egieerig Uiversity
More informationBuilding Blocks Problem Related to Harmonic Series
TMME, vol3, o, p.76 Buildig Blocks Problem Related to Harmoic Series Yutaka Nishiyama Osaka Uiversity of Ecoomics, Japa Abstract: I this discussio I give a eplaatio of the divergece ad covergece of ifiite
More informationHow to set up your GMC Online account
How to set up your GMC Olie accout Mai title Itroductio GMC Olie is a secure part of our website that allows you to maage your registratio with us. Over 100,000 doctors already use GMC Olie. We wat every
More informationClassic Problems at a Glance using the TVM Solver
C H A P T E R 2 Classc Problems at a Glace usg the TVM Solver The table below llustrates the most commo types of classc face problems. The formulas are gve for each calculato. A bref troducto to usg the
More informationExponential function: For a > 0, the exponential function with base a is defined by. f(x) = a x
MATH 11011 EXPONENTIAL FUNCTIONS KSU AND THEIR APPLICATIONS Defiitios: Expoetial fuctio: For a > 0, the expoetial fuctio with base a is defied by fx) = a x Horizotal asymptote: The lie y = c is a horizotal
More informationModule 4: Mathematical Induction
Module 4: Mathematical Iductio Theme 1: Priciple of Mathematical Iductio Mathematical iductio is used to prove statemets about atural umbers. As studets may remember, we ca write such a statemet as a predicate
More informationExample 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).
BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook  Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly
More informationMeasures of Spread and Boxplots Discrete Math, Section 9.4
Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,
More informationRepeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.
5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers
More informationDefinition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean
1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.
More informationFinance Practice Problems
Iteest Fiace Pactice Poblems Iteest is the cost of boowig moey. A iteest ate is the cost stated as a pecet of the amout boowed pe peiod of time, usually oe yea. The pevailig maket ate is composed of: 1.
More informationA Resource for Freestanding Mathematics Qualifications Working with %
Ca you aswer these questios? A savigs accout gives % iterest per aum.. If 000 is ivested i this accout, how much will be i the accout at the ed of years? A ew car costs 16 000 ad its value falls by 1%
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More informationCHAPTER 11 Financial mathematics
CHAPTER 11 Fiacial mathematics I this chapter you will: Calculate iterest usig the simple iterest formula ( ) Use the simple iterest formula to calculate the pricipal (P) Use the simple iterest formula
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 informationI. Chisquared Distributions
1 M 358K Supplemet to Chapter 23: CHISQUARED DISTRIBUTIONS, TDISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad tdistributios, we first eed to look at aother family of distributios, the chisquared distributios.
More informationCS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations
CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 007 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, diagram sheet ad a page formula sheet. Please tur over Mathematics/P DoE/November
More informationPreSuit Collection Strategies
PreSuit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process
More informationNATIONAL SENIOR CERTIFICATE GRADE 12
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 0 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages, diagram sheet ad iformatio sheet. Please tur over Mathematics/P DBE/November 0
More informationI apply to subscribe for a Stocks & Shares ISA for the tax year 20 /20 and each subsequent year until further notice.
IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form Please complete usig BLOCK CAPITALS ad retur the completed form
More informationQuantum Mechanics for Scientists and Engineers. David Miller
Quatum Mechaics for Scietists ad Egieers David Miller Measuremet ad expectatio values Measuremet ad expectatio values Quatummechaical measuremet Probabilities ad expasio coefficiets Suppose we take some
More informationUSING STATISTICAL FUNCTIONS ON A SCIENTIFIC CALCULATOR
USING STATISTICAL FUNCTIONS ON A SCIENTIFIC CALCULATOR Objective:. Improve calculator skills eeded i a multiple choice statistical eamiatio where the eam allows the studet to use a scietific calculator..
More informationInstitute of Actuaries of India Subject CT1 Financial Mathematics
Istitute of Actuaries of Idia Subject CT1 Fiacial Mathematics For 2014 Examiatios Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig i
More informationFor Educational Purposes Only
PCSYBLF For Educatioal Purposes ly The materials preseted i this course represet the opiios ad views of the developers ad/or reviewers. Although these materials may have bee reviewed, the views ad opiios
More informationHere are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
This documet was writte ad copyrighted by Paul Dawkis. Use of this documet ad its olie versio is govered by the Terms ad Coditios of Use located at http://tutorial.math.lamar.edu/terms.asp. The olie versio
More informationLearning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)
Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 21 22 Leaig
More informationPAYG instalments how to complete your activity statement
Istructios for busiesses ad ivestors PAYG istalmets how to complete your activity statemet For more iformatio visit www.ato.gov.au NAT 739311.2012 Our commitmet to you We are committed to providig you
More informationHow to use what you OWN to reduce what you OWE
How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other shortterm assets ito chequig ad savigs accouts.
