Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Carmen Venter CFP WORKSHOPS FINANCIAL CALCULATIONS presented by Geoff Brittain Q Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) Calculate the capital available at retirement (2) Calculate the shortfall at retirement. (2) Calculate the increasing monthly investment that Makhensa should make/save at the beginning of each month, in his retirement annuity fund to make up for the shortfall. He wants to increase the premium at 6% p.a. 1 3 Mr Makhensa, born 20 January Wants to receive a monthly income of at least R35,000 (after tax 40%) in today s value, when he retires at the age of 60. The monthly income should last for 25 years from the date of retirement and escalate by the rate of inflation per annum. (Given as 6% currently) His Current retirement savings only consist of a pension preservation fund at R350,000 current value. Growth on all investments 10% 714 Sept 2012 Q5.3 Addition Subtraction Multiplication Division Arithmetic

2 Fractions Fractions to Percentages A number that is anything from 0 to 1 Therefore a fraction is less than 1, but greater than 0 ¼ 1 divide by 4 (Long Division) Converting a fraction to a percentage requires multiplying by 100/1 Therefore: ¼ x 100/1 ¼ x 100/1 = 100/4 = 25% 5 7 2/10 6/10 55/100 73/80 60/ /200 Fractions as Decimal points Fractions to Percentages 32/50 75/100 12/71 25/ /200 Examples:

3 Simple Interest Simple Interest Bob invests R2,000 at 10%p.a. simple interest for 4 years Year Start 2000 Interest Year End Bob invests R2,000 at 10%p.a. simple interest for 4 years Year Start Interest Year End 9 Therefore: 2000 X 10% = x 4 yrs = = Simple Interest For how many years does one have to invest a lump sum of R at 15% pa simple interest in order to receive R at the end of the term? Bob invests R2,000 at 10%p.a. simple interest for 4 years Year Start Interest Year End Practice

4 Compound Interest - Monthly Bob Invests R2,000 at 10% p.a. compounding Monthly for 1 Year. Suggested Solution Compound Interest Bob Invests R2,000 at 10% p.a. compounding annually for 4 Years 2000 x (1+0.1) = 2200 x 1.1 = 2420 x 1.1 = 2662 x 1.1 = Year Start Int End Compounding Periods Per Year Annually 1 NACA Semi Annually 2 NACSA Quarterly 4 NACQ Monthly 12 NACM Daily 365 NACD

5 Compound Interest Mathematical Formula Future Value = Present Value x (1 + (Int rate / Comp Periods per year)) Total Compounding periods PV x (1 + (I/PY / P/YR) N = FV Power of A Bank advises you can earn 15% pa on a one year fixed deposit interest accumulates once a year: Capital Invested R 100 Plus interest R 15 Nominal and effective the same as there is no interest on interest. Effective /Nominal Rates Calculator N = TOTAL number of compounding periods in the calculation. I/YR = Nominal per annum interest / growth rate applicable PV = Present Value PMT = Any Regular payment (same as periods per year) 2 nd F P/YR= Number of compounding periods in 1 Year. FV = Future Value PV x (1 + (I/PY / P/YR) N = FV A Bank advises you can earn 15% pa on a one year fixed deposit interest accumulates monthly: Capital invested R100 Plus interest R p/yr 15 shift Nom % Shift eff% = 16.08% Effective/Nominal Rates

6 R1000 invested over a 5 year period with growth at 10%. What will I get at the end? Lump Sum Suggested Solution Billy wins the lotto and invest the money for 10 years at an interest rate of 11% per annum. After the 10 years he receives R What is the capital sum that Billy invested? If I invest R1000 a month for the next 5 years at 10%, what will the maturity value be? Extra Practice Recurring payments

7 Elizabeth invests a lump sum amount of R for a period of 5 years. The interest rate is 6.5% per annum which will be credited to the account on a monthly basis. Ignore income tax. At the end of the term she will receive an amount of? Mr A invests R550 at the beginning of each month for 10 years. What is the maturity value if the investment has an 8% effective interest rate? [3] Extra Practice 2008 UFS Preparation Suggested Solution Suggested Solution

