# 1. Annuity a sequence of payments, each made at equally spaced time intervals.

Size: px
Start display at page:

Transcription

1 Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology 1. Annuity a sequence of payments, each made at equally spaced time intervals. 2. Ordinary Annuity an annuity in which the interest on the previous payments made is compounded at the same time the new payment is made. Note: All the annuities in this class will be ordinary. Examples of Ordinary Annuities 1. A sequence of annual payments into an IRA (Individual Retirement Account); 2. A sequence of equal monthly payments to pay off a car loan; 3. A sequence of equal monthly payments to pay off a house loan; 4. A sequence of equal quarterly payments to save for tuition needed by a child in the future. Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 1

2 Future Value of an Ordinary Annuity Class Activity Suppose that we set up an ordinary annuity account, where payments of \$1,000 each are placed in the account at the end of each year for four years and that the interest is 3%, compounded annually. How much will be in the account (the future value of the annuity) at the end of the four years? (A) To assist you in answering this question, complete the table below, which traces the accumulated value of each payment made over the four years Years \$1000 \$1000 \$1000 \$1000 Payment # Amount of Payment Number of 3% Accumulated value of Payment 1 \$1,000 2 \$1,000 3 \$1,000 4 \$1,000 Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 2

3 (B) Fill in the total accumulated value, A, of the account for all the payments, written as a sum and find the value of this sum. A = Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 3

4 Class Activity (Optional) (A) The sum in part (B) of the previous class activity, A = (1.03)+1000(1.03) (1.03) 3 is called a geometric series. What we would like is a simple expression that gives the value of this sum without actually having to add up all the terms (this is convenient when there are many terms to add up). To find this expression fill in each equation below, writing sums in each case A = A= (B) Now use the equations above to compute (cancel all the terms that you can as you do this) 1.03 A A = Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 4

5 (C) Solve this last equation for A and you obtain the desired expression representing the sum, A without actually having to add all the terms together. (D) Verify that the expression in (C) gives the same value for the sum as you calculated in part (B) of the previous class activity. Answers:(A) 1.03A = 1000(1.03) +1000(1.03) (1.03) (1.03) 4,!A =!1000!1000(1.03)!1000(1.03) 2!1000(1.03) 3 ; (B) 1.03A! A = 1000(1.03) 4!1000 ; (C) A = 1000 (1.03)4! Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 5

6 Future Value of an Ordinary Annuity Let p = amount of each payment made at the END of each period (small case p and not P (principal)) t = number of years m = number of periods (payments) per year r = annual interest rate, compounded m times per year, as a decimal i = r = interest rate per period m n = m!t= total number of periods (payments) in t years Then the future value of the annuity is the sum of all the payments and interest earned on those payments and is found by the formula, Remark A = p ( *! *# " * * * )* 1+ r m% r m \$ mt + & 1, ( * = p (1+i)n 1 * i Solving the formula directly above for p using algebra gives, p = A! " r % \$ # m& 1 + r = A! % mt (1 m& " \$ # ) i (1 +i) n (1 The quantity, p, is the payment (a sinking fund payment) we must deposit each period to achieve the amount, A, after t years. Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 6 +,

7 Class Activity (Optional) Use the TVM Solver on your graphing calculator to find the amount in the previous class activity, which we repeat here: Suppose that we set up an ordinary annuity account, where payments of \$1,000 each are placed in the account at the end of each year for four years and that the interest is 3%, compounded annually. How much will be in the account (the future value of the annuity) at the end of the four years? [Hints: since we are starting with \$0, put PV = 0. Also, since payments are being made into the account enter the payment as a NEGATIVE number.] Answer: Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 7

8 Class Activity At the end of each year John invests \$1,000 in a company retirement plan in which the employer matches the employee s contribution. The plan pays 8% compounded annually and John plans to retire in 30 years (A) Make a guess as to how much money John will have in his account after 30 years. (B) What will be the total accumulated value of the account after 30 years? Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 8

