Chapter 22: Borrowings Models

Size: px
Start display at page:

Download "Chapter 22: Borrowings Models"

Transcription

1 October 21, 2013

2 Last Time The Consumer Price Index Real Growth

3 The Consumer Price index The official measure of inflation is the Consumer Price Index (CPI) which is the determined by the Bureau of Labor Statistics (BLS). CPI for other year 100 = cost of market basket in other year cost of market basket in base period The base period used to calculated the CPI-U is

4 Real Growth Under Inflation Real rate of Growth The real annual rate of growth of an investment at annual interest rate r with annual inflation rate a is g = r a 1 + a

5 Question Question: In mid 2013 you put a $1000 into a savings account with APY 1 %. Assuming there is a constant inflation rate of 2 % for the next 3 years, how much money will you have in the account in mid 2016 in constant mid-2013 dollars?

6 Question Question: In mid 2013 you put a $1000 into a savings account with APY 1 %. Assuming there is a constant inflation rate of 2 % for the next 3 years, how much money will you have in the account in mid 2016 in constant mid-2013 dollars? Answer: g = = = A = 1000( ) 3 =

7 Question Question: In mid 2013 you put a $1000 into a savings account. Assuming there is a constant inflation rate of 2 % for the next 3 years, what would the APY of the savings account have to be in order to have $1100 dollars in constant mid-2012 dollars in 3 years?

8 Question Question: In mid 2013 you put a $1000 into a savings account. Assuming there is a constant inflation rate of 2 % for the next 3 years, what would the APY of the savings account have to be in order to have $1100 dollars in constant mid-2012 dollars in 3 years? Answer: ( 1100 = r.02 ) r =

9 This Time Simple Interest Compound Interest Conventional Loans Annuities

10 Simple Interest If a friends loans you $100 at a rate of 5 %, with no compounding. How much money do you owe him after 2 years? Simple Interest For a principal P and an annual rate of interest r, the interest owed in t years is I = Prt and the total amount A accumulated in the account is Answer: A = P(1 + rt) A = 100(1 +.05(2)) = $110

11 Compound Interest Compound Interest Formula For a principal P loaned at a nominal annual rate of interest rate r with m compounding periods per year (so the interest rate i = r/m per compounding period), the amount owed after t years with no payments of interest or principal is ( A = P 1 + r ) mt m

12 Question If you borrowed $15,000 to buy a new car a 4.9 % interest per year, compounded monthly, and paid back all the principal and interest at the end of 5 years, how much would you pay back? Answer: A = 15000( )(5)12 = $

13 Annual Percentage Rate (APR) Annual Percentage Rate (APR) The annual percentage rate (APR) is the number of compounding periods per year times the rate of interest per compounding period: APR = m i

14 Question Suppose a credit card has a APR of 18 % that compoundes monthly. What is the effective annual rate?

15 Question Suppose a credit card has a APR of 18 % that compoundes monthly. What is the effective annual rate? Answer: ( ) 12 )12 1 = So if you borrow $1000 with that credit card, will owe back $ at the end of the year.

16 Motivating Question How will I have to pay off my mortgage?

17 Amortize a loan [ (1 + i) n ] [ 1 (1 + r ] m A = d = d 1 r i m where A = amount accumulated d = regular deposit of payment at the end of each period n = mt number of periods r= nominal annual interest rate m = number of compounding periods per year t= number of years i= r/m periodic rate, the interest rate per compounding period

18 Question Suppose that you buy a house with a $ 100,000 loan to be paid off over 30 years in equal monthly installments. Suppose that the interest rate for the loan is 6.00 %. How much is your monthly payment? Answer: How much money will you owe the bank if you wanted 30 years and paid them all at once? ( )12(30) = 602, Now to get that accumulated amount we set up the equation [ ] ( , = d )12(30) d = So you have to pay $ a month

19 Amortization Payment Formula Amortization Payment Formula A conventional loan amount P at a nominal annual rate of interest rate r with m compounding periods per year (so interest rate i = r/m per compounding period) for t years can be paid off by uniform payments at the end of each compounding period in the amount [ ] r/m d = P 1 (1 + r/m) mt

20 Definitions Equity Equity is the amount of principal of a loan that has been repaid. Annuity An annuity is a specified number of equal periodic payments.