8 Tish signed an investment contract where she will invest R a further R1000 pa at beginning of each year for next 5 years at 12% interest: Maturity value will be? Lump sum + instalment Adam Liaw has informed you that he would like to accumulate an amount of R500,000 within the next 5 years. He plans to make (level) payments every 3 months into an account that you have established will pay 11% per year, compounded quarterly. Calculate the amount that he must deposit at the beginning of every 3 month period in order to achieve his goal. (2) Sept Q Alma buys a house & takes a bond of R at an interest rate of 12% for 20 years calculate monthly instalment: A R18,575 B R16,575 C R19,085 D R20,101 Interest accrues monthly Sept Q1.7 cont

9 . Sept Q1.7 cont Suggested Solution Mr N s investment receives an annuity income of R pa in advance for 15 years as well as R at the end of the term. The interest rate is 10% calculated in advance. How much did Mr N invest initially? [4] Bond of R at an interest rate of 11% and term is 20 yrs. Calculate the monthly instalment: DO NOT CLEAR THE CALCULATOR!! 2008 UFS Preparation Bond instalments - Amortisation

10 What if after 2 yrs bond holder wants to reduce term by 2 yrs? use same example as above Answer? Amortisation Reducing term of bond repayment At beg of year 3 rates increase to 12% a) what is new monthly instalments? b) what is the balance at end of year 2? DO NOT CLEAR Change interest Rates Answer

11 Mr Nkosi has a mortgage bond of R repayable over 20 years at an interest rate of 13% 1.1 Calculate monthly repayments [2] 1.2 The interest rate drops from 13% to 11% at the beg of the 2 nd year. Mr Nkosi elects not to reduce his monthly payments. Calculate how long it will now take Mr Nkosi to repay his bond? [4] 2008 UFS PREPARATION Suggested Solution Frans buys a new car for R He pays a deposit of R and takes a loan from the bank for the balance for a period of 3 years. His monthly instalment is R What is the percentage interest that he pays on the loan? Suggested Solution 1.1 Extra Practice

12 Brad wants to invest 100 per year, escalating at 7% p.a. for 3 years. Growth on the investment is 10%. What will the maturity value be of his investment. Suggested Solution Example Problem Scenario Annual premium pd to an investment must increase each year by 7% and the investment s growth is 10% Can we account for 2 growth factors? Only 1 I/YR key no escalation key. Can t add them together! ie can t do a FV calc. Can deduct and get a net effect and thereby do an equivalent PV calc Escalating regular PMT (annuity) and Growth? Incorporates both interest and escalation rate: 1+i 1+e -1 x 100 I = interest or growth rate E = escalation Alternative method: Interest 12% Escalation rate 10% / 1,10 = 1,81818% = resultant rate NB: I AM BEFORE E IS Resultant Rate

13 PMT Resultant Rate PV Interest Rate 12mth pmt PMT PV Nominal (Eff Rate) Nominal Interest Resultant Interest Rate Rate Rate 12 p/yr Or 1/py with eff rate PV FV PV of annual PV of FV of Payment escalating invest annuity itself! Escalating Annuities Annual Escalating Annuities Monthly Carmen invests R175 pa at the beginning of each year, escalating at 7% pa for 5 years at an interest of 9%. What is the FV? Mr J wants to invest R2 500 pm for the next 5 years at an interest rate of 7.5% and wants to increase his premiums by 6% every year. How much will he receive after 5 years if he invests the R2 500 at the beg of each month? [6] Resultant rate example FV of escalating annuity 2008 UFS Preparation

14 Suggested Solution Suggested Solution Ann wants to invest R100 per month for 5 years. This monthly investment must increase by 6% per annum. The investment will earn 8%. What will the future value of this monthly investment be? We want to know the FV of an investment if we are investing MONTHLY. Suggested Solution Practice

15 Suggested Solution Suggested Solution Suggested Solution Suggested Solution

16 Tom pays out an amount of R and receives monthly payments of R3000, R6000, R6000, R22000 and R15000 Calculate internal rate of return If discounted at 12% what will the net present value be? Cash Flows irregular payment Cash Flows irregular payment DO NOT CLEAR CALCULATOR Cash flow irregular payment Your client has been making uneven adhoc contributions into her investment for the past year. Contributions made as follows: March R1000 April R2000 June R1750 September R350 October R900 December R175 January R1000 February R 250 The current value is R8 587 Calculate the annual rate of return, assuming the fund compounds monthly: Cash Flow example assignment

