EXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR


 Monica Cummings
 2 years ago
 Views:
Transcription
1 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 to accumulate $10,000 after Gven: j 4%, m 12, FV $10,000, Term 3.5 years Then j m 4% % an n m Term Enter the known varables an then compute the present value. 42 n FV 0 Answer: 8, years? Note that we entere the $10,000 as a postve value because t s the cash nflow you wll receve 3.5 years from now. The answer s negatve because t represents the nvestment (cash outflow) that must be mae toay. Roune to the cent, the ntal nvestment requre s $ EXAMPLE 8.4B CALCULATING AN EQUIVALENT VALUE OF TWO PAYMENTS Two payments of $10,000 each must be mae one year an four years from now. If money can earn 9% compoune monthly, what sngle payment two years from now woul be equvalent to the two scheule payments? Gven: j 9% compoune monthly makng m 12 an j m 9% % Other ata an the soluton strategy are shown on the tmelne below. FV 1 represents the future value of the frst scheule payment an 2 represents the present value of the secon payment Years $10,000 $10,000 = 0.75%, n = 24 = 0.75%, n = 12 2 FV 1
2 2 Example Problems Solve Usng the Sharp EL733A Calculator The sngle equvalent payment s FV 1 2. Before we start crunchng numbers, let s exercse your ntuton. Do you thnk the equvalent payment wll be greater or smaller than $20,000? It s clear that FV 1 s greater than $10,000 an that 2 s less than $10,000. When the two amounts are ae, wll the sum be more than or less than $20,000? We can answer ths queston by comparng the tme ntervals through whch we shft each of the $10,000 payments. The frst payment wll have one year s growth ae but the secon payment wll be scounte by two years growth. Therefore, 2 s farther below $10,000 than FV 1 s above $10,000. Hence, the equvalent payment wll be less than $20,000. If your calculate equvalent payment turne out to be more than $20,000, you woul know that your soluton ha an error. Returnng to the calculatons, FV 1 : n 0 FV Answer: 10, : Do not clear the values an settngs currently n memory. Then you nee enter only those values an settngs that change FV 24 n Answer: 8, The equvalent payment two years from now s $10, $ $19, EXAMPLE 8.4C CALCULATING TWO UNKNOWN LOAN PAYMENTS Kramer borrowe $4000 from George at an nterest rate of 7% compoune semannually. The loan s to be repa n three nstalments. The frst payment, $1000, s ue two years after the ate of the loan. The secon an thr payments are ue three an fve years, respectvely, after the ntal loan. Calculate the amounts of the secon an thr payments f the secon payment s to be twce the sze of the thr payment. Gven: j 7% compoune semannually makng m 2 an j m 7% 2 3.5% Let x represent the thr payment. Then the secon payment must be 2x. As ncate n the followng agram, 1, 2, an 3 represent the present values of the frst, secon, an thr payments Years $4000 n = 4, = 3.5% $1000 n = 6, = 3.5% n = 10, = 3.5% 2x x Snce the sum of the present values of all payments equals the orgnal loan, then $ : 1000 FV 4 n Answer: At frst, we may be stumpe as to how to procee for 2 an 3. Let s thnk about the thr payment of x ollars. We can compute the present value of just $1 from the x ollars. 1 FV 10 n Answer: The present value of $1 pa fve years from now s $ (almost $0.71). Conser the followng questons (Q) an ther answers (A). Q: What s the present value of $2? A: It s about 2 $0.71 $1.42. Q: What s the present value of $5? A: It s about 5 $0.71 $3.55. Q: What s the present value of $x? A: Extenng the preceng pattern, the present value of $x s about x $0.71 $0.71x. Precsely, t s 3 $ x. 1
3 Example Problems Solve Usng the Sharp EL733A Calculator 3 Smlarly, calculate the present value of $1 from the secon payment of 2x ollars. The only varable that changes from the prevous calculaton s n. 6 n Answer: Hence, the present value of $2x s 2 2x 1$ $ x Now, substtute the values for 1, 2, an 3 nto equaton 1 an solve for x. $ x x $ x $ x $ Kramer s secon payment wll be 21$ $ an the thr payment wll be $ EXAMPLE 8.5B ARING GICS HAVING DIFFERENT NOMINAL RATES Suppose a bank quotes nomnal annual nterest rates of 6.6% compoune annually, 6.5% compoune semannually, an 6.4% compoune monthly on fveyear compounnterest GICs. Whch rate shoul an nvestor choose? An nvestor shoul choose the rate that results n the hghest maturty value. The gven nformaton may be arrange n a table. j m j m n 6.6% 1 6.6% Choose an amount, say $1000, to nvest. Calculate the maturty values for the three alternatves. FV (1 ) n $1000(1.066) 5 $ for m 1 $1000(1.0325) 10 $ for m 2 $1000( ) 60 $ for m 12 Hereafter, we wll usually present the fnancal calculator keystrokes n a vertcal format. j 6.6% j 6.5% j 6.4% compoune compoune compoune annually semannually monthly / 0 n FV Same, 10 n 3.25 FV Ans: 1, Same, 60 n 0.53 FV Ans: 1, Ans: 1, In the secon an thr columns, we have shown only those values that change from the preceng step. The prevous values for an are automatcally retane f you o not clear the TVM memores. The nvestor shoul choose the GIC earnng 6.5% compoune semannually snce t prouces the hghest maturty value.
