# With compound interest you earn an additional \$ (\$ \$1500).

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 and the interest that has accumulated in the past. The compounding period is the interval of time between the occasions when interest is added to the account. If you invest \$1000 at a simple interest rate of 5% annually, you will receive \$50 dollars for every year your money remains invested. At the end of 1 year you will earn \$50, after 2 yrs you ll earn \$100, after 3 years you ll earn \$150, etc At the end of 10 years you will have earned \$500 and you would have \$1500. Now, if you invest the same amount of money with compound interest, you will earn interest on the original principle plus any investment income that is reinvested. Example: Invest \$1000 at a rate of 5% interest compounded annually (once a year). The following table shows how your investment will grow. Principle Interest Paid (principle * 5%) Annual Running Total YR YR YR YR YR YR YR YR YR YR With compound interest you earn an additional \$ (\$ \$1500). Rather than using a table, there is a formula for calculating simple compound interest. P = the principle invested r = annual interest rate as a percentage t = the length of the term (investment or loan) A = the amount accumulated after n periods In the above example, using the formula we get: A = 1000 ( ) 10 A = 1000 ( ) A =

2 Try another example: Suppose you invest \$1800 for 5 years at 6% interest that compounds annually. How much will you have at the end of 5 years? A = 1800 ( ) 5 A = 1800 ( ) A = There are instances where interest compounds more than once a year. The basis of the formula remains the same but you must adjust the annual interest rate to the rate per period and be careful to include the correct number of periods (n). Now the formula looks like this: P = the principle invested r = annual interest rate as a percentage n = the number of times per year interest is compounded t = the length of the term (investment or loan) A = the amount accumulated after n periods Example: How much money will you have at the end of 5 years if you invest \$5000 at 8% annual interest compounded quarterly? where r/n=0.08/4 = 0.02 nt= 5 years * 4 periods per year = 20 periods A = 5000 ( ) 20 A = 5000 ( ) A = Notice how the investment really adds up when you are earning interest on interest four times per year. The table below shows the different total amounts for the same investment above with different compounding schedules. Year 1 Year 5 Year 10 Simple Annual Compound Semiannually Quarterly Monthly Weekly Daily

3 The difference in the compounding method over 1 year is miniscule but over 10 years the more compounding periods, the greater the increase. In this example the difference between annual and daily compounding interest was \$332, or 6.6%. This is the magic of compound interest, but remember, bank loans and mortgages also use compound interest so borrowing money has a much higher fee than a simple interest calculation. Example: Calculate how much a 5-year loan of \$20,000 with annual interest of 5% compounded semiannually will cost you. A = ( /2) 10 A = (1.025) 10 A = ( ) A = Cost to you = A-P = \$ You can of course solve for any of the variables in the compound interest formula by algebraically rearranging the equation. Example: What interest rate was paid on a 5-year loan with a principle amount of \$10,000, a cost to borrow of 3439, and a semiannual compound period = (1 + x/2) = (1+ x/2) /10000 = (1 + x/2) = 10 ( 1+ x / 2) x/ x/ = x The interest rate is 6% Compound interest is a way of life in our society. Understanding how it works and how it can be used effectively to grow your investments is a critical lesson. Investing early and accumulating compound interest over the long term is an excellent and safe way to make your money work for you. Conversely, when borrowing money try to limit the length of the borrowing term and pay as little interest overall as possible. 3

4 Student Worksheet Compound Interest 1. How many compounding periods are there in a 12-year investment that compounds quarterly? a. 6 b. 12 c. 24 d Compound interest is calculated a. on a semiannual basis b. more than once a year c. on the principle and interest earned d. all of the above 3. The formula for Compound Interest is: a. b. c. A = P (1 + r/t) nt d. A = P (1 + n/r) nt 4. An investment of \$1425 earns 6.75% and compounds annually. What is the total amount after 8 years? 5. If you earn \$3500 over 10 years on an investment that pays 5.3% compounded annually, what was the principle amount you started with? 6. Fill in the following table for an investment earning 4.5% annually and compounded semiannually. Principle Interest Paid Per Year Annual Running Total YR 1 16,250 YR 2 YR 3 YR 4 YR 5 7. How much interest does a \$10,000 investment earn at 5.6% over 18 years compounded quarterly? 8. How much does the same investment as above earn if the interest is compounded semiannually? Annually? 9. Calculate the amount of interest paid on a 7-year loan of \$13,450 at 4.8% compounded semiannually. 10. A \$175,000 mortgage at 3.2% compounded monthly was paid off in 19 years. What was the amount paid in interest? 4