17 Cash Flow Example Assignment 2008 Activity 3.3 Solution Question 1 Activity 3.3 Mr Nel has just taken cession of a life assurance contract. The policy is due to mature in 4 years time. Premiums of R750 pa are payable towards the policy. The estimated maturity value of the policy in 4 years time is R The growth rate is assumed to be 10%. What is the PV of this policy? Financial Calculations Environment Workbook Activities Question 2 Activity 3.4 Mrs Waterman invests R The nominal rate of interest is 10% and the interest is compounded half-annually. What is her FV after 2 years? Financial Calculations Environment Workbook Activities

18 Activity 3.4 solution ACTIVITY 4.1 SOLUTION Question 3 - ACTIVITY 4.1 Mrs Van Wyk wants to invest R500 at the beginning of each year for 10 years. The interest payable on this investment will be 15% What will the future value of this investment be? Still using the same figures above, how much capital would she need to buy an annuity of R 500 per annum payable at beg of each year- for 10 years, if the life assurer pays 15% on her investment? What is the FV if we take the result from the previous calculation if she invests a lump sum of R for 10 years at 15% Financial Calculations Environment Workbook ActivitiesS 70 Capital needed to buy an annuity? ACTIVITY 4.1 SOLUTION

19 FV OF R2886? BEG MODE 1 shift P/YR PV 15 I/YR 10 shift N FV? ACTIVITY 4.1 SOLUTION ACTIVITY 5.1 SOLUTION Question 4 ACTIVITY 5.1 Mr Verwey wants to invest R800 pm for the next 5 years at an interest rate of 8% and wants to increase his premiums by 5% every year. STEP 2 CALCULATE RESULTANT RATE How much will he receive after 5 years if he invests the R800 at the beginning of each month? Financial Calculations Environment Workbook Activities ACTIVITY 5.1 SOLUTION

20 STEP 3 PV OF ESCALATING PAYMENTS Question 5 ACTIVITY 7.3 Susan has R in a fixed deposit which earns interest of 15%. The inflation rate is 6%. Sue s marginal tax rate is 40%. What effect will this have on her real rate of return? ACTIVITY 5.1 SOLUTION Financial Calculations Environment Workbook Activities STEP 4 CALCULATE FV ACTIVITY 5.1 SOLUTION ACTIVITY 7.3 SOLUTION

21 Question 6 ACTIVITY 7.4 Mpho owns a house. The interest she pays on the bond is 12%. She won R from the lotto. Her marginal tax rate is 40% What taxable rate of interest must she earn on the R to equal the 12% interest rate she is paying on her bond? Financial Calculations Environment Workbook Activities Question 7 ACTIVITY 8.22 Mr Greedy would like to double his inheritance of R within 5 years by speculation on the stock market. He is aware that he will have to give up approximately 40% to tax annually. Calculate the annual pre-tax yield rate he will have to achieve in order to reach his goal. Financial Calculations Environment Workbook Activities ACTIVITY 7.4 SOLUTION ACTIVITY 8.22 SOLUTION

22 Question 8 Mr R needs R in 5 years time. He will invest by way of annual installments. He will start with an amount Of R8 500 and then increase the Installment by a fixed %. He will earn interest at 7.5% pa. Calculate the % by which he has to increase his installments every year? JUST TO MAKE SURE YOU ARE VERY COMFORTABLE WITH CALCULATIONS..! STEP 2 DETERMINE THE RESULTANT RATE SUGGESTED SOLUTION STEP 1 - WHAT IS THE PV OF WHAT I WANT? STEP 3 CALCULATE ESCALATION RATE Suggested solution SUGGESTED SOLUTION

23 Calculation of Retirement Needs: Mr G who is currently 45 years of age would like to retire at the age of 65. His current salary is R pa and he will be happy to receive 75% of his salary. He believes that his salary will increase with 8% pa. What is the first year s income that he will need at the age of 65? Extra Practice Mr G would like this income (75% of his salary ) for at least until his age of 85 but the income he receives must be increased by 6% every year. The capital will be invested and will attract 8% growth. How much Capital will Mr G need to have at the age of 65 to address his needs? Extra practice Ist Yrs Income Required? Capital Required to address needs?

24 Mr G is very concerned as he will under no circumstances have this type of money! He would like to know: - with an investment growth of 12%. a) How much does he have to invest annually assuming it will be a level premium? b) What if he decides to increase the premium by 10% every year? Extra practice Escalating premiums? Level Premiums? Escalating premiums?