4 4 Example Problems Solve Usng the Sharp EL733A Calculator 9S CHAPTER 9 EXAMPLES EXAMPLE 9.1A CALCULATING THE PERIODIC AND NOMINAL RATES OF INTEREST The maturty value of a threeyear, $5000 compounnterest GIC s $ To threefgure accuracy, calculate the nomnal rate of nterest pa on the GIC f nterest s compoune a. annually. b. quarterly. Gven: $5000 an FV $ In Part (a), m 1, n m(term) 1(3) 3 compounng peros. In Part (b), m 4, n m(term) 4(3) 12 compounng peros. Formula (91) enables us to calculate the nterest rate for one compounng pero. a. b. a FV b 1/n 1 a $ $ b 1/ % The nomnal rate of nterest on the GIC s j m 1(5.000%) 5.00% compoune annually. a $ $ b 1/ % The nomnal rate of nterest on the GIC s j m 4(1.227%) 4.91% compoune quarterly. 3 n / FV Ans: Same,, FV 12 n Ans: EXAMPLE 9.2A CALCULATING THE NUMBER OF OUNDING PERIODS What s the term of a compounnterest GIC f $4000 nveste at 5.5% compoune annually earns nterest totallng $ ? Gven: $4000 j Total nterest $ m 5.5% 1 5.5% The maturty value of the GIC s FV Total nterest $4000 $ $
5 Example Problems Solve Usng the Sharp EL733A Calculator 5 Metho 1: Metho 2: Use the basc formula FV (1 ) n to calculate the number of compounng peros requre for $4000 to grow to $ Substtute the known values for, FV, an gvng $ $4000(1.055) n Therefore, n $ $ Now take logarthms of both ses. On the left se, use the rule that ln(a n ) n(ln a) Therefore, n(ln 1.055) ln ln an n ln Snce each compounng pero equals one year, the term of the GIC s fve years. Substtute the known values nto the erve formula (92). The number of compounng peros requre for $4000 to grow to $ s n ln a FV b ln 11 2 ln a $ $ b ln ln ln / FV n Ans: Snce each compounng pero equals one year, the term of the GIC s fve years. EXAMPLE 9.3A CONVERTING A NOMINAL INTEREST RATE TO AN EFFECTIVE INTEREST RATE What s the effectve rate of nterest corresponng to 10.5% compoune monthly? Gven: j 10.5% an m 12 Then j m 10.5% % per month an f (1 ) m % The effectve nterest rate s 11.02% (compoune annually) n / 0 FV Ans: f
6 6 Example Problems Solve Usng the Sharp EL733A Calculator 10S CHAPTER 10 EXAMPLES EXAMPLE 10.2A THE FUTURE VALUE OF REGULAR INVESTMENTS Henz has been contrbutng $300 at the en of each month for the past 15 months to a savngs plan that earns 6% compoune monthly. What amount wll he have one year from now f he contnues wth the plan? The total amount wll be the future value of n contrbutons of $300 each. Payments an compounng both occur at onemonth ntervals. Therefore, the payments form an ornary smple annuty havng 6% % per month. FV c 11 2n 1 $300 c $300 a b $ One year from now, Henz wll have $ n the plan n / FV Ans: 8, EXAMPLE 10.2B CALCULATING THE FUTURE VALUE WHEN THE RATE OF RETURN CHANGES DURING THE TERM OF THE ANNUITY Calculate the future value of an ornary annuty wth payments of $600 every 6 months for 16 years. The rate of return wll be 8% compoune semannually for the