9 (C) Suppose John delays making payments so that now he has 20 years before retirement. What will be the total accumulated value of the account after 20 years? (D) Suppose that John has really procrastinated in getting his retirement savings on track and thus has just 10 years to retirement. What will be the total accumulated value of the account after 10 years? Remark Notice that even after 20 years John has earned less than half the amount that he will get if he can save for an additional 10 years. This is the reason behind the old saying that the sooner you start saving for retirement, the better. Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 9

10 Class Activity A freight company estimates that it will need a forklift in 6 years. The cost of the forklift is \$40,000. The company sets up a sinking fund that pays 6% compounded semiannually, in which it will make semiannual payments to achieve the goal. Calculate the size of each payment. Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 10

11 The Ordinary Annuity Formula (Optional) Remark If an interestbearing account already has an amount P in it, and equal payments p are made into the account periodically, as in an ordinary annuity, then the amount in the account after n periods is given by, A= (Future value of principal, P) + (Future value of annuity) = P(1 + i) n + p \$ (1 + i)n!1 \$ i! = P 1 + r # " m \$ mt & % " # (! *# * * * ) + p 1 + r *" m % & \$ mt + & % 1, r m where, p = amount of each payment made at the END of each period (small case p and not P (principal)) t = number of years m = number of periods (payments) per year r = annual interest rate, compounded m times per year, as a decimal i = r = interest rate per period m n = m!t= total number of periods (payments) in t years Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 11

12 Class Activity (Optional) A freight company estimates that it will need a forklift in 6 years. The cost of the forklift is \$40,000. The company sets up a sinking fund that pays 6% compounded semiannually, in which it will make semiannual payments to achieve the goal. Calculate the size of each payment, assuming that the company currently has \$5,000 in the account. What payment will be needed now? Answer: \$ Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 12

13 Present Value of an Ordinary Annuity The present value of an ordinary annuity is defined to be the single deposit that will finance the annuity. To find a formula for the present value, P, of an annuity, solve for P in the following equation: P(1+ i) n " = p (1+ i)n!1 \$ i # \$ % & Accumulated value of a single deposit of P dollars after n periods under compound interest Future value of the annuity after n periods with payments of p dollars each period Using algebra we can solve for P to get: " P = p \$ (1 + i)n!1 \$ i(1 + i) n # % & " = p\$ 1! (1 + i) n \$ i # % & Divide the numerator and denominator in the first expression by (1+ i) n to get this equivalent expression. Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 13

14 Present Value of an Ordinary Annuity Formula For an annuity with, p = amount of each payment made at the END of each period (small case p and not P) t = number of years m = number of periods (payments) per year r = annual interest rate, compounded m times per year, as a decimal i = r = interest rate per period m n = m!t= total number of periods (payments) in t years the present value of the annuity is: " P = p (1+ i)n!1 \$ \$ i(1+ i) n # % & " = p 1! (1+ i) n \$ i # \$ % & Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 14

15 Class Activity You just retired and are planning a trip. You will need \$800 per month for the 8 months that you will be gone. How much should you invest in the account, which pays 6% annual interest, when you depart so that you can withdraw the desired \$800 each month for 8 months? Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 15

16 Remark The table below shows how the lump sum of \$ invested when you depart generates the \$6400 (= 8 x 800) that will be withdrawn from the account. Month New Balance = * (Old balance) 800 # [ i = 0.06/12 =.005 (monthly rate)] (initial deposit) ( ) 800 = ( ) 800 = ( ) 800 = ( ) 800 = ( ) 800 = ( ) 800 = ( ) 800 = (796.02) 800! \$0 Funds resulting from interest = \$6,400 \$ = \$ You can check your answer using the TVM Solver, as we did below. Note that the payment is entered as a negative number and that we set FV = 0 when computing present value: The present value of the payments is \$ Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 16

17 Remark Let s prove that the present value formula actually gives the correct lump sum payment, P, which will fund the withdrawals over the 8 months. Let P be the amount of money that we will deposit to fund our vacation. Then the balance in the account after: 1. one month is: P(1.005)! two months is: (P(1.005)! 800)1.005! three months is: = P(1.005) 2! 800(1.005)! 800! (P(1.005) 2! 800(1.005)! 800)1.005! 800 = P(1.005) 3! 800(1.005) 2! 800(1.005)! eight months is: P(1.005) 8! 800(1.005) 7! 800(1.005) 6!!! 800(1.005)! 800 But the balance after eight months will be zero, so P(1.005) 8! 800(1.005) 7! 800(1.005) 6!!! 800(1.005)! 800 = 0 Solving for P in this equation and simplifying yields: " P=800 1!(1.005)!8 % \$!6, # & Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 17

