CONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "CONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest"

Transcription

1 CONCEPT OF TIME AND VALUE OFMONEY Simple and Compound inteest What is the futue value of shs 10,000 invested today to ean an inteest of 12% pe annum inteest payable fo 10 yeas and is compounded; a. Annually (3 maks) b. Semi-quately (2 maks) c. Quately (3 maks) d. Monthly (2 maks) Solving (i) Annually FV = PV (1 +) = 10,000 x (1.12)¹⁰ = 310,584.8 (ii) Semi-annually FV = PV X (1 +)¹⁰(²) 2 = 10,000 (1+0.12)²⁰ = 320, (iii) Quately = FV= PV (1 +)ⁿm 4 = 100,000 ( )¹⁰(⁴) = 326,

2 (iv) Monthly FV = PV (1 +)ⁿm 12 Effective Annual Rate = (10,000 (1+0.12)¹² 12 = 330,038.6 QUESTION 2 (c) This is the inteest ate expessed as if it wee compounded once pe yea. The actual ate of inteest eaned (paid) afte adjusting the nominal ate fo factos such as the numbe of compounding peiods pe yea. The effective annual inteest ate is the inteest ate compounded annually but povides the same annual inteest as the nominal ate does when compounded m times pe yea. Example 1 Fo example, suppose you ae offeed 12 pecent compounded monthly. In this case, the inteest is compounded 12 times a yea; so m is 12. You can calculate the effective ate as: Solving EAR = [1 + (Quoted ate)/m]м - 1 = [1 +.12/12]¹² - 1 = 1.01¹² - 1 = = % Example 2 A bank is offeing 12 pecent compounded quately. If you put $ 100 in an account, how much will you have at the end of one yea? What s the EAR? How much will you have at the end of two yeas? Solving The bank is effectively offeing 12%/4 = 3% evey quate. If you invest $ 100 fo fou peiods at 3 pecent pe peiod, the futue value is: Futue value = $ 100 x (1.03)⁴ = $ 100 x = $ The EAR is pecent [$ 100 x ( ) = $ ].

3 We can detemine what you would have at the end of two yeas in two diffeent ways. One way is to ecognize that two yeas is the same as eight quates. At 3 pecent pe quate, afte eight quates, you would have: $ 100 x (1.03)⁸ = $ 100 x = $ Altenatively, we could detemine the value afte two yeas by using an EAR of pecent; so afte two yeas you would have: $ 100 x (1.1255)² = $ 100 x = $ Thus, the two calculations poduce the same answe. This illustates an impotant point. Anytime we do a pesent o futue value calculation, the ate we must be an actual o effective ate. In this case, the actual ate is 3 pecent pe quate. The effective annual ate is pecent. It doesn t matte which one we use once we know the EAR. Annuity An annuity is a seies of consecutive payment o eceipts of equal amount ove a defined peiod of time. Usually, the eceipts o payment ae assumed to occu at the end of the yea. Can also be defined as a seies of equal amount payment fo a specified numbe of yeas It is a level steam of cash flow fo a fixed peiod of time. Fo example, a loan epayment plan calls fo the boowe to epay the loan by making a seies of equal payment fo some length of time. A seies of constant o level cash flows that occus at the end of each peiod is called an odinay annuity. Compound Annuities: (ANNUITY FUTURE VALUE) It involves depositing o investing an equal sum of money at the end of each yea fo a cetain numbe of yeas and allowing it to gow Example 1 Assume you want to deposit $500 fo college education at the end of each yea fo the next 5 yeas in a bank. The money will ean 6 pecent inteest. How much money will be thee at the end of 5 th yea. FV5=PMT [1+] ⁿ-1 (ANNUITY FUTURE VALUE) FV5=$500 X(FVIFA) =500x5.637 $2818.5