frst years an 9% compoune semannually for the subsequent years Because the compounng nterval an the payment nterval are both sx months, we have an ornary smple annuty wth 1 1 j for the frst 5 years, an 9% m 8% 2 4% 2 4.5% for the subsequent 10 years n m(term) 2(5.5) 11 for the frst 52 years, an n 2(10.5) 21 for the subsequent 102 years Snce the rate of return changes urng the term of the annuty, we must conser the frst years separately from the subsequent years. The algebrac soluton has three steps, as ncate n the followng tme agram Years $600 every 6 months n = 11 Step 1 $600 every 6 months FV 1 n = 21 Step 2 n = 21 Step 3 FV 3 FV 2 Sum
7 Example Problems Solve Usng the Sharp EL733A Calculator 7 Step 1: Step 2: Step 3: Calculate the future value, FV 1, of the frst 11 payments. FV 1 c 11 2n 1 $600 c $600 c $ Determne the future value, FV 2, of the Step 1 result 1 after an atonal 102 years. FV 2 (1 ) n $ (1.045) 21 $20, Calculate the future value, FV 3, of the last 21 annuty payments. Then a FV 2 an FV 3. FV 3 $600 c $20, FV 2 FV 3 $40, The future value of the annuty s $40, $600 c n / FV Ans: 8, Same 21 n / FV Ans: 40, EXAMPLE 10.3A THE PRESENT VALUE OF AN ORDINARY SIMPLE ANNUITY Determne the present value of $500 pa at the en of each calenar quarter for 6% compoune quarterly years. Use a scount rate of Gven: $500, Term years, j 6% compoune quarterly Therefore, 6% 4 1.5% an n 4(6.5) n c $500 c $500 a b $10, The present value of the annuty s $10, Assume s are nflows. 26 n FV Ans: 10,699.32
8 8 Example Problems Solve Usng the Sharp EL733A Calculator EXAMPLE 10.4A CALCULATING THE PRESENT VALUE OF A DEFERRED ANNUITY Mr. an Ms. Templeton are settng up a fun to help fnance ther granaughter s college eucaton. They want her to be able to wthraw $3000 every three months for three years after she starts college. Her frst wthrawal wll be years from now. If the fun can earn 7.2% compoune quarterly, what sngle amount contrbute toay wll prove for the wthrawals? The money the Templetons nvest now wll have years to grow before wthrawals start. Thereafter, further earnngs of money stll n the fun wll help support the peroc wthrawals. The onetme up front contrbuton s the present value of the wthrawals. The tme agram s presente below. Vewe from toay, the wthrawals form a eferre annuty. In orer to have an ornary annuty followng the pero of eferral, the pero of eferral must en three months before the frst payment. Ths makes the pero of eferral only years Years Payments = Twelve $3000 payments n = 12 Snce payments an compounng both occur quarterly, we have a eferre smple annuty wth $3000 n an 7.2% 4 1.8% The present value of the payments 5 years from now s n 1 c $3000 a b $32, n FV Ans: 32, The present value of the payments toay s 2 FV(1 ) n $32,119.23(1.018) 21 $22, Same 21 n FV Ans: 22, The Templetons can prove the esre fnancal support for ther granaughter by puttng $22, nto the fun toay.