21 Question If you brought a house with a 30 year mortgage for $100,000 at an 8 % interest rate. After 20 years, how much equity would you have in the house? How much of the principal had been repaid? Answer: So the monthly payment would be.08/12 d = ( = (1 (1 +.08/12) 12(30) They would still owe 10 years of payment ( (1 (1 +.08/12)12(10) ) = /12 So you would have 100, = 39, in equity.

22 Questions Suppose that you buy a house with a $ 100,000 loan to be paid off over 30 years in equal monthly installments. Suppose that the interest rate for the loan is 6.00 %. How much money would pay? If it were a 15 year mortgage?

23 Questions Suppose that you buy a house with a $ 100,000 loan to be paid off over 30 years in equal monthly installments. Suppose that the interest rate for the loan is 6.00 %. How much money would pay? If it were a 15 year mortgage? Answer: = For a 15 year mortgage?.06/12 d = ( ) = (1 +.06/12) 12(15) = 151, So you would end paying over $50,000 dollars less.

24 Question Suppose that you want to retire at 65 with an annuity that pays $1000 per month for 25 years and the interest rate is 4 % per compounded monthly. What amount should you have save up to pay for this annuity?

25 Next time Review

Chapter 21: Savings Models

Chapter 21: Savings Models October 18, 2013 Last Time A Model for Saving Present Value and Inflation Problems Question 1: Suppose that you want to save up $2000 for a semester abroad two years from now. How much do you have to put

More information

Chapter 21: Savings Models

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

More information

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

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

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

Math 1332 Test 5 Review

Math 1332 Test 5 Review Name Find the simple interest. The rate is an annual rate unless otherwise noted. Assume 365 days in a year and 30 days per month. 1) $1660 at 6% for 4 months Find the future value of the deposit if the

More information

If P = principal, r = annual interest rate, and t = time (in years), then the simple interest I is given by I = P rt.

If P = principal, r = annual interest rate, and t = time (in years), then the simple interest I is given by I = P rt. 13 Consumer Mathematics 13.1 The Time Value of Money Start with some Definitions: Definition 1. The amount of a loan or a deposit is called the principal. Definition 2. The amount a loan or a deposit increases

More information

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

A = P (1 + r / n) n t Finance Formulas for College Algebra (LCU - Fall 2013) ---------------------------------------------------------------------------------------------------------------------------------- Formula 1: Amount

More information

Compound Interest Formula

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

More information

$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?

$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

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

Example. L.N. Stout () Problems on annuities 1 / 14

Example. L.N. Stout () Problems on annuities 1 / 14 Example A credit card charges an annual rate of 14% compounded monthly. This month s bill is $6000. The minimum payment is $5. Suppose I keep paying $5 each month. How long will it take to pay off the

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

MAT116 Project 2 Chapters 8 & 9

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

More information

CHAPTER 5. Interest Rates. Chapter Synopsis

CHAPTER 5. Interest Rates. Chapter Synopsis CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)

More information

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

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:

More information

Mathematics. Rosella Castellano. Rome, University of Tor Vergata

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

More information

21.1 Arithmetic Growth and Simple Interest

21.1 Arithmetic Growth and Simple Interest 21.1 Arithmetic Growth and Simple Interest When you open a savings account, your primary concerns are the safety and growth of your savings. Suppose you deposit $1000 in an account that pays interest at

More information

Future Value Sinking Fund Present Value Amortization. P V = P MT [1 (1 + i) n ] i

