# Section 8.3 Notes- Compound Interest

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Section 8.3 Notes- Compound The Difference between Simple and Compound : Simple is paid on your investment or principal and NOT on any interest added Compound paid on BOTH on the principal and on all interest that has been added SIMPLE Imagine you deposit \$1000 in Honest John s Money Holding Service, which promises to pay 5% interest each year. After one year: COMPOUND Suppose you place \$1000 in a bank account that pays the same 5% interest per year. But instead of paying you the interest directly, the bank adds the interest to your account. After one year: After the second year: After the second year: After the third year: After the third year:

2 Example: Savings Bond While banks almost always pay compound interest, bonds usually pay simple interest. Suppose you invest \$1000 in a savings bond that pays simple interest of 10% per year. How much total interest will you receive in 5 years? If the bond paid compound interest, would you receive more or less total interest? Explain. End of Year Simple New Balance Compound New Balance Calculating the Amount in an account for Compound Paid n times a year If you deposit P dollars at a rate r (in decimal form) subject to compound interest paid n times a year, then the amount, A, of money in the account after t years is given by A P1 r n ( nt) Annually n= Semi-Annually n= Quarterly n= Monthly n= Weekly n= Examples: 1) You deposit \$1000 in a savings account at a bank that has a rate of 4%. a) Find the amount, A, of money in the account after 5 years subject to interest compounded once a year. Round to the nearest cent. b) Find the interest.

3 2) You deposit \$4200 in a savings account that has a rate of 4%. The interest is compounded quarterly. a) How much money will you have after ten years? Round to the nearest cent. b) Find the interest after ten years. Calculating the Amount in an account when Compounding Continuously If you deposit P dollars at a rate r (in decimal form) and the interest is compounded continuously, then the amount, A, of money in the account after t years is given by (rt) A Pe where e Examples: (use the x e button on your calculator) 3) A sum of \$10,000 is invested at an annual rate of 8%. Find the balance in the account after 5 years subject to a) quarterly compounding b) compounding continuously 4) Calculating Present Value. How much money should be deposited today in an account that earns 7% compounded weekly so that it will accumulate to \$10,000 in eight years?

4 More Examples: 1) Find the accumulated value of an investment of \$5,000 for 10 years at an interest rate of 3.75% if the money is a) compounded quarterly b) compounded continuously 2) Suppose that you have \$10,000 to invest. Which investment yields the greater return over 5 years: 7.55% compounded quarterly or 7.6% compounded semiannually? 3) How much money should be deposited today in an account that earns 5% compounded quarterly so that it will accumulate to \$15,000 in ten years? 4) You deposit \$5000 in a bank account that pays an APR of 3% and compounds interest monthly. How much money will you have after 5 years? Compare this amount to the amount you d have if interest were paid only once each year. 5) You deposit \$100 in an account with an APR of 8% and continuous compounding. How much will you have after 10 years? 6) College Fund at 3% Suppose you put money in an investment with an interest rate of APR = 3%, compounded annually, and leave it there for the next 18 years. How much would you have to deposit now to realize \$100,000 after 18 years? 7) Repeat Example 6, but with an interest rate of 5% and monthly compounding. Compare the results.

5 Section 8.3 Day 2 Effective Annual Yield- (or the effective rate) is the simple interest rate that produces the same amount of money in an account at the end of one year as when the account is subjected to compound interest at a stated rate. The effective annual yield is often included in the information about investments or loans. Because it s the true interest rate you are earning or paying, it is the number you should pay attention to. If you are selecting the best investment from two or more investments, the best choice is the account with the greatest effective annual yield. When borrowing money, the effective rate or effective annual yield is called the annual percentage rate. If all other factors are equal and you are borrowing money, select the option with the least annual percentage rate. The stated interest rate is called the nominal rate. Example: 1) You deposit \$6000 in an account that pays 10% interest compounded monthly. a) Find the future value after one year. b) Determine the effective annual yield. (This is a simple interest rate.) We use the future value formula for simple interest to determine the simple interest rate that produces the future value found in part a for the deposit of \$6000 after one year 2) You deposit \$7,500 in an account that pays 4.75% interest compounded monthly. a) Find the future value after one year. b) Determine the effective annual yield.