9 Example Problems Solve Usng the Sharp EL733A Calculator 9 11S CHAPTER 11 EXAMPLES EXAMPLE 11.1A CALCULATING THE PERIODIC INVESTMENT NEEDED TO REACH A SAVINGS TARGET Markham Auto Boy wshes to accumulate a fun of $300,000 urng the next 18 months n orer to open at a secon locaton. At the en of each month, a fxe amount wll be nveste n a money market savngs account wth an nvestment ealer. What shoul the monthly nvestment be n orer to reach the savngs objectve? The plannng assumpton s that the account wll earn 3.6% compoune monthly. The savngs target of $300,000 represents the future value of the fxe monthly nvestments. Snce earnngs are compoune monthly, the enofmonth nvestments form an ornary smple annuty. We are gven Step 1: FV $300,000 n 18 an 3.6% % per month Step 2: Substtute the gven values nto formula (101). Step 3: $300,000 ( ) Step 4: FV c 11 2n 1 $300,000 c $300, $16, n ,000 FV Ans: 16, Markham Auto Boy shoul make monthly nvestments of $16, n orer to accumulate $300,000 after 18 months. EXAMPLE 11.1B CALCULATING THE PERIODIC LOAN PAYMENTS THAT FORM AN ORDINARY GENERAL ANNUITY A $5000 loan requres payments at the en of each quarter for four years. If the nterest rate on the loan s 9% compoune monthly, what s the sze of each payment? The orgnal loan equals the present value of all payments scounte at the loan s nterest rate. Snce nterest s compoune monthly an payments are mae at the en of each quarter, we have an ornary general annuty wth $5000 n an 9% % per month
10 10 Example Problems Solve Usng the Sharp EL733A Calculator Step 1: Then, an 12 compounngs per year c 3 4 payments per year c per quarter Step 2: Substtute the preceng values nto formula (102) n c $5000 c Step 3: $ Step 4: $ $ The sze of each quarterly payment s $ n FV Ans: EXAMPLE 11.2A CALCULATING n GIVEN THE FUTURE VALUE OF AN ORDINARY GENERAL ANNUITY One month from now, Maurce wll make hs frst monthly contrbuton of $250 to an RRSP. Over the long run, he expects to earn 8% compoune annually. How long wll t take for the contrbutons an accrue nterest to reach $100,000? (Roun n to the next larger nteger.) Snce compounng occurs annually but the contrbutons are mae monthly, the payments form a general annuty havng FV $100,000 $250 an 8% 1 8% To obtan the peroc rate matchng the monthly payment nterval, frst calculate Then 1 compounng per year c payments per year c per month Substtute these values nto formula (101n). n ln a 1 FV b ln11 2 ln c $100,0002 $ ln / FV n Ans:
11 Example Problems Solve Usng the Sharp EL733A Calculator 11 The annuty has 199 payments takng 199 months. We nee to express the tme requre n years an months. 199 months years years 16 years months2 16 years, 7 months It wll take 16 years an 7 months for Maurce to accumulate $100,000. EXAMPLE 11.3A FINDING THE RATE OF RETURN ON FUNDS USED TO PURCHASE AN ANNUITY A lfe nsurance company avertses that $50,000 wll purchase a 20year annuty payng $ at the en of each month. What nomnal rate of return an effectve rate of return oes the annuty nvestment earn? The purchase prce of an annuty equals the present value of all payments. Hence, the rate of return on the $50,000 purchase prce s the scount rate that makes the present value of the payments equal to $50,000. The payments form an ornary annuty wth $50,000 $ m 12 an n 12(20) 240 Enter these values n your calculator as ncate n the box at rght. The peroc rate of return we obtan s 0.45% (per month). Then j m 12(0.45%) 5.40% compoune monthly an the corresponng effectve nterest rate s f (1 ) m % / n FV Ans: S CHAPTER 12 EXAMPLES EXAMPLE 12.1A CALCULATING THE FUTURE VALUE OF A SIMPLE ANNUITY DUE To the nearest ollar, how much wll Stan accumulate n hs RRSP by age 60 f he makes semannual contrbutons of $2000 startng on hs twentyseventh brthay? Assume that the RRSP earns 8% compoune semannually an that no contrbuton s mae on hs sxteth brthay. The accumulate amount wll be the future value of the contrbutons on Stan s sxteth brthay. Vewe from the future value s focal ate at hs sxteth brthay, the RRSP contrbutons form an annuty ue. Snce the payment nterval equals the compounng nterval, we have a smple annuty ue wth $2000 8% 2 4% an n payments Substtute the preceng values nto formula (121) FV1ue2 c 11 2n $2000 a b $2000 a b $640,156 Stan wll have $640,156 n hs RRSP at age BGN moe 66 n / FV Ans: 640,156
