FINANCIAL MATHEMATICS 12 MARCH 2014


 Dorcas Howard
 2 years ago
 Views:
Transcription
1 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. Summary Smple Iterest The formula whch helps us to calculate the accumulated amout (future value) f a orgal amout s vested or loaed for years at a rate of r % smple terest s gve by: Compoud Iterest The formula whch helps us to calculate the accumulated amout (future value) f a orgal amout s vested or loaed for years at a rate of r % compoud terest s gve by: P( 1. ) P( 1 ) P = preset value of the vestmet or loa (orgal amout at the begg) = accumulated amout or future value of the vestmet or loa after perods r = 100 =tme perod s decmal form) for the smple terest rate r % ( FUTURE VLUE NNUITY P =preset value of the vestmet or loa (orgal amout at the begg) =accumulated amout or future value of the vestmet or loa after perods r = 100 =tme perod decmal form) for the smple terest rate r % ( s PRESENT VLUE NNUITIES x 1 F where : 1 x 1 1 P x paymet per perod x paymet per perod umber of paymets umber of paymets terest rate terest rate where :
2 Tmele Skg Fud T 0 T 1 T 2 T 3 T 4 T 5 The book value of a asset s ts value after deprecato has bee take to accout. The scrap value s the book value of a asset at the ed of ts useful lfe. The skg value s the fud set up to replace a asset at the ed of ts useful lfe. Compaes ofte purchase equpmet ad use t for a specfed tme perod. The old equpmet s the sold at scrap value ad ew, upgraded equpmet s bought. I order to face the purchasg of the ew equpmet, the compay wll have, well advace, set up a auty called a skg fud. skg fud s othg more tha a ormal savgs pla or future value auty. The proceeds from the skg fud ad the sale of the old equpmet are the used to purchase the ew equpmet. Skg Fud = Cost of ew mache Scrap value Cost of New Mache Scrap value Iflato P 1 Deprecato o reducg balace P 1 bass Balace of Loa Balace = Loa (Captal + terest accrued over years) repaymets for years (together wth terest) Balace P 1 Questo 1 1 x 1 Test Yourself vestmet of R9 000 ears 6% per aum compouded aually for a perod of 4 years. Thereafter, the terest rate chages to 7% per aum compouded aually for a further 2 years. Calculate the future value of the vestmet at the ed of the 6year perod.. R13 518,69 B. R23 008,69 C. R13 008,69 D. R ,69 Questo 2 James vests R4 000 a bak accout payg 6% per aum compouded mothly. Calculate the value of hs vestmet 10 years tme.. R18 266,59 B. R8 166,59 C. R2 2666,50 D. R7 277,59
3 Questo 3 How much more moey would you have over a perod of 15 years o a savgs of R f the terest rate of 12% per aum was compouded mothly, as compared to a terest rate of 12% compouded aually?. R ,19 B. R ,95 C. R31 334,17 D. o dfferece. Questo 4 R5 000 s deposted to a savgs accout. The terest rate for the frst four years s 7% per aum compouded quarterly. Thereafter, the terest rate chages to 8% per aum compouded semaually. Calculate the value of the vestmet at the ed of the teth year.. R10 222,23 B. R23 645,23 C. R10 566,28 D. R11 456,11 Questo 5 Joseph deposts x to a savgs accout. Two years later, he deposts a further R2 to the accout. Three years after ths, he deposts 3x to the accout. The terest rate for the fve years s 18% per aum compouded mothly. He receves R at the ed of the fve year perod. Calculate the value of x.. R6 350,31 B. R4 452,32 C. R5 652,30 D. R6 230,51 Questo 6 vestmet of R9 000 ears 6% per aum compouded quarterly for a perod of 4 years. Thereafter, the terest rate chages to 7% per aum compouded semaually for a further 2 years. Calculate the future value of the vestmet at the ed of the 6year perod.. R13 105,71 B. R12 235,62 C. R10 341,70 D. R18 900,50 Questo 7 a saves R6 000 a year ad deposts t at the ed of each year a savgs accout that pays her 7% p.a. compouded aually. Fd her accumulated savgs mmedately after the 12 th depost s made.. R ,71 B. R ,73 C. R ,72 D. R ,32