25 Mr Makhensa, born 20 January Wants to receive a monthly income of at least R35,000 (after tax 40%) in today s value, when he retires at the age of 60. The monthly income should last for 25 years from the date of retirement and escalate by the rate of inflation per annum. (Given as 6% currently) His Current retirement savings only consist of a pension preservation fund at R350,000 current value. Growth on all investments 10% 714 Sept 2012 Q Q Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) Calculate the capital available at retirement (2) Calculate the shortfall at retirement. (2) Calculate the increasing monthly investment that Makhensa should make/save at the beginning of each month, in his retirement annuity fund to make up for the shortfall. He wants to increase the premium at 6% p.a. (3)

26 PV of the first Years income Q5.3.2 Calculate Provision PV 25 years annualised incomes, discounted for escalation Q5.3.3 Calc Shortfall

27 Q5.3.4 Calculate Investment Monthly. Esc annually. Monthly Starting Prem Q5.3.4 Cont So have you changed at all after these sessions?

### FINANCIAL CALCULATIONS

FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N

### 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

### 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

### Time-Value-of-Money and Amortization Worksheets

2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or

### USING THE SHARP EL 738 FINANCIAL CALCULATOR

USING THE SHARP EL 738 FINANCIAL CALCULATOR Basic financial examples with financial calculator steps Prepared by Colin C Smith 2010 Some important things to consider 1. These notes cover basic financial

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The

### FinQuiz Notes 2 0 1 5

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

### 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

### THE TIME VALUE OF MONEY

QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost

### LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.

LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely

### Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the Hewlett-Packard

### Fin 5413 CHAPTER FOUR

Slide 1 Interest Due Slide 2 Fin 5413 CHAPTER FOUR FIXED RATE MORTGAGE LOANS Interest Due is the mirror image of interest earned In previous finance course you learned that interest earned is: Interest

### Integrated Case. 5-42 First National Bank Time Value of Money Analysis

Integrated Case 5-42 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money

### Time Value of Money Practice Questions Irfanullah.co

1. You are trying to estimate the required rate of return for a particular investment. Which of the following premiums are you least likely to consider? A. Inflation premium B. Maturity premium C. Nominal

### Chapter 3 Present Value

Chapter 3 Present Value MULTIPLE CHOICE 1. Which of the following cannot be calculated? a. Present value of an annuity. b. Future value of an annuity. c. Present value of a perpetuity. d. Future value

### Learning Objectives. Learning Objectives. Learning Objectives. Principles Used in this Chapter. Simple Interest. Principle 2:

Learning Objectives Chapter 5 The Time Value of Money Explain the mechanics of compounding, which is how money grows over a time when it is invested. Be able to move money through time using time value

### Time Value of Money 1

Time Value of Money 1 This topic introduces you to the analysis of trade-offs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households

### Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.

### Ehrhardt Chapter 8 Page 1

Chapter 2 Time Value of Money 1 Time Value Topics Future value Present value Rates of return Amortization 2 Time lines show timing of cash flows. 0 1 2 3 I% CF 0 CF 1 CF 2 CF 3 Tick marks at ends of periods,

### 3. Time value of money. We will review some tools for discounting cash flows.

1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned

### SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM SAMPLE QUESTIONS

SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Copyright 2005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions

### Suggested solutions to 3-mark and 4-mark problems contained in the Sample Paper - Exam 4: Tax Planning & Estate Planning

Suggested solutions to 3-mark and 4-mark problems contained in the Sample Paper - Exam 4: Tax Planning & Estate Planning Section II Question 6 Mrs. A whose date of birth is 30th March 1955 has a total

### APPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS

CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists

### CHAPTER 9 Time Value Analysis

Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams

### Value of Money Concept\$

Value of Money Concept\$ Time, not timing is the key to investing 2 Introduction Time Value of Money Application of TVM in financial planning : - determine capital needs for retirement plan - determine

### Topics. Chapter 5. Future Value. Future Value - Compounding. Time Value of Money. 0 r = 5% 1

Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series

### 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)

### Sample problems from Chapter 10.1

Sample problems from Chapter 10.1 This is the annuities sinking funds formula. This formula is used in most cases for annuities. The payments for this formula are made at the end of a period. Your book

### BUSI 121 Foundations of Real Estate Mathematics

Real Estate Division BUSI 121 Foundations of Real Estate Mathematics SESSION 2 By Graham McIntosh Sauder School of Business University of British Columbia Outline Introduction Cash Flow Problems Cash Flow