6 Calculating Effective Annual Yield Suppose that an investment has a nominal interest rate, r, in decimal form, pays compound interest n times per year. The investment s effective annual yield, Y, in decimal form is given by r 1 1 n n Y the decimal form of Y should then be converted to a percent. Example: 3) What is the effective annual yield of an account paying 8% compounded quarterly? 4) Determine the effective annual yield, to the nearest tenth of a percent, for each investment. Then select the better investment. a) 6% compounded semi-annually; 5.85% compounded daily b) 8% compounded monthly; 8.25% compounded quarterly

7 Additional Examples: 5) At the time of her grandson s birth, a grandmother deposits \$5,000 in an account that pays 6% compounded monthly. What will be the value of the account at the child s 21 st birthday, assuming no other deposits or withdrawals are made during this period? 6) Parents wish to have \$120,000 available for a child s education. If the child is now 1 year old, how much money must be set aside at 8% compounded monthly to meet their financial goal when the child is 18?

### 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?

### 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

### \$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

### 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)

### Mathematics of Finance. Learning objectives. Compound Interest

Mathematics of Finance Section 3.2 Learning objectives Compound interest Continuous compound interest Growth and time Annual percentage yield (APY) Compound Interest Compound interest arises when interest

### n=number of interest periods per year (see the table below for more information) q=q(t)=q 0 e rt

Compound interest formula P = the principal (the initial amount) A= r=annual interest rate (expressed as a decimal) n=number of interest periods per year (see the table below for more information) t=number

### 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

### Compound Interest and Continuous Growth

Warm Up 1 SECTION 6.3 Compound Interest and Continuous Growth 1 Use the compound interest formula to calculate the future value of an investment 2 Construct and use continuous growth models 3 Use exponential

### 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

### 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

### Chapter 4 Nominal and Effective Interest Rates

Chapter 4 Nominal and Effective Interest Rates Chapter 4 Nominal and Effective Interest Rates INEN 303 Sergiy Butenko Industrial & Systems Engineering Texas A&M University Nominal and Effective Interest

### 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

### Section Compound Interest. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 11.3 Compound Interest INB Table of Contents Date Topic Page # June 16, 2014 Section 11.3 Examples 32 June 16, 2014 Section 11.3 Notes 33 2.3-2 What You Will Learn Compound Interest Present Value

### Chapter 3 Understanding Money Management. Nominal and Effective Interest Rates Equivalence Calculations Changing Interest Rates Debt Management

Chapter 3 Understanding Money Management Nominal and Effective Interest Rates Equivalence Calculations Changing Interest Rates Debt Management 1 Understanding Money Management Financial institutions often

### 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:

### Ch 3 Understanding money management

Ch 3 Understanding money management 1. nominal & effective interest rates 2. equivalence calculations using effective interest rates 3. debt management If payments occur more frequently than annual, how

### 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

### 7.2 Compound Interest

7.2 Compound Interest For compound interest, the interest is reinvested at regular intervals. The interest is added to the principal to earn interest for the next interval of time, or compounding period.

### 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.

### Math of Finance Semester 1 Unit 2 Page 1 of 19

Math of Finance Semester 1 Unit 2 Page 1 of 19 Name: Date: Unit 2.1 Checking Accounts Use your book or the internet to find the following definitions: Account balance: Deposit: Withdrawal: Direct deposit:

### Accounting & Finance Foundations Math Skills A Review. Place Value Percentages Calculating Interest Discounts Compounding

Accounting & Finance Foundations Math Skills A Review Place Value Percentages Calculating Interest Discounts Compounding Place Value Ten Thousands Thousands Hundredths Tenths Ones Tens Hundreds Thousands

### Time Value of Money CAP P2 P3. Appendix. Learning Objectives. Conceptual. Procedural

Appendix B Time Value of Learning Objectives CAP Conceptual C1 Describe the earning of interest and the concepts of present and future values. (p. B-1) Procedural P1 P2 P3 P4 Apply present value concepts

### 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

### 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

### 1. At what interest rate, compounded monthly, would you need to invest your money so that you have at least \$5,000 accumulated in 4 years?