4 Example 2 How much must we deposit in an 8 pecent saving accounts at the end of each yea to accumulates $5000 at the end of 10 yeas. FV=PMT [1+]ⁿ =PMTX PMT= $ Example 3 An investo deposits sh at the end of each yea fo fou yeas in an account eaning inteest at the ate of 10% pe annum. What is the value at the end of the fouth yea? Futue value of an annuity is given by: FV = [(1+)ⁿ - 1] A= Peiodic annuity amount (1+ )ⁿ = Futue value inteest facto of annuity (FV) = Discount ate/inteest ate Annual annuity Amt (A) = sh Numbe of yeas (n) = 4 yeas Theefoe FV = 1000 (1.1⁴ 1) FV= 1000 X = 4641 Example What would an investo have to deposit at the end of each yea at an inteest ate of 6% if he wishes to accumulate sh. 10,000 in 5 yeas?

5 Annual Annuity Amount A =? Numbe of yeas = 5 Inteest = 6% 10,000 = A [(1.06)⁵ -1] 0.06 A = 1,774 If an annuity is made at the beginning athe than the end of the peiod, it is efeed to as annuity due. The futue value of an annuity due is elated to a futue value of a nomal annuity by the expession: FV annuity due = FV nomal annuity * (+ ) Example5 Suppose you plan to contibute $ 2,000 evey yea into a etiement account paying 8 pecent. If you etie in 30 yeas, how much will you have? Solution Futue value = Annuity pesent value x (1.08)³⁰ = $ FV=PMT [1+]ⁿ-1 x(1.08)ⁿ Annuity pesent value = $ 2000 x = $ 22, The futue value of this amount in 30 yeas is: 22, x1.08^30 $226,566.4

6 Pesent value fo annuity cash flow Pension payment, insuance obligation and the inteest owed on bond all involve annuities. To compae these thee types of investments, we need to know the pesent value of each The pesent value of an annuity is given by the expession: PV = A [1- (1/ (1 + ) ⁿ] Example 1 Suppose you ae eceiving $500 at the end of each yea fo the next 5 yeas. The discount ate is 6 pecent. What is the woth of this investment today? PV = A [1- (1/ (1 + ) ⁿ] =500x4.212 $2106 Example 2 What is the pesent value of sh. 10,000 to be eceived at the end of each yea fo 5 yeas at a ate of inteest of 10%? = 10,000 (1-1.1⁵) Annuity Pesent value facto = PMT [ 1 - ( 1/(1 + )t ] 0.1 = 10,000 x = 37,908 Example 3 Afte caefully going ove you budget, you have detemined you can affod to pay $ 632 pe month towads a new spots ca. You call up you local bank and find out that the ate is 1 pecent pe month fo 48 months. How much can you boow? Annuity pesent value = PMT x [pesent value facto)] Annuity Pesent value facto = PMT [ 1 - ( 1/(1 + )t ]

7 Theefoe pesent value = $ 632 x = $ 24,000 Theefoe, $ is what you can affod to boow and pay. Amotization of loan An impotant use pesent value concept is in detemining the payment equied fo an installment-type loan. The distinguishing featue of this loan is that it is epaid in equal peiod payment that includes both inteest and pincipal. This payment can be made monthly, quatetely, semi annually o annually. Installment payments ae pevalent in motgages loans, auto loans, consume loans and cetain business loans. Finding the payment/ amotizing a loan Example one Suppose you wished to stat up a new business that specializes in the latest of health food tends, fozen Yak milk. To poduce and maket you poduct, the Yankee Dandy, you need to boow $ 100,000. Because it stikes you as unlikely that this paticula food will be long lived, you popose to pay off the loan quickly by making five equal annual payments. If the inteest ate is 18%, what will be the payment? Annuity pesent value = $ 100,000 = PMTx [1 - pesent value facto] 100,000 = PMT X (1-1/(1.18)⁵ 0.18 PMTX (3.1272) PMT= $ 100,000 = $ 31, Theefoe, you will make a payment of $ 32,000 each. Example two You boow $10,000 at 14 pecent compound annual inteest fo fou yeas. The loan is epayable in fou equal annual installments payable at the end of each yea. a. What is the annual payment that will completely amotize the loan ove fou yeas? (You may wish to ound to the neaest dolla.) b. Of each equal payment, what is the amount of inteest? The amount of loan pincipal? Solving