### Investigating Investment Formulas Using Recursion Grade 11

Ohio Standards Connection Patterns, Functions and Algebra Benchmark C Use recursive functions to model and solve problems; e.g., home mortgages, annuities. Indicator 1 Identify and describe problem situations

### Pensions Freedom. What do the pension changes really mean? This is for information purposes only.

Pensions Freedom What do the pension changes really mean? This is for information purposes only. Pensions Freedom March Budget 2014 introduced unprecedented changes to how pension benefits can be taken

TABLE OF CONTENTS: PART A: EXAMPLES Compound interest calculations Example 1: Determine the future value of a single payment (lump sum)... 3 Example 2: Determine the annual rate of interest earned by an

### 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

### Statistical Models for Forecasting and Planning

Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information

### Topics Covered. Compounding and Discounting Single Sums. Ch. 4 - The Time Value of Money. The Time Value of Money

Ch. 4 - The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation

### Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS 7-1 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 \$10,000(1.10) 5 \$10,000(FVIF 10%, 5 ) \$10,000(1.6105) \$16,105. Alternatively, with a financial calculator enter the

### Time Value of Money Problems

Time Value of Money Problems 1. What will a deposit of \$4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. \$8,020.22 b. \$7,959.55 c. \$8,081.55 d. \$8,181.55 2. What will

### 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

### Chapter 5 & 6 Financial Calculator and Examples

Chapter 5 & 6 Financial Calculator and Examples Konan Chan Financial Management, Spring 2016 Five Factors in TVM Present value: PV Future value: FV Discount rate: r Payment: PMT Number of periods: N Get

### How Does Money Grow Over Time?

How Does Money Grow Over Time? Suggested Grade & Mastery Level High School all levels Suggested Time 45-50 minutes Teacher Background Interest refers to the amount you earn on the money you put to work

### MAT116 Project 2 Chapters 8 & 9

MAT116 Project 2 Chapters 8 & 9 1 8-1: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the

### 380.760: Corporate Finance. Financial Decision Making

380.760: Corporate Finance Lecture 2: Time Value of Money and Net Present Value Gordon Bodnar, 2009 Professor Gordon Bodnar 2009 Financial Decision Making Finance decision making is about evaluating costs

### Chapter 02 How to Calculate Present Values

Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of \$100 expected in two years from today at a discount rate of 6% is: A. \$116.64 B. \$108.00 C. \$100.00 D. \$89.00

### Interest Rates and Bond Valuation

and Bond Valuation 1 Bonds Debt Instrument Bondholders are lending the corporation money for some stated period of time. Liquid Asset Corporate Bonds can be traded in the secondary market. Price at which

### 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

### 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

### MGF 1107 Spring 11 Ref: 606977 Review for Exam 2. Write as a percent. 1) 3.1 1) Write as a decimal. 4) 60% 4) 5) 0.085% 5)

MGF 1107 Spring 11 Ref: 606977 Review for Exam 2 Mr. Guillen Exam 2 will be on 03/02/11 and covers the following sections: 8.1, 8.2, 8.3, 8.4, 8.5, 8.6. Write as a percent. 1) 3.1 1) 2) 1 8 2) 3) 7 4 3)

### 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

### Time Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam

Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value

### CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: \$5,000.08 = \$400 So after 10 years you will have: \$400 10 = \$4,000 in interest. The total balance will be

### TIME VALUE OF MONEY PROBLEM #7: MORTGAGE AMORTIZATION

TIME VALUE OF MONEY PROBLEM #7: MORTGAGE AMORTIZATION Professor Peter Harris Mathematics by Sharon Petrushka Introduction This problem will focus on calculating mortgage payments. Knowledge of Time Value

### Direct Transfer. Investment Banking. Investment Banking. Basic Concepts. Economics of Money and Banking. Basic Concepts

Basic Concepts Economics of Money and Banking 2014 South Carolina Bankers School Ron Best University of West Georgia rbest@westga.edu Risk and return: investors will only take on additional risk if they

### 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

### Solutions to Problems: Chapter 5

Solutions to Problems: Chapter 5 P5-1. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start

### Purpose EL-773A HP-10B BA-II PLUS Clear memory 0 n registers

D-How to Use a Financial Calculator* Most personal finance decisions involve calculations of the time value of money. Three methods are used to compute this value: time value of money tables (such as those

### E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is

E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =

### ICASL - Business School Programme

ICASL - Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business

### 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

### 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

### 14 ARITHMETIC OF FINANCE

4 ARITHMETI OF FINANE Introduction Definitions Present Value of a Future Amount Perpetuity - Growing Perpetuity Annuities ompounding Agreement ontinuous ompounding - Lump Sum - Annuity ompounding Magic?