Future Value Sinking Fund Present Value Amortization. P V = P MT [1 (1 + i) n ] i Math 141-copyright Joe Kahlig, 15C Page 1 Section 5.2: Annuities Section 5.3: Amortization and Sinking Funds Definition: An annuity is an instrument that involves fixed payments be made/received at equal

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the present value for the given future amount. Round to the nearest cent. 1) A = $4900,

More information

Chapter 4: Managing Your Money Lecture notes Math 1030 Section D

Chapter 4: Managing Your Money Lecture notes Math 1030 Section D Section D.1: Loan Basics Definition of loan principal For any loan, the principal is the amount of money owed at any particular time. Interest is charged on the loan principal. To pay off a loan, you must

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

Warm-up: Compound vs. Annuity!

Warm-up: Compound vs. Annuity! Warm-up: Compound vs. Annuity! 1) How much will you have after 5 years if you deposit $500 twice a year into an account yielding 3% compounded semiannually? 2) How much money is in the bank after 3 years

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

Percent, Sales Tax, & Discounts

Percent, Sales Tax, & Discounts Percent, Sales Tax, & Discounts Many applications involving percent are based on the following formula: Note that of implies multiplication. Suppose that the local sales tax rate is 7.5% and you purchase

More information

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. 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 =

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

Dick Schwanke Finite Math 111 Harford Community College Fall 2013

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

More information

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

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

More information

Section 8.1. I. Percent per hundred

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)

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

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

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

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

About Compound Interest

About Compound Interest About Compound Interest TABLE OF CONTENTS About Compound Interest... 1 What is COMPOUND INTEREST?... 1 Interest... 1 Simple Interest... 1 Compound Interest... 1 Calculations... 3 Calculating How Much to

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

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

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

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

Time Value Conepts & Applications. Prof. Raad Jassim

Time Value Conepts & Applications. Prof. Raad Jassim Time Value Conepts & Applications Prof. Raad Jassim Chapter Outline Introduction to Valuation: The Time Value of Money 1 2 3 4 5 6 7 8 Future Value and Compounding Present Value and Discounting More on

More information

Dick Schwanke Finite Math 111 Harford Community College Fall 2013

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

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

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

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

Pre-Session Review. Part 2: Mathematics of Finance

Pre-Session Review. Part 2: Mathematics of Finance Pre-Session Review Part 2: Mathematics of Finance For this section you will need a calculator with logarithmic and exponential function keys (such as log, ln, and x y ) D. Exponential and Logarithmic Functions

More information

Section 5.1 - Compound Interest

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

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

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

2.1 The Present Value of an Annuity

2.1 The Present Value of an Annuity 2.1 The Present Value of an Annuity One example of a fixed annuity is an agreement to pay someone a fixed amount x for N periods (commonly months or years), e.g. a fixed pension It is assumed that the

More information

Index Numbers ja Consumer Price Index

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

More information

Engineering Economy. Time Value of Money-3

Engineering Economy. Time Value of Money-3 Engineering Economy Time Value of Money-3 Prof. Kwang-Kyu Seo 1 Chapter 2 Time Value of Money Interest: The Cost of Money Economic Equivalence Interest Formulas Single Cash Flows Equal-Payment Series Dealing

More information

9. Time Value of Money 1: Present and Future Value

9. Time Value of Money 1: Present and Future Value 9. Time Value of Money 1: Present and Future Value Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this language, because

More information

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

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

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

Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later.

Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later. ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return

More information

Credit Card Loans. Student Worksheet

Credit Card Loans. Student Worksheet Student Worksheet Credit Card Loans Name: Recall the formula for simple interest where, I is the interest owed P is the principal amount outstanding r is the interest rate t is the time in years. Note:

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

Finance. Simple Interest Formula: I = P rt where I is the interest, P is the principal, r is the rate, and t is the time in years.