8 Annuity Pesent value facto = PMT [ 1 - ( 1/(1 + )t ] USE TABLE FOR ANNUITY a. PV₀ = $10,000 = R(PVIFA₁₄%,₄) = R(2.914) Theefoe R = $10, = $3,432 (to the neaest dolla). (1) (2) (3) (4) (END OF INSTALLMENT ANNUAL PRINCIPAL PRINCIPAL AMOUNT YEAR END PAYMENT INTEREST PAYMENT OWING AT YEAR END (4)t ₁ Χ 0.14 (1) (2) (4) t ₁ - 3) $10,000 1 $3,432 $1,400 $2,032 7, ,432 1,116 2,316 5, , ,641 3, , ,011 0 $13,728 $3,728 $10,000 Example 2 You boow $10,000 at 14 pecent compound annual inteest fo fou yeas. The loan is epayable in fou equal annual installments payable at the end of each yea. a. What is the annual payment that will completely amotize the loan ove fou yeas? (You may wish to ound to the neaest dolla.) b. Of each equal payment, what is the amount of inteest? The amount of loan pincipal? PV₀ = $10,000 = R(PVIFA₁₄%,₄) = R(2.914) Theefoe R = $10, = $3,432 (to the neaest dolla). (1) (2) (3) (4) (END OF INSTALLMENT ANNUAL PRINCIPAL PRINCIPAL AMOUNT YEAR END PAYMENT INTEREST PAYMENT OWING AT YEAR END (4)t ₁ Χ 0.14 (1) (2) (4) t ₁ - 3) $10,000 1 $3,432 $1,400 $2,032 7, ,432 1,116 2,316 5, , ,641 3, , ,011 0 $13,728 $3,728 $10,000

9 Example 3 You an a little shot on you sping beak vacation, so you can put $ 1000 on you cedit cad. You can only affod to make the minimum payment of $ 20 pe month. The inteest ate on the cedit cad is 1.5 pecent pe month. How long will you need to pay off the $ 1000? $ 1000 = $ 20 x 1 pesent value facto ($ 1000) x = 1- pesent value facto 20 Pesent value facto = 0.25 = 1/ (1+) t (1.015) t = 1/0.25 = 4 This boils down to asking this question How long does it take fo you money to quaduple at 1.5 pecent pe month? (1.015)⁹³ = 3.99 = 4 It will take you about 93/12 = 7.75 yeas at this ate. SUMMARY OF TIME VALUE OF MONEY EQUITION Calculation Futue value of single payment Equation FV=PV (1+) ⁿ Pesent value PV=FV(1 (1+)ⁿ Futue value fo an annuity FV of an annuity=pmt (1+) ⁿ Pesent value of annuity PV of an annuity=pmt (1-(1+)-ⁿ R Futue value of an annuity due FV (annuity due) =futue value of an annuity x (1+) Pesent value of an annuity due PV(annuity due)=pesent value of an annuity x (1+) Thee ae some chaacteistics that should help you to identify and solve the vaious types of annuity poblems:

10 1. Pesent value of an odinay annuity cash flows occu at the end of each peiod, and pesent value is calculated as of one peiod befoe the fist cash flow. 2. Pesent value of an annuity due cash flows occu at the beginning of each peiod, and pesent value is calculated as of the fist cash flow. 3. Futue value of an odinay annuity cash flows occu at the end of each peiod, and futue value is calculated as of the last cash flow. 4. Futue value of an annuity due cash flows occu at the beginning of each peiod, and futue value is calculated as of one peiod afte the last cash flow. Pactice questions 1. You company poposes to buy an asset fo $335.This investment is vey safe and will be sold in thee yeas time fo $400.You knows that you could invest the $335 elsewhee at 10% with vey little isk. What do you think of the poposed investment? $335 x(1+)^t= 2. You ae consideing a one yea investment. If you put up $1250,you will get back $1350.What is the ate this investment is paying $1250=$1350/(1+)^t 3. You estimate that you will need about $80000 to send you child to college in 8 yeas.you have about $35000 now. If you can ean 20 pecent pe yea, will you make it? At what ate will you just each you goal? - FV=$35000 x(1.2)^8 - FV=$35000 x(1+)^8=$ (1+)=$80000/35000= use table 4. You ae offeed an investment that will pay you $200 in one yea, $400 the next yea,$600 the next yea, and $800 at the end of last yea. You can ean 12 pecent on vey simila investment. What is the most will you be willing to pay? $200 x1/1.12^1= $400 x1/1.12^2= $600 x1/1.12^3= $800 x1/1.12^4= $ An insuance company offes to pay you $1000 pe yea fo 10 yeas if you pay $6710 up font. What ates is implicit in this 10 yeas annuity. $6710=$1000 x(1-pesent annuity value facto)/