### Compound Interest. Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate:

Compound Interest Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate: Table 1 Development of Nominal Payments and the Terminal Value, S.

### 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

### Note: The paid up value would be payable only on due maturity of the policy.

Section II Question 6 The earning member of a family aged 35 years expects to earn till next 25 years. He expects an annual growth of 8% in his existing net income of Rs. 5 lakh p.a. If he considers an

### The Time Value of Money

The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time

### FinQuiz Notes 2 0 1 4

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

### Chapter 3. Understanding The Time Value of Money. Prentice-Hall, Inc. 1

Chapter 3 Understanding The Time Value of Money Prentice-Hall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,

### Hewlett-Packard 17BII Tutorial

To begin, look at the face of the calculator. Most keys on the 17BII have two functions: a key's primary function is noted in white on the key itself, while the key's secondary function is noted in gold

### CHAPTER 8 INTEREST RATES AND BOND VALUATION

CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are

### 2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?

CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equal-sized

### Actuarial Speak 101 Terms and Definitions

Actuarial Speak 101 Terms and Definitions Introduction and Caveat: It is intended that all definitions and explanations are accurate. However, for purposes of understanding and clarity of key points, the

### EXAM 2 OVERVIEW. Binay Adhikari

EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing

### 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

### Sharp EL-733A Tutorial

To begin, look at the face of the calculator. Almost every key on the EL-733A has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in

### TIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction

TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 1-5, which are prerequisites. In this

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The

### Chapter 3 Mathematics of Finance

Chapter 3 Mathematics of Finance Section 3 Future Value of an Annuity; Sinking Funds Learning Objectives for Section 3.3 Future Value of an Annuity; Sinking Funds The student will be able to compute the

### 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

### Prepared by: Dalia A. Marafi Version 2.0

Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC-200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version

### 3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.

Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the

### 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

### Compounding Quarterly, Monthly, and Daily

126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,

### Excel Financial Functions

Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint() Future Value How much will your money

### 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.

### Time Value of Money, Part 4 Future Value aueof An Annuity. Learning Outcomes. Future Value

Time Value of Money, Part 4 Future Value aueof An Annuity Intermediate Accounting I Dr. Chula King 1 Learning Outcomes The concept of future value Future value of an annuity Ordinary annuity versus annuity

### Chapter 4: Net Present Value

4.1 a. Future Value = C 0 (1+r) T Chapter 4: Net Present Value = \$1,000 (1.05) 10 = \$1,628.89 b. Future Value = \$1,000 (1.07) 10 = \$1,967.15 c. Future Value = \$1,000 (1.05) 20 = \$2,653.30 d. Because interest

### HILDA & JOHN ENHANCED ANNUITIES

HILDA & JOHN ENHANCED ANNUITIES 20 July 2015 OBJECTIVES 1. John would like to secure a known income stream so Hilda can live a bit better should he die in the next few years 2. Ensure you don t have to

### INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 15 th November 2010 Subject CT1 Financial Mathematics Time allowed: Three Hours (15.00 18.00 Hrs) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1. Please

### 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

### Index Numbers ja Consumer Price Index

1 Excel and Mathematics of Finance Index Numbers ja Consumer Price Index The consumer Price index measures differences in the price of goods and services and calculates a change for a fixed basket of goods

### Time Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)

Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for

### CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value

### Mathematics. Rosella Castellano. Rome, University of Tor Vergata

and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings

### \$496. 80. Example If you can earn 6% interest, what lump sum must be deposited now so that its value will be \$3500 after 9 months?

Simple Interest, Compound Interest, and Effective Yield Simple Interest The formula that gives the amount of simple interest (also known as add-on interest) owed on a Principal P (also known as present

### Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e

Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,

### The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-738 Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### Main 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

### Using Financial Calculators

Chapter 4 Discounted Cash Flow Valuation 4B-1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your Hewlett-Packard or Texas Instruments BA II Plus financial calculator