Finance. Simple Interest Formula: I = P rt where I is the interest, P is the principal, r is the rate, and t is the time in years. MAT 142 College Mathematics Finance Module #FM Terri L. Miller & Elizabeth E. K. Jones revised December 16, 2010 1. Simple Interest Interest is the money earned profit) on a savings account or investment.

More information

Finance 197. Simple One-time Interest

Finance 197. Simple One-time Interest Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for

More information

Homework 4 Solutions

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.

More information

Interest Cost of Money Test - MoneyPower

Interest Cost of Money Test - MoneyPower Interest Cost of Money Test - MoneyPower Multiple Choice Identify the choice that best completes the statement or answers the question. 1. To determine the time value of depositing $100 in a savings account,

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

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

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

More information

With compound interest you earn an additional $128.89 ($1628.89 - $1500).

With compound interest you earn an additional $128.89 ($1628.89 - $1500). Compound Interest Interest is the amount you receive for lending money (making an investment) or the fee you pay for borrowing money. Compound interest is interest that is calculated using both the principle

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

Outstanding Loan Balances and Nonlevel Annuities. 1 Oustanding Loan Balances

Outstanding Loan Balances and Nonlevel Annuities. 1 Oustanding Loan Balances Outstanding Loan Balances and Nonlevel Annuities 1 Oustanding Loan Balances 1 Oustanding Loan Balances Outstanding Loan Balances Retrospective method Assume that a loan amount L is supposed to be repaid

More information

5 More on Annuities and Loans

5 More on Annuities and Loans 5 More on Annuities and Loans 5.1 Introduction This section introduces Annuities. Much of the mathematics of annuities is similar to that of loans. Indeed, we will see that a loan and an annuity are just

More information

8.1 Simple Interest and 8.2 Compound Interest

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.

More information

5. Time value of money

5. Time value of money 1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned

More information

10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans

10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans 10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans Introduction This chapter continues the discussion on the time value of money. In this chapter, you will learn how inflation

More information

Activity 3.1 Annuities & Installment Payments

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.

More information

ISE 2014 Chapter 3 Section 3.11 Deferred Annuities

ISE 2014 Chapter 3 Section 3.11 Deferred Annuities ISE 2014 Chapter 3 Section 3.11 Deferred Annuities If we are looking for a present (future) equivalent sum at time other than one period prior to the first cash flow in the series (coincident with the

More information

Chapter 2 The Time Value of Money

Chapter 2 The Time Value of Money Chapter 2 The Time Value of Money 2-1 The effective interest rate is 19.56%. If there are 12 compounding periods per year, what is the nominal interest rate? i eff = (1 + (r/m)) m 1 r/m = (1 + i eff )

More information

Chapter 2 Finance Matters

Chapter 2 Finance Matters Chapter 2 Finance Matters Chapter 2 Finance Matters 2.1 Pe r c e n t s 2.2 Simple and Compound Interest 2.3 Credit Cards 2.4 Annuities and Loans Chapter Summary Chapter Review Chapter Test Handling personal

More information

4 Annuities and Loans

4 Annuities and Loans 4 Annuities and Loans 4.1 Introduction In previous section, we discussed different methods for crediting interest, and we claimed that compound interest is the correct way to credit interest. This section

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

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

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

More information

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) 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

More information

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?

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

More information

Chapter 5 Discounted Cash Flow Valuation

Chapter 5 Discounted Cash Flow Valuation Chapter Discounted Cash Flow Valuation Compounding Periods Other Than Annual Let s examine monthly compounding problems. Future Value Suppose you invest $9,000 today and get an interest rate of 9 percent

More information

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

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

More information

Chapter 3 Mathematics of Finance

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

More information

Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...

Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future... Lecture: II 1 Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...! The intuitive basis for present value what determines the effect of timing on the value

More information

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

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

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

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

HOW TO CALCULATE PRESENT VALUES

HOW TO CALCULATE PRESENT VALUES Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

More information

10.6 Functions - Compound Interest

10.6 Functions - Compound Interest 10.6 Functions - Compound Interest Objective: Calculate final account balances using the formulas for compound and continuous interest. An application of exponential functions is compound interest. When

More information

Assist. Financial Calculators. Technology Solutions. About Our Financial Calculators. Benefits of Financial Calculators. Getting Answers.

