Section Compound Interest


 Jocelyn James
 2 years ago
 Views:
Transcription
1 Section 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 Amount: Example 1: Find the simple interest on a $2,000 investment made for 3 months at an interest rate of 6% per year. What is the accumulated amount? Example 2: An investment paying simple interest at the rate of 5% per year grew to $3,100 in 10 months. Find the principal. Example 3: Find the accumulated amount after 3 years if $3,500 is invested at 5% interest per year compounded annually. Example 4: Find the accumulated amount after 3 months if $1,000 is invested at an annual interest rate of 4.5% compounded monthly. 1
2 Compound Interest Formula where A = Accumualated amount at the end of the time period, P =Principal, r =Nominal interest rate per year as a decimal, m = Number of compounding periods per year, and t =number of years Example 5: Find the accummulated amount after 5 years if $3,500 is invested at 3.8% interest per year compounded quarterly. TVM Solver: We can also use the TVM Solver on our calculator to solve problems involving compound interest. To access the Finance Menu, you need to press APPS > 1:Finance (Please note that if you have a plain TI83, you need to press 2nd x 1 to access the Finance Menu). Below we define the inputs on the TVM Solver: N =the total number of compounding periods I% = interest rate (as a percentage) PV = present value (principal amount). Entered as a negative number if invested, a positive number if borrowed. PMT = payment amount (0 if no payments are involved) FV =future value (accummulated amount) P/Y = C/Y =the number of compounding periods per year. Move the cursor to the value you are solving for and hit ALPHA and then ENTER. In all of the problems we do make sure that END is highlighted at the bottom of the screen. This represents that payments are received at the end of each period. Example 6: How much is in an account after 10 years if $1000 is invested at 2.4% annual interest compounded a) annually? b) quarterly? c) monthly? d) weekly? 2
3 e) daily? f) continuously? Continuous Compound Interest Formula A = Pe rt where P =principal, r=annual interest rate compounded continously (as a decimal), t =Time in years, A =Accumulated amount at the end of t years. Definition: The effective rate of interest is the equivalent interest rate if compounding was only done once a year. It allows us to compare different interest rates with different compounding frequencies. We use the C:Eff( option on the Finance Menu to compute the effective rate of interest. The inputs are as follows: Eff(annual interest rate as a percentage, the number of compounding periods per year) Example 7: You have been doing some research and have found that you can either invest your money at 3.55% compounded daily or 3.60% compounded quarterly. Which one would you choose? Example 8: Find the present value of $30,000 due in 6 years at an interest rate of 8%/year compounded monthly. Example 9: How long will it take an investment of $8,000 to grow to $10,000 if the investment earns interest at the rate of 6%/year compounded daily? 3
4 Sections 5.2 and Annuities Definition: An annuity is a sequence of payments made at regular time intervals. In general, the amounts in the payments need not be equal. Definition: An Ordinary Annuity is an annuity in which payments are made of at the end of each payment period. Definition: An Annuity Due is an annuity in which payments are made at the beginning of each payment period. Definition: A Simple Annuity is an annuity in which the payment period coincides with the conversion period. In this course, we will study annuities with the following properties: 1. The terms are given by fixed time intervals. 2. The periodic payments are equal in size. 3. The payments are made at the end of the payment periods. 4. The payment periods coincide with the interest conversion periods. Example 1: Since you are a poor college student you currently have $10 in your bank account. If you put $50 each month into your bank account that earns 3.45% compounded monthly, how much would you have when you retire? (Let s assume that is 46 years from now) Example 2: How much would you need to put into the bank account from Example 1 if you want $1,000,000 when you retire? (i.e. 46 years from now) How much money did you actually put into the bank account? Example 3: If instead you waited 10 years to start putting payments into your bank account, how much would the payments need to be to have $1,000,000 when you retire? How much money did you actually put into the bank account? (Use the same information from Example 2) 4