More informationMath 113 HW #11 Solutions
Math 3 HW # Solutios 5. 4. (a) Estimate the area uder the graph of f(x) = x from x = to x = 4 usig four approximatig rectagles ad right edpoits. Sketch the graph ad the rectagles. Is your estimate a uderestimate
More information8.1 Arithmetic Sequences
MCR3U Uit 8: Sequeces & Series Page 1 of 1 8.1 Arithmetic Sequeces Defiitio: A sequece is a comma separated list of ordered terms that follow a patter. Examples: 1, 2, 3, 4, 5 : a sequece of the first
More information7 b) 0. Guided Notes for lesson P.2 Properties of Exponents. If a, b, x, y and a, b, 0, and m, n Z then the following properties hold: 1 n b
Guided Notes for lesso P. Properties of Expoets If a, b, x, y ad a, b, 0, ad m, Z the the followig properties hold:. Negative Expoet Rule: b ad b b b Aswers must ever cotai egative expoets. Examples: 5
More informationRadicals and Fractional Exponents
Radicals ad Roots Radicals ad Fractioal Expoets I math, may problems will ivolve what is called the radical symbol, X is proouced the th root of X, where is or greater, ad X is a positive umber. What it
More informationChapter One BASIC MATHEMATICAL TOOLS
Chapter Oe BAIC MATHEMATICAL TOOL As the reader will see, the study of the time value of moey ivolves substatial use of variables ad umbers that are raised to a power. The power to which a variable is
More informationSequences and Series Using the TI89 Calculator
RIT Calculator Site Sequeces ad Series Usig the TI89 Calculator Norecursively Defied Sequeces A orecursively defied sequece is oe i which the formula for the terms of the sequece is give explicitly. For
More informationCHAPTER 3: FINANCIAL ANALYSIS WITH INFLATION
Up to ow, we have mostly igored iflatio. However, iflatio ad iterest are closely related. It was oted i the last chapter that iterest rates should geerally cover more tha iflatio. I fact, the amout of
More informationProject Deliverables. CS 361, Lecture 28. Outline. Project Deliverables. Administrative. Project Comments
Project Deliverables CS 361, Lecture 28 Jared Saia Uiversity of New Mexico Each Group should tur i oe group project cosistig of: About 612 pages of text (ca be loger with appedix) 612 figures (please
More informationTime Value of Money. If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
More informationCHAPTER Factors: How Time and Interest Affect Money
2 CHAPTER Factors: How Time ad Iterest Affect Moey I the previous chapter we leared the basic cocepts of egieerig ecoomy ad their role i decisio makig. The cash flow is fudametal to every ecoomic study.
More informationEngineering 323 Beautiful Homework Set 3 1 of 7 Kuszmar Problem 2.51
Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log
More informationInfinite Sequences and Series
CHAPTER 4 Ifiite Sequeces ad Series 4.1. Sequeces A sequece is a ifiite ordered list of umbers, for example the sequece of odd positive itegers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29...
More informationSequences and Series
CHAPTER 9 Sequeces ad Series 9.. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their
More informationNATIONAL SENIOR CERTIFICATE GRADE 12
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS
More informationINVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology
Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology
More informationSavings and Retirement Benefits
60 Baltimore Couty Public Schools offers you several ways to begi savig moey through payroll deductios. Defied Beefit Pesio Pla Tax Sheltered Auities ad Custodial Accouts Defied Beefit Pesio Pla Did you
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationThe Euler Totient, the Möbius and the Divisor Functions
The Euler Totiet, the Möbius ad the Divisor Fuctios Rosica Dieva July 29, 2005 Mout Holyoke College South Hadley, MA 01075 1 Ackowledgemets This work was supported by the Mout Holyoke College fellowship
More informationFor customers Key features of the Guaranteed Pension Annuity
For customers Key features of the Guarateed Pesio Auity The Fiacial Coduct Authority is a fiacial services regulator. It requires us, Aego, to give you this importat iformatio to help you to decide whether
More informationThe Mathematics of Amortization Schedules on the TI83. Floyd Vest, Nov (Preliminary Version)
The Mathematics of Amortizatio Schedules o the TI83 Note: TI 83/84 letters are ot i italics. Floyd Vest, Nov. 2011 (Prelimiary Versio) Moey wisely ivested i a home ca provide a secure form of ivestmet.