5 ANSWERS - Student Worksheet Compound Interest 1. How many compounding periods are there in a 12-year investment that compounds quarterly? a. 6 b. 12 c. 24 d Compound interest is calculated a. on a semiannual basis b. more than once a year c. on the principle and interest earned d. all of the above 3. The formula for Compound Interest is: a. b. c. A = P (1 + r/t) nt d. A = P (1 + n/r) nt 4. An investment of \$1425 earns 6.75% and compounds annually. What is the total amount after 8 years? \$ If you earn \$3500 over 10 years on an investment that pays 5.3% compounded annually, what was the principle amount you started with? ~ \$5, Fill in the following table for an investment earning 4.5% annually and compounded semiannually. Principle YR 1 16,250 YR 2 YR 3 YR 4 YR 5 Answer: Interest Paid Per Year Annual Running Total Principle YR 1 16, YR YR YR YR Interest Paid Per Year Annual Running Total 7. How much interest does a \$10,000 investment earn at 5.6% over 18 years compounded quarterly? \$17,210.26? 8. How much does the same investment as above earn if the interest is compounded semiannually? 17, Annually? 16, Calculate the amount of interest paid on a 7-year loan of \$13,450 at 4.8% compounded semiannually. \$ A \$175,000 mortgage at 3.2% compounded monthly was paid off in 19 years. What was the amount paid in interest? 146,

### \$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

### 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?

### 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

Ch. 11.2: Installment Buying When people take out a loan to make a big purchase, they don t often pay it back all at once in one lump-sum. Instead, they usually pay it back back gradually over time, in

### 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 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

### 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 =

### 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

### Comparing Simple and Compound Interest

Comparing Simple and Compound Interest GRADE 11 In this lesson, students compare various savings and investment vehicles by calculating simple and compound interest. Prerequisite knowledge: Students should

### 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:

### 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

### 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

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

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

### 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

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

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

### 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.

### 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

### 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

### 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

### 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

### 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

### 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)

### MAT12X Intermediate Algebra

MAT12X Intermediate Algebra Workshop I - Exponential Functions LEARNING CENTER Overview Workshop I Exponential Functions of the form y = ab x Properties of the increasing and decreasing exponential functions

### 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.

### 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

### 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

### 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

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

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

### 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

### 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

### 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

### 14 ARITHMETIC OF FINANCE

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

### For additional information, see the Math Notes boxes in Lesson B.1.3 and B.2.3.

EXPONENTIAL FUNCTIONS B.1.1 B.1.6 In these sections, students generalize what they have learned about geometric sequences to investigate exponential functions. Students study exponential functions of the

### 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

### 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

### Finding Rates and the Geometric Mean

Finding Rates and the Geometric Mean So far, most of the situations we ve covered have assumed a known interest rate. If you save a certain amount of money and it earns a fixed interest rate for a period

### Simple and Compound Interest

8 Simple and Compound Interest Interest is the fee paid for borrowed money. We receive interest when we let others use our money (for example, by depositing money in a savings account or making a loan).

### Loans Practice. Math 107 Worksheet #23

Math 107 Worksheet #23 Loans Practice M P r ( 1 + r) n ( 1 + r) n =, M = the monthly payment; P = the original loan amount; r = the monthly interest rate; n = number of payments 1 For each of the following,

### YIELD CURVE GENERATION

1 YIELD CURVE GENERATION Dr Philip Symes Agenda 2 I. INTRODUCTION II. YIELD CURVES III. TYPES OF YIELD CURVES IV. USES OF YIELD CURVES V. YIELD TO MATURITY VI. BOND PRICING & VALUATION Introduction 3 A

### Logarithmic and Exponential Equations

11.5 Logarithmic and Exponential Equations 11.5 OBJECTIVES 1. Solve a logarithmic equation 2. Solve an exponential equation 3. Solve an application involving an exponential equation Much of the importance

### Lesson TVM-10-040-xx Present Value Ordinary Annuity Clip 01

- - - - - - Cover Page - - - - - - Lesson TVM-10-040-xx Present Value Ordinary Annuity Clip 01 This workbook contains notes and worksheets to accompany the corresponding video lesson available online at:

### 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

### Week 2: Exponential Functions

Week 2: Exponential Functions Goals: Introduce exponential functions Study the compounded interest and introduce the number e Suggested Textbook Readings: Chapter 4: 4.1, and Chapter 5: 5.1. Practice Problems:

### Step 1 Getting Pre-Qualified

Step 1 Getting Pre-Qualified Now that you ve made the decision to purchase a home, the next step is to get pre-qualified from a lending institution, like Michigan Mortgage Solutions, to determine how much

### What is a Credit Score and Why Do I Care What It Is?

What is a Credit Score and Why Do I Care What It Is? Your Credit Score is a lot like the score you get on a test. You get points for good credit decisions and behavior and you get points taken away for