11 6. Suppose you plan to contibute $2000 evey yea into etiement account paying 8 pecent. If you etie in 30 yeas, how much will you have? Annuity pesent value=$2000 x(1-1/1.08^30)/ Assume you want to deposit $500 fo college education at the end of each yea fo the next 5 yeas in a bank. The money will ean 6 pecent inteest. How much money will be thee at the end of 5 th yea? 8. How much must we deposit in an 8 pecent saving accounts at the end of each yea to accumulate $5000 at the end of 10 yeas. 9. An investo deposits sh at the end of each yea fo fou yeas in an account eaning inteest at the ate of 10% pe annum. What is the value at the end of the fouth yea? 10. You boow $10,000 at 14 pecent compound annual inteest fo fou yeas. The loan is epayable in fou equal annual installments payable at the end of each yea. c. What is the annual payment that will completely amotize the loan ove fou yeas? (You may wish to ound to the neaest dolla.) d. Of each equal payment, what is the amount of inteest? The amount of loan pincipal?

FI3300 Corporate Finance

FI3300 Corporate Finance Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multi-peiod multi-cf time-value-of-money poblems: Geneal case Pepetuity

More information

AMB111F Financial Maths Notes

AMB111F Financial Maths Notes AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed

More information

Basic Financial Mathematics

Basic Financial Mathematics Financial Engineeing and Computations Basic Financial Mathematics Dai, Tian-Shy Outline Time Value of Money Annuities Amotization Yields Bonds Time Value of Money PV + n = FV (1 + FV: futue value = PV

More information

The Time Value of Money

The Time Value of Money he ime Value of Money Inteest Rates and Futue Value Inteest ates ae a facto in the valuation of vitually all financial instuments. While all money maket ates () ae quoted on an annual basis (PR nnual Pecentage

More information

YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE

YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE Septembe 1999 Quoted Rate Teasuy Bills [Called Banke's Discount Rate] d = [ P 1 - P 1 P 0 ] * 360 [ N ] d = Bankes discount yield P 1 = face

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

More information

Continuous Compounding and Annualization

Continuous Compounding and Annualization Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

More information

9.5 Amortization. Objectives

9.5 Amortization. Objectives 9.5 Aotization Objectives 1. Calculate the payent to pay off an aotized loan. 2. Constuct an aotization schedule. 3. Find the pesent value of an annuity. 4. Calculate the unpaid balance on a loan. Congatulations!

More information

Valuation of Floating Rate Bonds 1

Valuation of Floating Rate Bonds 1 Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned

More information

Finance Practice Problems

Finance 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 information

Ignorance is not bliss when it comes to knowing credit score

Ignorance is not bliss when it comes to knowing credit score NET GAIN Scoing points fo you financial futue AS SEEN IN USA TODAY SEPTEMBER 28, 2004 Ignoance is not bliss when it comes to knowing cedit scoe By Sanda Block USA TODAY Fom Alabama comes eassuing news

More information

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero. Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the

More information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request. Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to

More information

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in

More information

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR John R. Gaham Adapted fom S. Viswanathan FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1 In this lectue we conside the effect of govenment

More information

9.4 Annuities. Objectives. 1. Calculate the future value of an ordinary annuity. 2. Perform calculations regarding sinking funds.