18 Class Activity (Optional) You just purchased a new gourmet oven for your kitchen. You will make payments of \$100 a month for 3 years. The company that you purchased your oven from has decided to sell your loan to a bank and to receive a lump sum now, instead of collecting all the payments from you. How much should the company receive from the bank for your loan? Assume that interest rates on loans of this type are currently 9% per year. Answer: Compute the present value of the payments and get \$ Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 18

19 Remark You can check your work in the previous example using the TVM Solver. The values that were inputted are captured below. Notice that the payment is entered as a negative number and the future value is entered as zero (i.e., FV = 0). The present value is \$3, to the nearest cent. Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 19

20 Young 6.2 Survival Guide Notes copyright 2008 Knobel/Stanley 20

### 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

### Future Value of an Annuity Sinking Fund. MATH 1003 Calculus and Linear Algebra (Lecture 3)

MATH 1003 Calculus and Linear Algebra (Lecture 3) Future Value of an Annuity Definition An annuity is a sequence of equal periodic payments. We call it an ordinary annuity if the payments are made at the

### Chapter F: Finance. Section F.1-F.4

Chapter F: Finance Section F.1-F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given

### The values in the TVM Solver are quantities involved in compound interest and annuities.

Texas Instruments Graphing Calculators have a built in app that may be used to compute quantities involved in compound interest, annuities, and amortization. For the examples below, we ll utilize the screens

### 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

### 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

### 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

### Lesson 4 Annuities: The Mathematics of Regular Payments

Lesson 4 Annuities: The Mathematics of Regular Payments Introduction An annuity is a sequence of equal, periodic payments where each payment receives compound interest. One example of an annuity is a Christmas

### In Section 5.3, we ll modify the worksheet shown above. This will allow us to use Excel to calculate the different amounts in the annuity formula,

Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout

### 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

### 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.

### Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

### 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

### 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

### 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,

### CALCULATOR HINTS ANNUITIES

CALCULATOR HINTS ANNUITIES CALCULATING ANNUITIES WITH THE FINANCE APP: Select APPS and then press ENTER to open the Finance application. SELECT 1: TVM Solver The TVM Solver displays the time-value-of-money

### Review Page 468 #1,3,5,7,9,10

MAP4C Financial Student Checklist Topic/Goal Task Prerequisite Skills Simple & Compound Interest Video Lesson Part Video Lesson Part Worksheet (pages) Present Value Goal: I will use the present value formula

### Regular Annuities: Determining Present Value

8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded

### Annuities: Present Value

8.5 nnuities: Present Value GOL Determine the present value of an annuity earning compound interest. INVESTIGTE the Math Kew wants to invest some money at 5.5%/a compounded annually. He would like the

### Chapter The Time Value of Money

Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

### 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

### Finance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization

CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need

### 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

### A = P (1 + r / n) n t

Finance Formulas for College Algebra (LCU - Fall 2013) ---------------------------------------------------------------------------------------------------------------------------------- Formula 1: Amount

### TIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;

In following we will introduce one of the most important and powerful concepts you will learn in your study of finance; the time value of money. It is generally acknowledged that money has a time value.

### Finite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan

Finite Mathematics Helene Payne CHAPTER 6 Finance 6.1. Interest savings account bond mortgage loan auto loan Lender Borrower Interest: Fee charged by the lender to the borrower. Principal or Present Value:

### Activity 3.1 Annuities & Installment Payments

Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.