4 Questo 8 Fra buys a large house wth fve bedrooms. She plas to occupy oe room herself ad let the other rooms to teats. She expects the retal wll cover the loa repaymets o her house. She takes out a loa of R The terest o the loa s 8% compouded mothly. How much must she charge each teat f the loa s to be repad over 20 years?. R 1150,11 B. R 1261,12 C. R 1373,12 D. R 1000,17 Questo 9 Thado dreamt of becomg a mlloare. Whe she was 30 years old, she vested R wth a vestmet compay. If the terest rate was 8,5% p.a. compouded mothly, how old was she whe she acheved her dream? Gve your aswer correct to the earest year.. 50 years old B. 48 years old C. 49 years old D. 39 years old Questo 10 tax ower buys fve mbuses. Each bus costs hm R Determe the book value of the fleet of mbuses after four years f the deprecato s calculated at 20% p.a. o: a reducg balace.. R B. R C. R D. Noe of the above Questo 1 Improve your Sklls R3 000 s deposted to a savgs accout at a bak ad the terest pad s 15% p.a. compoud terest. fter how may years wll the vestmet be worth R5 250? Questo 2 Suppose R1 000 s deposted mmedately to a savgs accout ad cotues to make mothly paymets at the ed of each moth for a perod of 5 moths. Iterest s 18% p.a. compouded mothly. How much moey wll have accumulated at the ed of the 5 th moth? Questo 3 vestor aged 25 wshes to accumulate R by her 50 th brthday. She wll pay equal mothly paymets to a accout payg 15% per aum compouded mothly. Paymets start o her 25 th brthday ad ed o her 50 th brthday. Fd the mothly paymets. Questo 4 How much ca be borrowed ow f a perso agrees to repay a loa by meas of quarterly paymets of R7 000, startg three moths from ow? The paymets wll cotue for 3 years ad the terest rate s 16% per aum compouded quarterly. Questo 5 loa of R s to be repad by meas of mothly paymets of R5 000, startg oe moth after the gratg of the loa. Iterest s fxed at 18% per aum compouded mothly. How log wll t take to repay the loa?
5 Questo 6 school purchases a photocopyg mache for R The mache deprecates value at 22% p.a. o a reducg balace. The school wats to buy a ew mache 5 year s tme. ew mache wll cost much more the future ad ts cost wll escalate at 19% per aum effectve. The old mache wll be sold at scrap value after 5 years. skg fud s set up mmedately order to save up for the ew mache. The proceeds from the sale of the old mache wll be used together wth the skg fud ad the terest eared s 14,4% p.a. compouded mothly. The frst paymet wll be made mmedately ad the last paymet wll be made at the ed of the 5year perod. a) Fd the scrap value of the old mache. b) Fd the cost of the ew mache 5 years from ow. c) Fd the amout requred the skg fud 5 years from ow. d) Fd the equal mothly paymets made to the skg fud. Questo 7 car s bought for R If 10% s pad cash ad the balace s pad usg a bak loa. The loa s repad over sx years. The terest rate s 10,5% p.a. compouded mothly. a) Determe the mothly repaymets. b) Determe the balace o the loa at the ed of two years mmedately after the 24 th paymet.