5 Example 4: You are searching for a new car and not sure what you can afford. You ve discovered that you can get a 60 month loan with a 5.24% interest rate compounded monthly. Looking at your current income, you ve decided that you can afford a $400 monthly car payment. What s the most expensive car that you can afford? Example 5: At the beginning of 2000 Jenny and Eddie bought a house for $170,000. They financed it for 30 years at a 6.9% annual interest rate compounded monthly on the unpaid balance. a) What were their monthly payments? b) How much total interest would they end up paying? c) At the beginning of 2004 they decided to refinance their house with a 30 year mortgage that has a 5.325% annual interest rate compounded monthly on the unpaid balance. What are their new monthly payments? d) How much total interest are they saving by refinancing? 5
6 Example 6: Angie has graduated from college and is ready to start paying back her student loans. She has determined that she will need to make monthly payments to pay back her student loans of $30,000 over a 20 year period with a 6.125% annual interest rate compounded monthly on the unpaid balance. a) What will her monthly payments be? b) How much total interest will she be paying? c) Angie has received good advice from her family and friends and has decided to pay $100 extra each month towards the principal. How long will it take her to payoff the student loans now? d) How much total interest will she be paying now that she is paying an extra $100 a month? e) How much money is Angie saving in interest by paying the extra $100 each month? 6
7 Example 7: You purchase a $150,000 home and decide to finance it with an 80/15/5. The interest rate of the primary lien is 5.75%/year compounded monthly whereas the interest rate for the second lien is 7.75%/year compounded monthly. If you are going to make monthly payments over a 30 year period, a) What is your total monthly payment? b) If you decide to pay $200 extra each month on the second lien, how long will it take you to payoff the second lien? c) Create an amortization schedule for the first two payments and the 61st payment of the second lien without the extra payment. d) Create an amortization schedule for the first two payments and the 61st payment of the second lien with the extra payment. 7
Future Value or Accumulated Amount: F = P + I = P + P rt = P (1 + rt)
F.1 Simple Interest If P dollars (called the principal or present value) earns interest at a simple interest rate of r per year (as a decimal) for t years, then: Interest: I = P rt Examples: Future Value
More informationfirst 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
More informationThe values in the TVM Solver are quantities involved in compound interest and annuities.
Texas Instruments Graphing Calculators have a built in app that may be used to compute quantities involved in compound interest, annuities, and amortization. For the examples below, we ll utilize the screens
More informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.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 informationUsing the Finance Menu of the TI83/84/Plus calculators KEY
Using the Finance Menu of the TI83/84/Plus calculators KEY To get to the FINANCE menu On the TI83 press 2 nd x 1 On the TI83, TI83 Plus, TI84, or TI84 Plus press APPS and then select 1:FINANCE The
More informationReview 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
More informationTHE VALUE OF MONEY PROBLEM #3: ANNUITY. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction
THE VALUE OF MONEY PROBLEM #3: ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction Earlier, we explained how to calculate the future value of a single sum placed on deposit
More informationTIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY
TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value
More informationTVM Appendix B: Using the TI83/84. Time Value of Money Problems on a Texas Instruments TI83 1
Before you start: Time Value of Money Problems on a Texas Instruments TI83 1 To calculate problems on a TI83, you have to go into the applications menu, the blue APPS key on the calculator. Several applications
More informationMain TVM functions of a BAII Plus Financial Calculator
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
More informationCALCULATOR HINTS ANNUITIES
CALCULATOR HINTS ANNUITIES CALCULATING ANNUITIES WITH THE FINANCE APP: Select APPS and then press ENTER to open the Finance application. SELECT 1: TVM Solver The TVM Solver displays the timevalueofmoney
More informationActivity 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 informationBEST INTEREST RATE. To convert a nominal rate to an effective rate, press
FINANCIAL COMPUTATIONS George A. Jahn Chairman, Dept. of Mathematics Palm Beach Community College Palm Beach Gardens Location http://www.pbcc.edu/faculty/jahng/ The TI83 Plus and TI84 Plus have a wonderful
More informationChapter 2 Applying Time Value Concepts
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
More informationKey Concepts and Skills
McGrawHill/Irwin Copyright 2014 by the McGrawHill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash
More informationDick 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 informationThe explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.
USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas
More informationWeek in Review #10. Section 5.2 and 5.3: Annuities, Sinking Funds, and Amortization
WIR Math 141copyright Joe Kahlig, 10B Page 1 Week in Review #10 Section 5.2 and 5.3: Annuities, Sinking Funds, and Amortization an annuity is a sequence of payments made at a regular time intervals. For
More informationIn Section 5.3, we ll modify the worksheet shown above. This will allow us to use Excel to calculate the different amounts in the annuity formula,
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
More informationRegular Annuities: Determining Present Value
8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded
More informationChapter 4: Time Value of Money
Chapter 4: Time Value of Money BASIC KEYS USED IN FINANCE PROBLEMS The following two key sequences should be done before starting any "new" problem: ~ is used to separate key strokes (3~N: enter 3 then
More information1. 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 informationDISCOUNTED 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 informationTIME 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
More informationFinance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date
1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand
More information10. 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 informationDick Schwanke Finite Math 111 Harford Community College Fall 2015
Using Technology to Assist in Financial Calculations Calculators: TI83 and HP12C Software: Microsoft Excel 2007/2010 Session #4 of Finite Mathematics 1 TI83 / 84 Graphing Calculator Section 5.5 of textbook
More informationTIME 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 informationLoans 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,
More information1. 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 informationChapter 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
More informationMAT116 Project 2 Chapters 8 & 9
MAT116 Project 2 Chapters 8 & 9 1 81: 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 informationChapter 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 informationANNUITIES. Ordinary Simple Annuities
An annuity is a series of payments or withdrawals. ANNUITIES An Annuity can be either Simple or General Simple Annuities  Compounding periods and payment periods coincide. General Annuities  Compounding
More information1. % of workers age 55 and up have saved less than $50,000 for retirement (not including the value of a primary residence).
Toward Quantitative Literacy: Interesting Problems in Finance 2008 AMATYC Conference, Washington, D.C., Saturday, November 22, 2008 http://www.delta.edu/jaham Fill in the blanks. 1. % of workers age 55
More informationReducing balance loans
Reducing balance loans 5 VCEcoverage Area of study Units 3 & 4 Business related mathematics In this chapter 5A Loan schedules 5B The annuities formula 5C Number of repayments 5D Effects of changing the
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationSample 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
More informationTIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!
TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest $1,000 it becomes $1,050 $1,000 return of $50 return on Factors to consider when assessing Return on
More informationChapter 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 informationChapter 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 informationDiscounted 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 informationKey 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 informationFuture Value Sinking Fund Present Value Amortization. P V = P MT [1 (1 + i) n ] i
Math 141copyright 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 informationChapter 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 informationTime Value of Money. If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
More informationChapter 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 informationExample. 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 informationChapter 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 informationPV Tutorial Using Excel
EYK 153 PV Tutorial Using Excel TABLE OF CONTENTS Introduction Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise 8: Exercise 9: Exercise 10: Exercise 11: Exercise
More informationOklahoma 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 signin bonus for your new job? 1. $15,000 cash upon signing the
More informationTIME VALUE OF MONEY. HewlettPackard HP12C Calculator
SECTION 1, CHAPTER 6 TIME VALUE OF MONEY CHAPTER OUTLINE Clues, Hints, and Tips Present Value Future Value Texas Instruments BA II+ Calculator HewlettPackard HP12C Calculator CLUES, HINTS, AND TIPS Present
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More information10.3 Future Value and Present Value of an Ordinary General Annuity
360 Chapter 10 Annuities 10.3 Future Value and Present Value of an Ordinary General Annuity 29. In an ordinary general annuity, payments are made at the end of each payment period and the compounding period
More informationTimeValueofMoney and Amortization Worksheets
2 TimeValueofMoney and Amortization Worksheets The TimeValueofMoney and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or
More informationChapter 4 Discounted Cash Flow Valuation
University of Science and Technology Beijing Dongling School of Economics and management Chapter 4 Discounted Cash Flow Valuation Sep. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Be able to compute
More informationsubstantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus
for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society
More informationFinance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.