9.4 Annuities. Objectives. 1. Calculate the future value of an ordinary annuity. 2. Perform calculations regarding sinking funds. 9.4 Annuities Objectives 1. Calculate the futue value of an odinay annuity. 2. Pefo calculations egading sinking funds. Soewhee ove the ainbow... skies ae blue,... and the deas that you dae to dea...eally

More information

Introduction to Stock Valuation. Background

Introduction to Stock Valuation. Background Intoduction to Stock Valuation (Text efeence: Chapte 5 (Sections 5.4-5.9)) Topics backgound dividend discount models paamete estimation gowth oppotunities pice-eanings atios some final points AFM 271 -

More information

Questions for Review. By buying bonds This period you save s, next period you get s(1+r)

Questions for Review. By buying bonds This period you save s, next period you get s(1+r) MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk - Risk to shaeholdes esulting fom the use of debt. Financial Leveage - Incease in the vaiability of shaeholde etuns that

More information

GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS

GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 2010-2011 Chapte 1 The Copoation 1-13. What is the diffeence

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions

Understanding 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 isk-etu tadeoff ad time value of

More information

Compound Interest Doubling Time Rule: Extensions and Examples from Antiquities

Compound Interest Doubling Time Rule: Extensions and Examples from Antiquities Communications in Mathematical Finance, vol. 5, no. 2, 2016, 1-11 ISSN: 2241-1968 (pint), 2241 195X (online) Scienpess Ltd, 2016 Compound Inteest Doubling Time Rule: Extensions and Examples fom Antiquities

More information

Personal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit (-) Total Private Saving Rate (S Private /Y) 12/18/2009

Personal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit (-) Total Private Saving Rate (S Private /Y) 12/18/2009 1 Pesonal Saving Rate (S Households /Y) 2 SAVING AND INVESTMENT 16.0 14.0 12.0 10.0 80 8.0 6.0 4.0 2.0 0.0-2.0-4.0 1959 1961 1967 1969 1975 1977 1983 1985 1991 1993 1999 2001 2007 2009 Pivate Saving Rate

More information

Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition

Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future

More information

Discounted Cash Flow Valuation

Discounted Cash Flow Valuation BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?

More information

Exam #1 Review Answers

Exam #1 Review Answers xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%

More information

DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one

More information

Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1

Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1 Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation

More information

Money Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version

Money 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 information

Appendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C- 1

Appendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C- 1 C Time Value of Money C- 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C- 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.

More information

Definitions and terminology

Definitions and terminology I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve

More information

Chapter 4: Time Value of Money

Chapter 4: Time Value of Money FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)

More information

Problem Set: Annuities and Perpetuities (Solutions Below)

Problem Set: Annuities and Perpetuities (Solutions Below) Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

Week 4. Chonga Zangpo, DFB

Week 4. Chonga Zangpo, DFB Week 4 Time Value of Money Chonga Zangpo, DFB What is time value of money? It is based on the belief that people have a positive time preference for consumption. It reflects the notion that people prefer

More information

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates 9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated

More information

Present Value and Annuities. Chapter 3 Cont d

Present Value and Annuities. Chapter 3 Cont d Present Value and Annuities Chapter 3 Cont d Present Value Helps us answer the question: What s the value in today s dollars of a sum of money to be received in the future? It lets us strip away the effects

More information

1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?

1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? Chapter 2 - Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in

More information

Learning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)

Learning 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 2-1 2-2 Leaig

More information

Discounted Cash Flow Valuation

Discounted Cash Flow Valuation 6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

More information

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

More information

The Time Value of Money

The Time Value of Money The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future

More information

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26 Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.