More informationHypergeometric Distributions
7.4 Hypergeometric Distributios Whe choosig the startig lieup for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you
More informationTIEE Teaching Issues and Experiments in Ecology  Volume 1, January 2004
TIEE Teachig Issues ad Experimets i Ecology  Volume 1, Jauary 2004 EXPERIMENTS Evirometal Correlates of Leaf Stomata Desity Bruce W. Grat ad Itzick Vatick Biology, Wideer Uiversity, Chester PA, 19013
More informationHandling. Collection Calls
Hadlig the Collectio Calls We do everythig we ca to stop collectio calls; however, i the early part of our represetatio, you ca expect some of these calls to cotiue. We uderstad that the first few moths
More informationCS103X: Discrete Structures Homework 4 Solutions
CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible sixfigure salaries i whole dollar amouts are there that cotai at least
More informationFlexible Trust. (Settlor as trustee with optional survivorship clause) Your questions answered. What is a trust? What is a Flexible Trust?
Flexible Trust (Settl as trustee with optioal survivship clause) Your questios aswered Uderstadig trusts ad their implicatios ca be pretty complicated. You should always get advice from your legal adviser
More information*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.
Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.
More informationTO: Users of the ACTEX Review Seminar on DVD for SOA Exam MLC
TO: Users of the ACTEX Review Semiar o DVD for SOA Eam MLC FROM: Richard L. (Dick) Lodo, FSA Dear Studets, Thak you for purchasig the DVD recordig of the ACTEX Review Semiar for SOA Eam M, Life Cotigecies
More informationSwaps: Constant maturity swaps (CMS) and constant maturity. Treasury (CMT) swaps
Swaps: Costat maturity swaps (CMS) ad costat maturity reasury (CM) swaps A Costat Maturity Swap (CMS) swap is a swap where oe of the legs pays (respectively receives) a swap rate of a fixed maturity, while
More informationTime Value of Money and Investment Analysis
Time Value of Moey ad Ivestmet Aalysis Explaatios ad Spreadsheet Applicatios for Agricultural ad Agribusiess Firms Part I. by Bruce J. Sherrick Paul N. Elliger David A. Lis V 1.2, September 2000 The Ceter
More informationNPTEL STRUCTURAL RELIABILITY
NPTEL Course O STRUCTURAL RELIABILITY Module # 0 Lecture 1 Course Format: Web Istructor: Dr. Aruasis Chakraborty Departmet of Civil Egieerig Idia Istitute of Techology Guwahati 1. Lecture 01: Basic Statistics
More informationPENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place.
PENSION ANNUITY Policy Coditios Documet referece: PPAS1(7) This is a importat documet. Please keep it i a safe place. Pesio Auity Policy Coditios Welcome to LV=, ad thak you for choosig our Pesio Auity.
More informationChapter 6: Variance, the law of large numbers and the MonteCarlo method
Chapter 6: Variace, the law of large umbers ad the MoteCarlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value
More informationThe Time Value of Money
The Tme Value of Moey 1 Iversemet Optos Year: 1624 Property Traded: Mahatta Islad Prce : $24.00, FV of $24 @ 6%: FV = $24 (1+0.06) 388 = $158.08 bllo Opto 1 0 1 2 3 4 5 t ($519.37) 0 0 0 0 $1,000 Opto
More informationInstallment Joint Life Insurance Actuarial Models with the Stochastic Interest Rate
Iteratioal Coferece o Maagemet Sciece ad Maagemet Iovatio (MSMI 4) Istallmet Joit Life Isurace ctuarial Models with the Stochastic Iterest Rate NiaNia JI a,*, Yue LI, DogHui WNG College of Sciece, Harbi
More informationDesktop Management. Desktop Management Tools
Desktop Maagemet 9 Desktop Maagemet Tools Mac OS X icludes three desktop maagemet tools that you might fid helpful to work more efficietly ad productively: u Stacks puts expadable folders i the Dock. Clickig
More information