### 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

### 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

### CHAPTER 6 Accounting and the Time Value of Money

CHAPTER 6 Accounting and the Time Value of Money 6-1 LECTURE OUTLINE This chapter can be covered in two to three class sessions. Most students have had previous exposure to single sum problems and ordinary

### Section 5.1 - Compound Interest

Section 5.1 - Compound Interest Simple Interest Formulas If I denotes the interest on a principal P (in dollars) at an interest rate of r (as a decimal) per year for t years, then we have: Interest: Accumulated

### 8.1 Simple Interest and 8.2 Compound Interest

8.1 Simple Interest and 8.2 Compound Interest When you open a bank account or invest money in a bank or financial institution the bank/financial institution pays you interest for the use of your money.

### Chapter 03 - Basic Annuities

3-1 Chapter 03 - Basic Annuities Section 7.0 - Sum of a Geometric Sequence The form for the sum of a geometric sequence is: Sum(n) a + ar + ar 2 + ar 3 + + ar n 1 Here a = (the first term) n = (the number

### Chapter 2 Applying Time Value Concepts

Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the

### 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

### 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

### Calculations for Time Value of Money

KEATMX01_p001-008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with

### Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

### The Compound Amount : If P dollars are deposited for n compounding periods at a rate of interest i per period, the compound amount A is

The Compound Amount : If P dollars are deposited for n compounding periods at a rate of interest i per period, the compound amount A is A P 1 i n Example 1: Suppose \$1000 is deposited for 6 years in an

### SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective

### CHAPTER 4. The Time Value of Money. Chapter Synopsis

CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money

### Chapter 21: Savings Models

October 16, 2013 Last time Arithmetic Growth Simple Interest Geometric Growth Compound Interest A limit to Compounding Problems Question: I put \$1,000 dollars in a savings account with 2% nominal interest

### 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

### Question 31 38, worth 5 pts each for a complete solution, (TOTAL 40 pts) (Formulas, work

Exam Wk 6 Name Questions 1 30 are worth 2 pts each for a complete solution. (TOTAL 60 pts) (Formulas, work, or detailed explanation required.) Question 31 38, worth 5 pts each for a complete solution,

### 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)

### The Time Value of Money

C H A P T E R6 The Time Value of Money When plumbers or carpenters tackle a job, they begin by opening their toolboxes, which hold a variety of specialized tools to help them perform their jobs. The financial

### 5.1 Simple and Compound Interest

5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?

### 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

### ANNUITIES. Ordinary Simple Annuities

An annuity is a series of payments or withdrawals. ANNUITIES An Annuity can be either Simple or General Simple Annuities - Compounding periods and payment periods coincide. General Annuities - Compounding

### Homework 4 Solutions

Homework 4 Solutions Chapter 4B Does it make sense? Decide whether each of the following statements makes sense or is clearly true) or does not make sense or is clearly false). Explain your reasoning.

### Chapter 4: Managing Your Money Lecture notes Math 1030 Section C

Section C.1: The Savings Plan Formula The savings plan formula Suppose you want to save money for some reason. You could deposit a lump sum of money today and let it grow through the power of compounding

### Annuities and Sinking Funds

Annuities and Sinking Funds Sinking Fund A sinking fund is an account earning compound interest into which you make periodic deposits. Suppose that the account has an annual interest rate of compounded

### 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

### 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

### THE VALUE OF MONEY PROBLEM #3: ANNUITY. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction

THE VALUE OF MONEY PROBLEM #3: ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction Earlier, we explained how to calculate the future value of a single sum placed on deposit

### Introduction to Real Estate Investment Appraisal

Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has

### 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

### Week in Review #10. Section 5.2 and 5.3: Annuities, Sinking Funds, and Amortization

WIR Math 141-copyright Joe Kahlig, 10B Page 1 Week in Review #10 Section 5.2 and 5.3: Annuities, Sinking Funds, and Amortization an annuity is a sequence of payments made at a regular time intervals. For

### The 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 9-1 Relationship of present value and future value PPT 9-1 \$1,000 present value \$ 10% interest \$1,464.10 future value 0 1 2 3 4 Number of periods Figure

### Time Value of Money. Background

Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple

### 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

### Check off these skills when you feel that you have mastered them.

Chapter Objectives Check off these skills when you feel that you have mastered them. Know the basic loan terms principal and interest. Be able to solve the simple interest formula to find the amount of

### CHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6

CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use

### Key Concepts and Skills

McGraw-Hill/Irwin Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash

### 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

### Undergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics

Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics A Semester Course in Finite Mathematics for Business and Economics Marcel B. Finan c All Rights Reserved August 10,

### 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

### Section 8.1. I. Percent per hundred

1 Section 8.1 I. Percent per hundred a. Fractions to Percents: 1. Write the fraction as an improper fraction 2. Divide the numerator by the denominator 3. Multiply by 100 (Move the decimal two times Right)

### Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 2) 15% compounded semiannually

Exam Name Find the compound amount for the deposit. Round to the nearest cent. 1) \$1200 at 4% compounded quarterly for 5 years Find the effective rate corresponding to the given nominal rate. Round results

### 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.

### KENT FAMILY FINANCES

FACTS KENT FAMILY FINANCES Ken and Kendra Kent have been married twelve years and have twin 4-year-old sons. Kendra earns \$78,000 as a Walmart assistant manager and Ken is a stay-at-home dad. They give

### Ing. Tomáš Rábek, PhD Department of finance

Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,

### 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

### T12-1 REVIEW EXERCISES CHAPTER 12 SECTION I

T12-1 REVIEW EXERCISES CHAPTER 12 SECTION I Use Table 12-1 to calculate the future value of the following ordinary annuities: Annuity Payment Time Nominal Interest Future Value Payment Frequency Period

### 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

### Compound Interest Formula

Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt \$100 At

### Financial Literacy in Grade 11 Mathematics Understanding Annuities

Grade 11 Mathematics Functions (MCR3U) Connections to Financial Literacy Students are building their understanding of financial literacy by solving problems related to annuities. Students set up a hypothetical

Chapter 13 Annuities and Sinking Funds McGraw-Hill/Irwin Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved. #13 LU13.1 Annuities and Sinking Funds Learning Unit Objectives Annuities:

### PRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.

PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values

### Finance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date

1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand

### 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

### 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 =

### Lesson 1. Key Financial Concepts INTRODUCTION

Key Financial Concepts INTRODUCTION Welcome to Financial Management! One of the most important components of every business operation is financial decision making. Business decisions at all levels have

### 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

### CHAPTER 1. Compound Interest

CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.

### TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY

TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value

### Matt 109 Business Mathematics Notes. Spring 2013

1 To be used with: Title: Business Math (Without MyMathLab) Edition: 8 th Author: Cleaves and Hobbs Publisher: Pearson/Prentice Hall Copyright: 2009 ISBN #: 978-0-13-513687-4 Matt 109 Business Mathematics

### 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

### 10.3 Future Value and Present Value of an Ordinary General Annuity

360 Chapter 10 Annuities 10.3 Future Value and Present Value of an Ordinary General Annuity 29. In an ordinary general annuity, payments are made at the end of each payment period and the compounding period

### TVM Appendix B: Using the TI-83/84. Time Value of Money Problems on a Texas Instruments TI-83 1

Before you start: Time Value of Money Problems on a Texas Instruments TI-83 1 To calculate problems on a TI-83, you have to go into the applications menu, the blue APPS key on the calculator. Several applications

### 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

### 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

### 1 Interest rates, and risk-free investments

Interest rates, and risk-free investments Copyright c 2005 by Karl Sigman. Interest and compounded interest Suppose that you place x 0 (\$) in an account that offers a fixed (never to change over time)

### Dick Schwanke Finite Math 111 Harford Community College Fall 2015

Using Technology to Assist in Financial Calculations Calculators: TI-83 and HP-12C Software: Microsoft Excel 2007/2010 Session #4 of Finite Mathematics 1 TI-83 / 84 Graphing Calculator Section 5.5 of textbook

### 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.

### CHAPTER 17 ENGINEERING COST ANALYSIS

CHAPTER 17 ENGINEERING COST ANALYSIS Charles V. Higbee Geo-Heat Center Klamath Falls, OR 97601 17.1 INTRODUCTION In the early 1970s, life cycle costing (LCC) was adopted by the federal government. LCC

### 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