12 12 Example Problems Solve Usng the Sharp EL733A Calculator EXAMPLE 12.1B CALCULATING THE FUTURE VALUE OF A GENERAL ANNUITY DUE Repeat Example 12.1A wth the change that the RRSP earns 8% compoune annually nstea of semannually. We now have a general annuty snce the compounng nterval (one year) ffers from the payment nterval (sx months). The value we must use for n the FV formula s the peroc rate for the sxmonth payment nterval. 8% (It wll be about 2 4%.) Substtute nto formula (94c) gvng Number of compounngs per year 8% 1 8% an c 1 Number of payments per year Use ths value for n formula (121) gvng 2 (1 ) c 1 (1.08) per sx months FV1ue2 c 11 2n $2000 a b $2000 a b $618,606 Stan wll have $618,606 n hs RRSP at age 60. BGN moe n / FV Ans: 618,606 EXAMPLE 12.3A CALCULATING THE SIZE OF LEASE PAYMENTS A lease that has years to run s recore on a company s books as a lablty of $27,369. If the company s cost of borrowng was 6% compoune monthly when the lease was sgne, what s the amount of the lease payment at the begnnng of each month? The book value of the lease lablty s the present value of the remanng lease payments. The scount rate employe shoul be the nterest rate the company woul have pa to borrow funs. The lease payments consttute a smple annuty ue wth 1ue2 $27, 369 n an 6% % per month Substtute the gven values nto formula (122) an solve for n 1ue2 c 11 2 $27, 369 a b ( )(1.005) ( ) $ The monthly lease payment s $ BGN moe 30 n FV Ans:
13 Example Problems Solve Usng the Sharp EL733A Calculator 13 EXAMPLE 12.3E CALCULATING n GIVEN THE PRESENT VALUE OF A GENERAL ANNUITY DUE An nvestment fun s worth $210,000 an earns 9% compoune semannually. If $2000 s wthrawn at the begnnng of each month startng toay, when wll the fun become eplete? The ntal amount n the account equals the present value of the future wthrawals. Snce the frst wthrawal occurs toay, an the payment nterval ffers from the compounng nterval, the wthrawals form a general annuty ue havng The value we must use for n formula (122n) s the peroc rate for the onemonth payment nterval. Substtute nto 2 (1 ) c 1 (1.045) Substtute the known values nto formula (122n). n $210, 0002 ln c 1 $ ln ue2 $210,000 $2000 an 9% 2 4.5% c Number of compounngs per year Number of payments per year ln c 1 1ue ln per month BGN moe / 0 FV Ans: The fun wll permt 199 monthly wthrawals. The fnal wthrawal, smaller than $2000, wll occur at the begnnng of the 199th payment nterval. But that wll be 198 months from now. So, the fun wll be eplete at the tme of the 199th payment, whch s 198 months or 16 years an 6 months from now. n EXAMPLE 12.3F CALCULATING THE INTEREST RATE FOR AN ANNUITY DUE Therese ntens to contrbute $3000 at the begnnng of each sxmonth pero to an RRSP. What rate of return must her RRSP earn n orer to reach $600,000 after 25 years? The payments form an annuty ue whose future value after 25 years s to be $600,000. That s, FV(ue) $600,000 $3000 an n m(term) 2(25) 50 Enter these values n the calculator memores an compute. Ths gves the peroc nterest rate for one payment nterval (sx months). Then j m 2(4.713%) 9.43% compoune semannually. Therese s RRSP must earn 9.43% compoune semannually. BGN moe 50 0 n / FV Ans: 4.713
14 14 Example Problems Solve Usng the Sharp EL733A Calculator EXAMPLE 12.3G CALCULATING THE INTEREST RATE BUILT INTO AN INSTALMENT PAYMENT OPTION A $100,000 lfe nsurance polcy requres an annual premum of $420 or a monthly premum of $ In ether case, the premum s payable at the begnnng of the pero of coverage. What s the effectve rate of nterest polcyholers pay when they choose the monthly payment plan? In effect, the nsurance company lens the $420 annual premum to polcyholers choosng the monthly payment opton. These polcyholers then repay the loan wth 12 begnnngofmonth payments of $ Hence, $420 s the present value of the 12 payments that form an annuty ue. We have (ue) $420 $37 an n 12 Enter these values n the calculator memory an compute. Ths gves the peroc nterest rate for one payment nterval (one month). Then f (1 ) m 1 ( ) % The effectve nterest rate on the monthly payment plan s 13.04%. 37 BGN moe 12 n / 0 FV Ans:
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 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 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 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 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 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 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 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 information= i δ δ s n and PV = a n = 1 v n = 1 e nδ