10.5 Future Value and Present Value of a General Annuity Due
Chapter 10 Autes 371 5. Thomas leases a car worth $4,000 at.99% compouded mothly. He agrees to make 36 lease paymets of $330 each at the begg of every moth. What s the buyout prce (resdual value of the
More informationChapter 3 0.06 = 3000 ( 1.015 ( 1 ) Present Value of an Annuity. Section 4 Present Value of an Annuity; Amortization
Chapter 3 Mathematcs of Face Secto 4 Preset Value of a Auty; Amortzato Preset Value of a Auty I ths secto, we wll address the problem of determg the amout that should be deposted to a accout ow at a gve
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 informationFuture Value of an Annuity
Future Value of a Auty After payg all your blls, you have $200 left each payday (at the ed of each moth) that you wll put to savgs order to save up a dow paymet for a house. If you vest ths moey at 5%
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 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 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 informationMathematics of Finance
CATE Mathematcs of ace.. TODUCTO ths chapter we wll dscuss mathematcal methods ad formulae whch are helpful busess ad persoal face. Oe of the fudametal cocepts the mathematcs of face s the tme value of
More informationChapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R =
Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS Objectves of the Topc: Beg able to formalse ad solve practcal ad mathematcal problems, whch the subjects of loa amortsato ad maagemet of cumulatve fuds are
More informationThe analysis of annuities relies on the formula for geometric sums: r k = rn+1 1 r 1. (2.1) k=0
Chapter 2 Autes ad loas A auty s a sequece of paymets wth fxed frequecy. The term auty orgally referred to aual paymets (hece the ame), but t s ow also used for paymets wth ay frequecy. Autes appear may
More informationTime Value of Money. (1) Calculate future value or present value or annuity? (2) Future value = PV * (1+ i) n
Problem 1 Happy Harry has just bought a scratch lottery tcket ad wo 10,000. He wats to face the future study of hs ewly bor daughter ad vests ths moey a fud wth a maturty of 18 years offerg a promsg yearly
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 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 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 informationFINANCIAL FORMULAE. Amount of One or Future Value of One ($1, 1, 1, etc.)... 2. Present Value (or Present Worth) of One ($1, 1, 1, etc.)...
Amout of Oe or Future Value of Oe ($,,, etc.)... 2 Preset Value (or Preset Worth) of Oe ($,,, etc.)... 2 Amout of Oe per Perod... 3 or Future Value of Oe per Perod Preset Value (or Preset Worth) of Oe
More informationANNEX 77 FINANCE MANAGEMENT. (Working material) Chief Actuary Prof. Gaida Pettere BTA INSURANCE COMPANY SE
ANNEX 77 FINANCE MANAGEMENT (Workg materal) Chef Actuary Prof. Gada Pettere BTA INSURANCE COMPANY SE 1 FUNDAMENTALS of INVESTMENT I THEORY OF INTEREST RATES 1.1 ACCUMULATION Iterest may be regarded as
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 informationof the relationship between time and the value of money.
TIME AND THE VALUE OF MONEY Most agrbusess maagers are famlar wth the terms compoudg, dscoutg, auty, ad captalzato. That s, most agrbusess maagers have a tutve uderstadg that each term mples some relatoshp
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 informationBanking (Early Repayment of Housing Loans) Order, 5762 2002 1
akg (Early Repaymet of Housg Loas) Order, 5762 2002 y vrtue of the power vested me uder Secto 3 of the akg Ordace 94 (hereafter, the Ordace ), followg cosultato wth the Commttee, ad wth the approval of
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 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 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 informationAverage Price Ratios
Average Prce Ratos Morgstar Methodology Paper August 3, 2005 2005 Morgstar, Ic. All rghts reserved. The formato ths documet s the property of Morgstar, Ic. Reproducto or trascrpto by ay meas, whole or
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 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 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 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 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 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 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 informationThe Present Value of an Annuity
Module 4.4 Page 492 of 944. Module 4.4: The Preset Value of a Auty Here we wll lear about a very mportat formula: the preset value of a auty. Ths formula s used wheever there s a seres of detcal paymets
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 informationAbraham Zaks. Technion I.I.T. Haifa ISRAEL. and. University of Haifa, Haifa ISRAEL. Abstract
Preset Value of Autes Uder Radom Rates of Iterest By Abraham Zas Techo I.I.T. Hafa ISRAEL ad Uversty of Hafa, Hafa ISRAEL Abstract Some attempts were made to evaluate the future value (FV) of the expected