Assist. Financial Calculators. Technology Solutions. About Our Financial Calculators. Benefits of Financial Calculators. Getting Answers. Assist. Financial s Technology Solutions. About Our Financial s. Helping members with their financial planning should be a key function of every credit union s website. At Technology Solutions, we provide

More information

The following is an article from a Marlboro, Massachusetts newspaper.

The following is an article from a Marlboro, Massachusetts newspaper. 319 CHAPTER 4 Personal Finance The following is an article from a Marlboro, Massachusetts newspaper. NEWSPAPER ARTICLE 4.1: LET S TEACH FINANCIAL LITERACY STEPHEN LEDUC WED JAN 16, 2008 Boston - Last week

More information

Annuities and Sinking Funds

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

More information

Math 120 Basic finance percent problems from prior courses (amount = % X base)

Math 120 Basic finance percent problems from prior courses (amount = % X base) Math 120 Basic finance percent problems from prior courses (amount = % X base) 1) Given a sales tax rate of 8%, a) find the tax on an item priced at $250, b) find the total amount due (which includes both

More information

Chapter 3 Equivalence A Factor Approach

Chapter 3 Equivalence A Factor Approach Chapter 3 Equivalence A Factor Approach 3-1 If you had $1,000 now and invested it at 6%, how much would it be worth 12 years from now? F = 1,000(F/P, 6%, 12) = $2,012.00 3-2 Mr. Ray deposited $200,000

More information

Chapter 10 Expectations. NOTE: Whenever you see the word communicate, it is implied that it means to communicate both verbally and in writing!

Chapter 10 Expectations. NOTE: Whenever you see the word communicate, it is implied that it means to communicate both verbally and in writing! Chapter 10 Expectations NOTE: Whenever you see the word communicate, it is implied that it means to communicate both verbally and in writing! Section 1: Expectations for Interest 1. Communicate to your

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

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

Interest Rates: Loans, Credit Cards, and Annuties. Interest Rates: Loans, Credit Cards, and Annuties 1/43

Interest Rates: Loans, Credit Cards, and Annuties. Interest Rates: Loans, Credit Cards, and Annuties 1/43 Interest Rates: Loans, Credit Cards, and Annuties Interest Rates: Loans, Credit Cards, and Annuties 1/43 Last Time Last time we discussed compound interest and saw that money can grow very large given

More information

COMPOUND INTEREST AND ANNUITY TABLES

COMPOUND INTEREST AND ANNUITY TABLES COMPOUND INTEREST AND ANNUITY TABLES COMPOUND INTEREST AND ANNUITY TABLES 8 Percent VALUE OF AN NO. OF PRESENT PRESENT VALUE OF AN COM- AMORTIZ ANNUITY - ONE PER YEARS VALUE OF ANNUITY POUND ATION YEAR

More information

MTH 150 SURVEY OF MATHEMATICS. Chapter 11 CONSUMER MATHEMATICS

MTH 150 SURVEY OF MATHEMATICS. Chapter 11 CONSUMER MATHEMATICS Your name: Your section: MTH 150 SURVEY OF MATHEMATICS Chapter 11 CONSUMER MATHEMATICS 11.1 Percent 11.2 Personal Loans and Simple Interest 11.3 Personal Loans and Compound Interest 11.4 Installment Buying

More information

Undergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics

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,

More information

hp calculators HP 20b Time value of money basics The time value of money The time value of money application Special settings

hp calculators HP 20b Time value of money basics The time value of money The time value of money application Special settings The time value of money The time value of money application Special settings Clearing the time value of money registers Begin / End mode Periods per year Cash flow diagrams and sign conventions Practice

More information