Exam 2 s Th March 19 You are allowe 7 sheets of notes an a calculator 41) An mportant fact about smple nterest s that for smple nterest A(t) = K[1+t], the amount of nterest earne each year s constant =
More 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 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 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 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 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 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 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 informationStock Profit Patterns
Stock Proft Patterns Suppose a share of Farsta Shppng stock n January 004 s prce n the market to 56. Assume that a September call opton at exercse prce 50 costs 8. A September put opton at exercse prce
More 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 informationAS 2553a Mathematics of finance
AS 2553a Mathematcs of fnance Formula sheet November 29, 2010 Ths ocument contans some of the most frequently use formulae that are scusse n the course As a general rule, stuents are responsble for all
More informationLevel Annuities with Payments Less Frequent than Each Interest Period
Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Symoblc approach
More 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 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 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 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 informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationMathematics of Finance
Mathematcs of Fnance 5 C H A P T E R CHAPTER OUTLINE 5.1 Smple Interest and Dscount 5.2 Compound Interest 5.3 Annutes, Future Value, and Snkng Funds 5.4 Annutes, Present Value, and Amortzaton CASE STUDY
More 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 informationA Master Time Value of Money Formula. Floyd Vest
A Master Tme Value of Money Formula Floyd Vest For Fnancal Functons on a calculator or computer, Master Tme Value of Money (TVM) Formulas are usually used for the Compound Interest Formula and for Annutes.
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More informationMathematics of Finance
5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty;Amortzaton Chapter 5 Revew Extended Applcaton:Tme, Money, and Polynomals Buyng a car
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationMathematics of Finance
CHAPTER 5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty; Amortzaton Revew Exercses Extended Applcaton: Tme, Money, and Polynomals Buyng
More informationPresent Values and Accumulations
Present Values an Accumulatons ANGUS S. MACDONALD Volume 3, pp. 1331 1336 In Encyclopea Of Actuaral Scence (ISBN 47846763) Ete by Jozef L. Teugels an Bjørn Sunt John Wley & Sons, Lt, Chchester, 24 Present
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationAn Overview of Financial Mathematics
An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationANALYSIS OF FINANCIAL FLOWS
ANALYSIS OF FINANCIAL FLOWS AND INVESTMENTS II 4 Annutes Only rarely wll one encounter an nvestment or loan where the underlyng fnancal arrangement s as smple as the lump sum, sngle cash flow problems
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationInterest Rate Forwards and Swaps
Interest Rate Forwards and Swaps Forward rate agreement (FRA) mxn FRA = agreement that fxes desgnated nterest rate coverng a perod of (nm) months, startng n m months: Example: Depostor wants to fx rate
More informationTexas Instruments 30Xa Calculator
Teas Instruments 30Xa Calculator Keystrokes for the TI30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount in the account, the balance, is
Payout annutes: Start wth P dollars, e.g., P = 100, 000. Over a 30 year perod you receve equal payments of A dollars at the end of each month. The amount of money left n the account, the balance, earns
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount owed is. P (1 + i) A
Amortzed loans: Suppose you borrow P dollars, e.g., P = 100, 000 for a house wth a 30 year mortgage wth an nterest rate of 8.25% (compounded monthly). In ths type of loan you make equal payments of A dollars