More information

I = Prt. = P(1+i) n. A = Pe rt

I = 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 information

Chapter 11: Aggregate Demand II, Applying the IS-LM Model Th LM t

Chapter 11: Aggregate Demand II, Applying the IS-LM Model Th LM t Equilibium in the - model The cuve epesents equilibium in the goods maket. Chapte :, Applying the - Model Th t C ( T) I( ) G The cuve epesents money maket equilibium. M L(, ) The intesection detemines

More information

PowerPoint. to accompany. Chapter 5. Interest Rates

PowerPoint. to accompany. Chapter 5. Interest Rates PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When

More information

Converting knowledge Into Practice

Converting knowledge Into Practice Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading

More information

Chapter 4. The Time Value of Money

Chapter 4. The Time Value of Money Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return

More information

TIME VALUE OF MONEY (TVM)

TIME VALUE OF MONEY (TVM) TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate

More information

TVM Applications Chapter

TVM Applications Chapter Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (long-term receivables) 7 Long-term assets 10

More information

Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows 1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter

More information

Farming: It s a Fact! Career & Technical Education, Introduction

Farming: It s a Fact! Career & Technical Education, Introduction Faming: It s a Fact! Caee & Technical Education, Intoduction Whee Does You Food Dolla Go? Mateials Compute Lab o Compute & Pojecto fo Pesentation Compute Speakes o Headphones Compute Intenet Access o Agicultual

More information

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved. 2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical defined-contribution

More information

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011 The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility

More information

Agenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar

Agenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar Agenda Exchange Rates, Business Cycles, and Macoeconomic Policy in the Open Economy, Pat 2 How Exchange Rates ae Detemined (again) The IS-LM Model fo an Open Economy Macoeconomic Policy in an Open Economy

More information

Solutions to Problems: Chapter 7

Solutions to Problems: Chapter 7 Solution to Poblem: Chapte 7 P7-1. P7-2. P7-3. P7-4. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b.

More information

Real Estate Equity Derivatives

Real Estate Equity Derivatives Real Estate Equity Deivatives Geltne Mille 2 nd Edition Chapte 26 Section 26.3 Real Estate Deivatives (Index Retun Swaps) Real Estate Equity Deivatives A deivative is an asset whose value depends completely

More information

Firstmark Credit Union Commercial Loan Department

Firstmark Credit Union Commercial Loan Department Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and

More information

Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.

Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years. 6-1 Chapter 6 Time Value of Money Concepts 6-2 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in

More information

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value. Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values

More information

FIN 3000. Chapter 6. Annuities. Liuren Wu

FIN 3000. Chapter 6. Annuities. Liuren Wu FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate

More information

Annuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments

Annuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments 8 8A Futue value of a auity 8B Peset value of a auity 8C Futue ad peset value tables 8D Loa epaymets Auities ad loa epaymets Syllabus efeece Fiacial mathematics 5 Auities ad loa epaymets Supeauatio (othewise

More information

Financial Planning and Risk-return profiles

Financial Planning and Risk-return profiles Financial Planning and Risk-etun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 2010-16 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risk-etun

More information

SUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014

SUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014 SUGGESTED SOLUTIONS 21404 Stategic Financial Management CA Pofessional (Stategic Level II) Examination June 2014 THE INSTITUTE OF CHARTERED ACCOUNTANTS OF SRI LANKA All Rights Reseved Answe No. 01 (a)

More information

first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest.

first complete prior knowlegde -- to refresh knowledge of Simple and Compound Interest. ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability

More information

The Capital Asset Pricing Model. Chapter 9

The Capital Asset Pricing Model. Chapter 9 The Capital Asset Picing odel Chapte 9 Capital Asset Picing odel CAP centepiece of moden finance gives the elationship that should be obseved between isk and etun of an asset it allows fo the evaluation

More information

Faithful Comptroller s Handbook

Faithful Comptroller s Handbook Faithful Comptolle s Handbook Faithful Comptolle s Handbook Selection of Faithful Comptolle The Laws govening the Fouth Degee povide that the faithful comptolle be elected, along with the othe offices

More information

Discounted Cash Flow Valuation

Discounted Cash Flow Valuation Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

More information

CHAPTER 10 Aggregate Demand I

CHAPTER 10 Aggregate Demand I CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income

More information

TIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!

TIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest! TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest $1,000 it becomes $1,050 $1,000 return of $50 return on Factors to consider when assessing Return on

More information

F V P V = F V = P (1 + r) n. n 1. FV n = C (1 + r) i. i=0. = C 1 r. (1 + r) n 1 ]

F V P V = F V = P (1 + r) n. n 1. FV n = C (1 + r) i. i=0. = C 1 r. (1 + r) n 1 ] 1 Week 2 1.1 Recap Week 1 P V = F V (1 + r) n F V = P (1 + r) n 1.2 FV of Annuity: oncept 1.2.1 Multiple Payments: Annuities Multiple payments over time. A special case of multiple payments: annuities

More information

1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000

1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000 D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of

More information

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi e-mail: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,

More information

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109 Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,

More information

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok

More information

METHODOLOGICAL APPROACH TO STRATEGIC PERFORMANCE OPTIMIZATION

METHODOLOGICAL APPROACH TO STRATEGIC PERFORMANCE OPTIMIZATION ETHODOOGICA APPOACH TO STATEGIC PEFOANCE OPTIIZATION ao Hell * Stjepan Vidačić ** Željo Gaača *** eceived: 4. 07. 2009 Peliminay communication Accepted: 5. 0. 2009 UDC 65.02.4 This pape pesents a matix

More information

Chapter 4. The Time Value of Money

Chapter 4. The Time Value of Money Chapter 4 The Time Value of Money 4-2 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest

More information

Chapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.

Chapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved. Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

More information

Chapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)

Chapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.) Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

More information

How to calculate present values

How to calculate present values How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance

More information

Future Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.

Future Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr. Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated

More information

Practice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.

Practice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4. PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor

More information

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com

More information

Solutions to Time value of money practice problems

Solutions to Time value of money practice problems Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,

More information

Products of the Second Pillar Pension

Products of the Second Pillar Pension Óbuda Univesity e-bulletin Vol. 4, No. 1, 2014 Poducts of the Second Pilla Pension Jana Špiková Depatent of Quantitative Methods and Infoation Systes, Faculty of Econoics, Matej Bel Univesity Tajovského

More information

International Monetary Economics Note 1

International Monetary Economics Note 1 36-632 Intenational Monetay Economics Note Let me biefly ecap on the dynamics of cuent accounts in small open economies. Conside the poblem of a epesentative consume in a county that is pefectly integated

More information

Business 2019. Fundamentals of Finance, Chapter 6 Solution to Selected Problems

Business 2019. Fundamentals of Finance, Chapter 6 Solution to Selected Problems Business 209 Fundamentals of Finance, Chapter 6 Solution to Selected Problems 8. Calculating Annuity Values You want to have $50,000 in your savings account five years from now, and you re prepared to

More information

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued 6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

More information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics

More information

Define What Type of Trader Are you?

Define What Type of Trader Are you? Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this

More information

Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key

Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key Instuctions Economics 1 Micoeconomic Theoy I Final Exam June 008 Faculty of Ats and Sciences ueen s Univesity Anse Key The exam is thee hous in length. The exam consists of to sections: Section A has five

More information

CHAPTER 2. Time Value of Money 2-1

CHAPTER 2. Time Value of Money 2-1 CHAPTER 2 Time Value of Money 2-1 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 2-2 Time lines 0 1 2 3

More information

International Financial Strategies Time Value of Money

International Financial Strategies Time Value of Money International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value

More information

Ordinary Annuities Chapter 10

Ordinary Annuities Chapter 10 Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate

More information

FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1

FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1 FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems - Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 3-1 a) Future Value = FV(n,i,PV,PMT)

More information

Module Availability at Regent s School of Drama, Film and Media Autumn 2016 and Spring 2017 *subject to change*

Module Availability at Regent s School of Drama, Film and Media Autumn 2016 and Spring 2017 *subject to change* Availability at Regent s School of Dama, Film and Media Autumn 2016 and Sping 2017 *subject to change* 1. Choose you modules caefully You must discuss the module options available with you academic adviso/

More information