Suppose your grandparents offer you \$3,500 as a graduation gift. However, you will receive the gift only if you agree to invest the money for at least 4 years. At that time, you hope to purchase a new

### 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)

### Chapter 28 Time Value of Money

Chapter 28 Time Value of Money Lump sum cash flows 1. For example, how much would I get if I deposit \$100 in a bank account for 5 years at an annual interest rate of 10%? Let s try using our calculator:

### Chapter 22: Borrowings Models

October 21, 2013 Last Time The Consumer Price Index Real Growth The Consumer Price index The official measure of inflation is the Consumer Price Index (CPI) which is the determined by the Bureau of Labor

### 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

### Exercise 6 Find the annual interest rate if the amount after 6 years is 3 times bigger than the initial investment (3 cases).

Exercise 1 At what rate of simple interest will \$500 accumulate to \$615 in 2.5 years? In how many years will \$500 accumulate to \$630 at 7.8% simple interest? (9,2%,3 1 3 years) Exercise 2 It is known that

### 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

### Chapter 07 Interest Rates and Present Value

Chapter 07 Interest Rates and Present Value Multiple Choice Questions 1. The percentage of a balance that a borrower must pay a lender is called the a. Inflation rate b. Usury rate C. Interest rate d.

### 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

### 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

### Money Math for Teens. Introduction to Earning Interest: Middle School Version

Money Math for Teens Introduction to Earning Interest: Middle School Version This Money Math for Teens lesson is part of a series created by Generation Money, a multimedia financial literacy initiative

University of Virginia - math1140: Financial Mathematics Fall 2011 Exam 1 7:00-9:00 pm, 26 Sep 2011 Honor Policy. For this exam, you must work alone. No resources may be used during the quiz. The only

### 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

### 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

### 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

### 15.407 Sample Mid-Term Examination Fall 2008. Some Useful Formulas

15.407 Sample Mid-Term Examination Fall 2008 Please check to be certain that your copy of this examination contains 18 pages (including this one). Write your name and MIT ID number on every page. You are

### Chapter 4. Time Value of Money

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

### APPENDIX 3 TIME VALUE OF MONEY. Time Lines and Notation. The Intuitive Basis for Present Value

1 2 TIME VALUE OF MONEY APPENDIX 3 The simplest tools in finance are often the most powerful. Present value is a concept that is intuitively appealing, simple to compute, and has a wide range of applications.

### 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

### 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

### Review Solutions FV = 4000*(1+.08/4) 5 = \$4416.32

Review Solutions 1. Planning to use the money to finish your last year in school, you deposit \$4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen

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

Exam # Extra Practice Problems, Math 100, Professor Wilson MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Kate decides to replace all the lights

### A = P [ (1 + r/n) nt 1 ] (r/n)

April 23 8.4 Annuities, Stocks and Bonds ---- Systematic Savings Annuity = sequence of equal payments made at equal time periods i.e. depositing \$1000 at the end of every year into an IRA Value of an annuity

### 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

### Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = 0.75 1 for six months.

Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at

### Mathematics of Finance

5 Not for Sale Mathematics of Finance 5.1 Simple and Compound Interest 5.2 Future Value of an Annuity 5.3 Present Value of an Annuity; Amortization Chapter 5 Review Extended Application: Time, Money, and

### Present Value (PV) Tutorial

EYK 15-1 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,

### 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.

### 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

### Slide 11-1. Copyright 2005 Pearson Education, Inc. SEVENTH EDITION and EXPANDED SEVENTH EDITION. Chapter 11. Consumer Mathematics 11.1.

SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 11-1 Chapter 11 Consumer Mathematics 11.1 Percent 1 Percent The word percent comes from the Latin per centum, meaning per hundred. A percent is simply

### January 22. Interest Rates

January 22 Interest Rates Compound Interest If you put \$100 in a bank account at 5% interest per year, you will have \$105 after one year. You earn \$5 in interest. How much do you have after two years if

### 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.

### 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

### 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

### 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

### 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

### Example 1 - Solution. Since the problém is of the form "find F when given P" the formula to use is F = P(F/P, 8%, 5) = \$10,000(1.4693) = \$14,693.

Example 1 Ms. Smith loans Mr. Brown \$10,000 with interest compounded at a rate of 8% per year. How much will Mr. Brown owe Ms. Smith if he repays the loan at the end of 5 years? Example 1 - Solution Since

### Overview of Lecture 5 (part of Lecture 4 in Reader book)

Overview of Lecture 5 (part of Lecture 4 in Reader book) Bond price listings and Yield to Maturity Treasury Bills Treasury Notes and Bonds Inflation, Real and Nominal Interest Rates M. Spiegel and R. Stanton,

### 6 Rational Inequalities, (In)equalities with Absolute value; Exponents and Logarithms

AAU - Business Mathematics I Lecture #6, March 16, 2009 6 Rational Inequalities, (In)equalities with Absolute value; Exponents and Logarithms 6.1 Rational Inequalities: x + 1 x 3 > 1, x + 1 x 2 3x + 5

### 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.

### Chapter 5 Time Value of Money

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 of Cash Flows 7. Other Compounding

### 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 =

### What You ll Learn. And Why. Key Words. interest simple interest principal amount compound interest compounding period present value future value

What You ll Learn To solve problems involving compound interest and to research and compare various savings and investment options And Why Knowing how to save and invest the money you earn will help you

### 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

### Present Value Concepts

Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts

### 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:

### 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

### 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.

### Basic Concept of Time Value of Money

Basic Concept of Time Value of Money CHAPTER 1 1.1 INTRODUCTION Money has time value. A rupee today is more valuable than a year hence. It is on this concept the time value of money is based. The recognition

### 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

### 3 More on Accumulation and Discount Functions

3 More on Accumulation and Discount Functions 3.1 Introduction In previous section, we used 1.03) # of years as the accumulation factor. This section looks at other accumulation factors, including various

### 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

### 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

### 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

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

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

### 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,

### Concept 5. Inflation What is inflation? Inflation means prices are rising and the purchasing power of the dollar is declining.

Concept 5. Inflation What is inflation? Inflation means prices are rising and the purchasing power of the dollar is declining. What is inflation rate? The inflation rate is the percentage increase in prices

### 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

### 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

### The Time Value of Money Guide

The Time Value of Money Guide Institute of Financial Planning CFP Certification Global Excellence in Financial Planning TM Page 1 Contents Page Introduction 4 1. The Principles of Compound Interest 5 2.

### Oklahoma State University Spears School of Business. Time Value of Money

Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a sign-in bonus for your new job? 1. \$15,000 cash upon signing the

### 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

### Chapter Two. THE TIME VALUE OF MONEY Conventions & Definitions

Chapter Two THE TIME VALUE OF MONEY Conventions & Definitions Introduction Now, we are going to learn one of the most important topics in finance, that is, the time value of money. Note that almost every

### ROUND(cell or formula, 2)

There are many ways to set up an amortization table. This document shows how to set up five columns for the payment number, payment, interest, payment applied to the outstanding balance, and the outstanding

### 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

### VOCABULARY INVESTING Student Worksheet

Vocabulary Worksheet Page 1 Name Period VOCABULARY INVESTING Student Worksheet PRIMARY VOCABULARY 1. Savings: 2. Investments: 3. Investing: 4. Risk: 5. Return: 6. Liquidity: 7. Stocks: 8. Bonds: 9. Mutual

### CE 231 NOMINAL AND EFFECTIVE INTEREST RATE STATEMENTS. r = interest rate per period x number of periods

CE 231 NOMINAL AND EFFECTIVE INTEREST RATE STATEMENTS The primary difference between simple and compound interest is that compound interest includes interest on the interest earned in the previous record,

### 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

### 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

### 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

### 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

### 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.

### 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