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 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 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 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 informationNumerical Methods with MS Excel
TMME, vol4, o.1, p.84 Numercal Methods wth MS Excel M. ElGebely & B. Yushau 1 Departmet of Mathematcal Sceces Kg Fahd Uversty of Petroleum & Merals. Dhahra, Saud Araba. Abstract: I ths ote we show how
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 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 informationCommercial Pension Insurance Program Design and Estimated of Tax Incentives Based on Analysis of Enterprise Annuity Tax Incentives
Iteratoal Joural of Busess ad Socal Scece Vol 5, No ; October 204 Commercal Peso Isurace Program Desg ad Estmated of Tax Icetves Based o Aalyss of Eterprse Auty Tax Icetves Huag Xue, Lu Yatg School
More informationT = 1/freq, T = 2/freq, T = i/freq, T = n (number of cash flows = freq n) are :
Bullets bods Let s descrbe frst a fxed rate bod wthout amortzg a more geeral way : Let s ote : C the aual fxed rate t s a percetage N the otoal freq ( 2 4 ) the umber of coupo per year R the redempto of
More informationCHAPTER 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 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 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 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 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 informationSimple Linear Regression
Smple Lear Regresso Regresso equato a equato that descrbes the average relatoshp betwee a respose (depedet) ad a eplaator (depedet) varable. 6 8 Slopetercept equato for a le m b (,6) slope. (,) 6 6 8
More informationANOVA Notes Page 1. Analysis of Variance for a OneWay Classification of Data
ANOVA Notes Page Aalss of Varace for a OeWa Classfcato of Data Cosder a sgle factor or treatmet doe at levels (e, there are,, 3, dfferet varatos o the prescrbed treatmet) Wth a gve treatmet level there
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 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 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 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 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 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 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 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 informationBest of security and convenience
Get More with Additioal Cardholders. Importat iformatio. Add a coapplicat or authorized user to your accout ad you ca take advatage of the followig beefits: RBC Royal Bak Visa Customer Service Cosolidate
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 informationIDENTIFICATION OF THE DYNAMICS OF THE GOOGLE S RANKING ALGORITHM. A. Khaki Sedigh, Mehdi Roudaki
IDENIFICAION OF HE DYNAMICS OF HE GOOGLE S RANKING ALGORIHM A. Khak Sedgh, Mehd Roudak Cotrol Dvso, Departmet of Electrcal Egeerg, K.N.oos Uversty of echology P. O. Box: 163151355, ehra, Ira sedgh@eetd.ktu.ac.r,
More informationLecture 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 informationMeasures of Dispersion, Skew, & Kurtosis (based on Kirk, Ch. 4) {to be used in conjunction with Measures of Dispersion Chart }
Percetles Psych 54, 9/8/05 p. /6 Measures of Dsperso, kew, & Kurtoss (based o Krk, Ch. 4) {to be used cojucto wth Measures of Dsperso Chart } percetle (P % ): a score below whch a specfed percetage of
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 informationReport 52 Fixed Maturity EUR Industrial Bond Funds
Rep52, Computed & Prted: 17/06/2015 11:53 Report 52 Fxed Maturty EUR Idustral Bod Fuds From Dec 2008 to Dec 2014 31/12/2008 31 December 1999 31/12/2014 Bechmark Noe Defto of the frm ad geeral formato:
More informationMDM 4U PRACTICE EXAMINATION
MDM 4U RCTICE EXMINTION Ths s a ractce eam. It does ot cover all the materal ths course ad should ot be the oly revew that you do rearato for your fal eam. Your eam may cota questos that do ot aear o ths
More informationChapter Eight. f : R R
Chapter Eght f : R R 8. Itroducto We shall ow tur our atteto to the very mportat specal case of fuctos that are real, or scalar, valued. These are sometmes called scalar felds. I the very, but mportat,
More informationSole trader financial statements
3 Sole trader fiacial statemets this chapter covers... I this chapter we look at preparig the year ed fiacial statemets of sole traders (that is, oe perso ruig their ow busiess). We preset the fiacial
More informationCurrent Year Income Assessment Form
Curret Year Icome Assessmet Form Academic Year 2015/16 Persoal details Perso 1 Your Customer Referece Number Your Customer Referece Number Name Name Date of birth Address / / Date of birth / / Address
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 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 informationInformation about Bankruptcy
Iformatio about Bakruptcy Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea What is the? The Isolvecy Service of Irelad () is a idepedet
More informationI apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice.
IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form Please complete usig BLOCK CAPITALS ad retur the completed form
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 informationAP Statistics 2006 FreeResponse Questions Form B
AP Statstcs 006 FreeRespose Questos Form B The College Board: Coectg Studets to College Success The College Board s a otforproft membershp assocato whose msso s to coect studets to college success ad
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 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 informationThe Consumer Price Index for All Urban Consumers (Inflation Rate)
The Cosumer Prce Idex for All Urba Cosumers (Iflato Rate) Itroducto: The Cosumer Prce Idex (CPI) s the crtero of the average prce chage of goods ad servces cosumed by Iraa households. Ths crtero, as a
More informationMoney Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version
Moey Math fo Tees Itoductio to Eaig Iteest: 11th ad 12th Gades Vesio This Moey Math fo Tees lesso is pat of a seies ceated by Geeatio Moey, a multimedia fiacial liteacy iitiative of the FINRA Ivesto Educatio
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 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 informationLecture 4. Materials Covered: Chapter 7 Suggested Exercises: 7.1, 7.5, 7.7, 7.10, 7.11, 7.19, 7.20, 7.23, 7.44, 7.45, 7.47.
TT 430, ummer 006 Lecture 4 Materals Covered: Chapter 7 uggested Exercses: 7., 7.5, 7.7, 7.0, 7., 7.9, 7.0, 7.3, 7.44, 7.45, 7.47.. Deftos. () Parameter: A umercal summary about the populato. For example:
More informationECONOMIC CHOICE OF OPTIMUM FEEDER CABLE CONSIDERING RISK ANALYSIS. University of Brasilia (UnB) and The Brazilian Regulatory Agency (ANEEL), Brazil
ECONOMIC CHOICE OF OPTIMUM FEEDER CABE CONSIDERING RISK ANAYSIS I Camargo, F Fgueredo, M De Olvera Uversty of Brasla (UB) ad The Brazla Regulatory Agecy (ANEE), Brazl The choce of the approprate cable
More informationA Guide to the Pricing Conventions of SFE Interest Rate Products
A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios
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 informationAn Effectiveness of Integrated Portfolio in Bancassurance
A Effectveess of Itegrated Portfolo Bacassurace Taea Karya Research Ceter for Facal Egeerg Isttute of Ecoomc Research Kyoto versty Sayouu Kyoto 606850 Japa arya@eryotouacp Itroducto As s well ow the
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 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 informationSTATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y  ˆ " 1
STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ
More informationMEASURES OF CENTRAL TENDENCY
MODULE  6 Statstcs Measures of Cetral Tedecy 25 MEASURES OF CENTRAL TENDENCY I the prevous lesso, we have leart that the data could be summarsed to some extet by presetg t the form of a frequecy table.
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 informationProtection. Insurance. Real Data To Help You Plan. A SPECIAL REPORT ON LongTerm Care A CONSUMER S GUIDE TO LONGTERM CARE INSURANCE PROTECTION
NSUMER S GUIDE T LNGTERM RE INSURNE PRTETIN g r o F ew V e y l l I T L SPEIL REPRT N LogTerm are Isurace Protecto Real Data To Help You Pla What s Your Real Rsk f Needg LogTerm are? How Log Do lams
More informationEnhance Your Financial Legacy Variable Annuity Death Benefits from Pacific Life
Ehace Your Fiacial Legacy Variable Auity Death Beefits from Pacific Life 7/15 2017215B As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three death beefits that
More informationCurve Fitting and Solution of Equation
UNIT V Curve Fttg ad Soluto of Equato 5. CURVE FITTING I ma braches of appled mathematcs ad egeerg sceces we come across epermets ad problems, whch volve two varables. For eample, t s kow that the speed
More informationA) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.
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
More informationn. We know that the sum of squares of p independent standard normal variables has a chi square distribution with p degrees of freedom.
UMEÅ UNIVERSITET Matematskstatstska sttutoe Multvarat dataaalys för tekologer MSTB0 PA TENTAMEN 00409 LÖSNINGSFÖRSLAG TILL TENTAMEN I MATEMATISK STATISTIK Multvarat dataaalys för tekologer B, 5 poäg.
More informationGrow your business with savings and debt management solutions
Grow your busiess with savigs ad debt maagemet solutios A few great reasos to provide bak ad trust products to your cliets You have the expertise to help your cliets get the best rates ad most competitive
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 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 informationDT Filter Application
DT Flter Applcato These otes explore the use of DT flters to remove a terferece ( ths case a sgle toe) from a audo sgal. Image that you are the your home recordg studo ad have just recorded what you feel
More information