Chapter 1 Finance 331 What is finance?  Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: 
More informationFIN 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 information14 Financial. Functions. Financial Functions 141. Contents
14 Financial Functions Contents Getting Started: Financing a Car... 142 Getting Started: Computing Compound Interest... 143 Using the TVM Solver... 144 Using the Financial Functions... 145 Calculating
More informationA = P (1 + r / n) n t
Finance Formulas for College Algebra (LCU  Fall 2013)  Formula 1: Amount
More information4 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 informationFINA 351 Managerial Finance, Ch.45, TimeValueofMoney (TVM), Notes
FINA 351 Managerial Finance, Ch.45, TimeValueofMoney (TVM), Notes The concept of timevalueofmoney is important to know, not only for this class, but for your own financial planning. It is a critical
More informationAppendix 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 informationUnit VI. Complete the table based on the following information:
Aqr Review Unit VI Name 1. You have just finished medical school and you have been offered two jobs at a local hospital. The first one is a physical therapist for the hospital with a salary of $45,500.
More informationCheck 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 informationSome Mathematics of Investing in Rental Property. Floyd Vest
Some Mathematics of Investing in Rental Property Floyd Vest Example 1. In our example, we will use some of the assumptions from Luttman, Frederick W. (1983) Selected Applications of Mathematics of Finance
More informationPurpose EL773A HP10B BAII PLUS Clear memory 0 n registers
DHow to Use a Financial Calculator* Most personal finance decisions involve calculations of the time value of money. Three methods are used to compute this value: time value of money tables (such as those
More informationChapter 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 information2. How many months will it take to pay off a $9,000 loan with monthly payments of $225? The APR is 18%.
Lesson 1: The Time Value of Money Study Questions 1. Your mother, who gave you life (and therefore everything), has encouraged you to borrow $65,000 in student loans. The interest rate is a recordlow
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 42 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More informationThe Time Value of Money C H A P T E R N I N E
The Time Value of Money C H A P T E R N I N E Figure 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure
More informationhp calculators HP 12C Loan Amortizations Amortization The HP12C amortization approach Practice amortizing loans
Amortization The HP12C amortization approach Practice amortizing loans Amortization The word 'amortization' comes from a Latin word meaning "about to die". When a loan earning interest has regular, fixed
More informationSection 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 information2 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 definedcontribution
More informationMathematics. 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 informationChapter 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 informationChapter. Discounted Cash Flow Valuation. CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG.
Chapter 6 Discounted Cash Flow Valuation CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG. Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute
More informationFinite 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 informationE 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 informationhp 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 informationFuture 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 informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationSolutions 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 informationAppendix. 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 informationPresent 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 information8.1 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 informationCompound 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 informationCompounding Quarterly, Monthly, and Daily
126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,
More informationTopics. 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 informationMath 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 informationMidterm 1 Practice Problems
Midterm 1 Practice Problems 1. Calculate the present value of each cashflow using a discount rate of 7%. Which do you most prefer most? Show and explain all supporting calculations! Cashflow A: receive
More information21.1 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 informationTVM Applications Chapter
Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (longterm receivables) 7 Longterm assets 10
More informationThe Time Value of Money
The Time Value of Money 1 Learning Objectives The time value of money and its importance to business. The future value and present value of a single amount. The future value and present value of an annuity.
More informationSolutions to Problems: Chapter 5
Solutions to Problems: Chapter 5 P51. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start
More informationIntroduction. Turning the Calculator On and Off
Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction
More informationInternational 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 informationThe Interest Rate: A loan, expressed as a percentage of the amount loaned per year.
Interest Rates Time Value of Money The Interest Rate Simple Interest Amortizing a Loan The Interest Rate: A loan, expressed as a percentage of the amount loaned per year. Interest rate is the "price" of
More informationUnit 4: Finance and Spreadsheets Applied Math 30. Unit 4: Finance and Spreadsheet
41A: Investing Money Unit 4: Finance and Spreadsheet Compound Interest:  interest is incurred on the existing balance.  usually interest incurs at each term. (A term can be annually, semiannually,
More information