More informationChapter 15 Debt and Taxes
hapter 15 Debt and Taxes 151. Pelamed Pharmaceutcals has EBIT of $325 mllon n 2006. In addton, Pelamed has nterest expenses of $125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationInterest Rate Futures
Interest Rate Futures Chapter 6 6.1 Day Count Conventons n the U.S. (Page 129) Treasury Bonds: Corporate Bonds: Money Market Instruments: Actual/Actual (n perod) 30/360 Actual/360 The day count conventon
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationChapter 11 Practice Problems Answers
Chapter 11 Practce Problems Answers 1. Would you be more wllng to lend to a frend f she put all of her lfe savngs nto her busness than you would f she had not done so? Why? Ths problem s ntended to make
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 3575200 Fax: (617) 3575250 www.ersalawyers.com
More informationI = Prt. = P(1+i) n. A = Pe rt
11 Chapte 6 Matheatcs of Fnance We wll look at the atheatcs of fnance. 6.1 Sple and Copound Inteest We wll look at two ways nteest calculated on oney. If pncpal pesent value) aount P nvested at nteest
More informationChapter 15: Debt and Taxes
Chapter 15: Debt and Taxes1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationTrivial lump sum R5.0
Optons form Once you have flled n ths form, please return t wth your orgnal brth certfcate to: Premer PO Box 2067 Croydon CR90 9ND. Fll n ths form usng BLOCK CAPITALS and black nk. Mark all answers wth
More informationUncrystallised funds pension lump sum payment instruction
For customers Uncrystallsed funds penson lump sum payment nstructon Don t complete ths form f your wrapper s derved from a penson credt receved followng a dvorce where your ex spouse or cvl partner had
More informationDEGREES OF EQUIVALENCE IN A KEY COMPARISON 1 Thang H. L., Nguyen D. D. Vietnam Metrology Institute, Address: 8 Hoang Quoc Viet, Hanoi, Vietnam
DEGREES OF EQUIVALECE I A EY COMPARISO Thang H. L., guyen D. D. Vetnam Metrology Insttute, Aress: 8 Hoang Quoc Vet, Hano, Vetnam Abstract: In an nterlaboratory key comparson, a ata analyss proceure for
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationgreatest common divisor
4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no
More informationUnderwriting Risk. Glenn Meyers. Insurance Services Office, Inc.
Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationMultiple discount and forward curves
Multple dscount and forward curves TopQuants presentaton 21 ovember 2012 Ton Broekhuzen, Head Market Rsk and Basel coordnator, IBC Ths presentaton reflects personal vews and not necessarly the vews of
More informationMain TVM functions of a BAII Plus Financial Calculator
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
More informationEffective December 2015
Annuty rates for all states EXCEPT: NY Prevous Index Annuty s effectve Wednesday, December 7 Global Multple Index Cap S&P Annual Pt to Pt Cap MLSB Annual Pt to Pt Spread MLSB 2Yr Pt to Pt Spread 3 (Annualzed)
More informationEffective September 2015
Annuty rates for all states EXCEPT: NY Lock Polces Prevous Prevous Sheet Feld Bulletns Index Annuty s effectve Monday, September 28 Global Multple Index Cap S&P Annual Pt to Pt Cap MLSB Annual Pt to Pt
More informationWeek 4 Lecture: PairedSample Hypothesis Tests (Chapter 9)
Week 4 Lecture: PareSample Hypothess Tests (Chapter 9) The twosample proceures escrbe last week only apply when the two samples are nepenent. However, you may want to perform a hypothess tests to ata
More informationInterest 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 informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More information6. EIGENVALUES AND EIGENVECTORS 3 = 3 2
EIGENVALUES AND EIGENVECTORS The Characterstc Polynomal If A s a square matrx and v s a nonzero vector such that Av v we say that v s an egenvector of A and s the correspondng egenvalue Av v Example :
More informationn + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)
MATH 16T Exam 1 : Part I (InClass) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total
More informationFINANCIAL 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 informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationInstitute 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 informationSUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.
SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976761000
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationDISCLOSURES I. ELECTRONIC FUND TRANSFER DISCLOSURE (REGULATION E)... 2 ELECTRONIC DISCLOSURE AND ELECTRONIC SIGNATURE CONSENT... 7
DISCLOSURES The Dsclosures set forth below may affect the accounts you have selected wth Bank Leum USA. Read these dsclosures carefully as they descrbe your rghts and oblgatons for the accounts and/or
More informationMacro Factors and Volatility of Treasury Bond Returns
Macro Factors and Volatlty of Treasury Bond Returns Jngzh Huang Department of Fnance Smeal Colleage of Busness Pennsylvana State Unversty Unversty Park, PA 16802, U.S.A. Le Lu School of Fnance Shangha
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationTuition Fee Loan application notes
Tuton Fee Loan applcaton notes for new parttme EU students 2012/13 About these notes These notes should be read along wth your Tuton Fee Loan applcaton form. The notes are splt nto three parts: Part 1
More informationMorningstar AfterTax Return Methodology
Mornngstar AfterTax Return Methodology Mornngstar Research Report March 1, 2013 2013 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property of Mornngstar, Inc. Reproducton or
More informationQuasiHyperbolic Discounting and Social Security Systems
QuasHyperbolc Dscountng and Socal Securty Systems Mordecha E. Schwarz a and Eytan Sheshnsk b May 22, 26 Abstract Hyperbolc countng has become a common assumpton for modelng bounded ratonalty wth respect
More informationThe CoxRossRubinstein Option Pricing Model
Fnance 400 A. Penat  G. Pennacc Te CoxRossRubnsten Opton Prcng Model Te prevous notes sowed tat te absence o arbtrage restrcts te prce o an opton n terms o ts underlyng asset. However, te noarbtrage
More information1.1 The University may award Higher Doctorate degrees as specified from timetotime in UPR AS11 1.
HIGHER DOCTORATE DEGREES SUMMARY OF PRINCIPAL CHANGES General changes None Secton 3.2 Refer to text (Amendments to verson 03.0, UPR AS02 are shown n talcs.) 1 INTRODUCTION 1.1 The Unversty may award Hgher
More informationProfessor Iordanis Karagiannidis. 2010 Iordanis Karagiannidis
Fnancal Modelng Notes Basc Excel Fnancal Functons Professor Iordans Karagannds Excel Functons Excel Functons are preformatted formulas that allow you to perform arthmetc and other operatons very quckly
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationA Critical Note on MCEV Calculations Used in the Life Insurance Industry
A Crtcal Note on MCEV Calculatons Used n the Lfe Insurance Industry Faban Suarez 1 and Steven Vanduffel 2 Abstract. Snce the begnnng of the development of the socalled embedded value methodology, actuares
More informationThe Time Value of Money C H A P T E R N I N E
The Time Value of Money C H A P T E R N I N E Figure 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure
More informationHedging InterestRate Risk with Duration
FIXEDINCOME SECURITIES Chapter 5 Hedgng InterestRate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cashflows Interest rate rsk Hedgng prncples DuratonBased Hedgng Technques Defnton of duraton
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationOn some special nonlevel annuities and yield rates for annuities
On some specal nonlevel annutes and yeld rates for annutes 1 Annutes wth payments n geometrc progresson 2 Annutes wth payments n Arthmetc Progresson 1 Annutes wth payments n geometrc progresson 2 Annutes
More informationEE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN
EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson  3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson  6 Hrs.) Voltage
More informationEfficient Algorithms for Computing the Triplet and Quartet Distance Between Trees of Arbitrary Degree
Effcent Algorthms for omputng the Trplet an Quartet Dstance Between Trees of Arbtrary Degree Gerth Støltng Broal, Rolf Fagerberg Thomas Malun hrstan N. S. Peersen, Anreas San, Abstract The trplet an quartet
More informationPerformance attribution for multilayered investment decisions
Performance attrbuton for multlayered nvestment decsons 880 Thrd Avenue 7th Floor Ne Yor, NY 10022 212.866.9200 t 212.866.9201 f qsnvestors.com Inna Oounova Head of Strategc Asset Allocaton Portfolo Management
More informationADVA 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 informationISLM Model 1 C' dy = di
 odel Solow Assumptons  demand rrelevant n long run; assumes economy s operatng at potental GDP; concerned wth growth  Assumptons  supply s rrelevant n short run; assumes economy s operatng below potental
More information