### 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

### 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)

### 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)

### 380.760: Corporate Finance. Financial Decision Making

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

### 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

### 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.

### The Concept of Present Value

The Concept of Present Value If you could have \$100 today or \$100 next week which would you choose? Of course you would choose the \$100 today. Why? Hopefully you said because you could invest it and make

### Borrowing Solutions. 5 Principles for Better Borrowing

Borrowing Solutions 5 Principles for Better Borrowing Better borrowing lets you get more from your money Most people end up borrowing money at some point in their lives. But we know life isn t about borrowing

### 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:

### Time Value of Money. Appendix

1 Appendix Time Value of Money After studying Appendix 1, you should be able to: 1 Explain how compound interest works. 2 Use future value and present value tables to apply compound interest to accounting

### Section 2.5 Average Rate of Change

Section.5 Average Rate of Change Suppose that the revenue realized on the sale of a company s product can be modeled by the function R( x) 600x 0.3x, where x is the number of units sold and R( x ) is given

### 1 Present and Future Value

Lecture 8: Asset Markets c 2009 Je rey A. Miron Outline:. Present and Future Value 2. Bonds 3. Taxes 4. Applications Present and Future Value In the discussion of the two-period model with borrowing and

### 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

### Money Math for Teens. Opportunity Costs

Money Math for Teens This Money Math for Teens lesson is part of a series created by Generation Money, a multimedia financial literacy initiative of the FINRA Investor Education Foundation, Channel One

### 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.

### 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

### EXPONENTIAL FUNCTIONS 8.1.1 8.1.6

EXPONENTIAL FUNCTIONS 8.1.1 8.1.6 In these sections, students generalize what they have learned about geometric sequences to investigate exponential functions. Students study exponential functions of the

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

### Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010

P a g e 1 Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010 P a g e 2 Background The purpose of my senior project is to prepare myself, as well as other students who may read my senior

### The Time Value of Money Part 2B Present Value of Annuities

Management 3 Quantitative Methods The Time Value of Money Part 2B Present Value of Annuities Revised 2/18/15 New Scenario We can trade a single sum of money today, a (PV) in return for a series of periodic

### Time Value of Money Concepts

BASIC ANNUITIES There are many accounting transactions that require the payment of a specific amount each period. A payment for a auto loan or a mortgage payment are examples of this type of transaction.

### Continuous Compounding and Discounting

Continuous Compounding and Discounting Philip A. Viton October 5, 2011 Continuous October 5, 2011 1 / 19 Introduction Most real-world project analysis is carried out as we ve been doing it, with the present

### 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

### 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

### 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

### 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

### Mortgage Basics 101. Talk to your CIBC Mobile Mortgage Advisor today.

Mortgage Basics 101 Mortgages are big investments that require financial stability and dedication. Start the process on the right foot by familiarizing yourself with different types of mortgages and rates,

### 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

### 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

### NPV calculation. Academic Resource Center

NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year

### 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

### It Is In Your Interest

STUDENT MODULE 7.2 BORROWING MONEY PAGE 1 Standard 7: The student will identify the procedures and analyze the responsibilities of borrowing money. It Is In Your Interest Jason did not understand how it

### Multifamily MBS Update: Yield Maintenance Using the Constant Maturity Treasury Rate

Multifamily Mortgage-Backed Securities Multifamily MBS Update: Yield Maintenance Using the Constant Maturity Treasury Rate Each Fannie Mae multifamily loan may have a voluntary prepayment protection provision.

### Interest Rate and Credit Risk Derivatives

Interest Rate and Credit Risk Derivatives Interest Rate and Credit Risk Derivatives Peter Ritchken Kenneth Walter Haber Professor of Finance Weatherhead School of Management Case Western Reserve University

### 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

### 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

### Time Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology

Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations

### 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)

### 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

### Chapter 5 & 6 Financial Calculator and Examples

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

### 1 (1 + i) 12 = ( 1 + r 2 1 + i = ( 1 + r 2 i = ( 1 + r 2

1. Mortgages Mortage loans are commonly quoted with a nominal rate compounded semi-annually; but the payments are monthly. To find the monthly payments in this case one finds the effective monthly rate

### 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.

### Personal Financial Literacy

Personal Financial Literacy 7 Unit Overview Being financially literate means taking responsibility for learning how to manage your money. In this unit, you will learn about banking services that can help

### 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

### Helpful Information for a First Time Mortgage

Helpful Information for a First Time Mortgage Getting Started Many people buying their first home are afraid lenders don't really want to work with them. But that's simply not true. Without you, there

### What is the difference between simple and compound interest and does it really matter?

Module gtf1 Simple Versus Compound Interest What is the difference between simple and compound interest and does it really matter? There are various methods for computing interest. Do you know what the

### 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

### 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

### 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 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

### 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

### 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