Chapter Review Problems
|
|
- Augustus Golden
- 5 years ago
- Views:
Transcription
1 Chapter Review Problems Unit 9. Time-value-of-money terminology For Problems 9, assume you deposit $,000 today in a savings account. You earn 5% compounded quarterly. You deposit an additional $50 each quarter, starting in 3 months. At the end of 3 years you withdraw the balance of $, Identify each value.. Compounding period? 3 months 2. Periods per year? 4 (There are four 3-month periods in a year) 3. Term, in years? 3 years 4. n? 2 (3 years 4 periods per year) 5. Present value? $,000 (This is the amount that happens at the beginning of the first period) 6. Future value? $, (This is the amount that happens at the end of the last period) 7. Periodic payment? $50 (This is the amount that happens every period) 8. Nominal rate? 5% 9. Periodic rate?.25% (5 4 =.25) For Problems 0 4, assume you borrow $400 from a friend and repay your friend $05 at the end of each month for 4 months. 0. Periods per year? 2. n? 4 2. Present value? $ Future value? None 4. Periodic payment? $05 Unit 9.2 Compound interest formulas For problems in this unit, use the formulas of Illustration You invest $5,800 in a savings plan, earning 8% compounded semiannually. What will your balance be at the end of 5 years? We are solving for FV and know PV, so we use Formula 2A of Illustration 9-. PV = $5,800 i = 8% 2 = 4% =.04 n = 5 2 = 0 FV = PV( + i) n = $5,800(.04) 0 = $8, You invest $00 each 6 months (starting in 6 months) in a savings plan, earning 8% compounded semiannually. What will your balance be at the end of 5 years? We are solving for FV and know PMT, so we use Formula 2B. PMT = $00 i = 8% 2 = 4% =.04 n = 5 2 = 0 [ n ] FV = PMT ( + i) - = $00 (.04) - = $,200.6 i.04 [ 0 7. Refer to Problems 5 and 6. Suppose you invest $5,800 today and $00 each 6 months (starting in 6 months). What will your balance be at the end of 5 years? We simply add the two previous answers. To help visualize the process, pretend you deposit $5,800 with one bank and $00 each 6 months with a second bank. You would have an ending balance of $8, with the first bank and $,200.6 with the second, for a total of $9, ($8, $,200.6 = $9,786.03). The result would, of course, be the same if your deposits were made with one bank. ] 88 Chapter 9 Time-Value-of-Money Problems: An Introduction
2 8. Bob s grandfather gives all of his grandchildren $5,000 on their 30th birthdays. Bob just turned 20. What is the value of the $5,000 gift in today s dollars, assuming that Bob can earn 0% compounded annually? We are solving for PV and know FV, so we use Formula A: FV = $5,000; i = 0% =.0; n = 0. PV = FV = $5,000 = $, ( + i) n (.0) 0 9. You win 3rd place in the lottery and will receive ten $50,000 annual payments, starting in year. What is the real value of your prize, in today s dollars, assuming that you can earn 8% compounded annually? We are solving for PV and know PMT, so we use Formula B: PMT = $50,000; i = 8% =.08; n = Refer to Problem 9. What is the real value of your prize if payments are made at the beginning of each year? The formula used in Problem 9 assumes payments are made at the end of each period. If payments are made at the beginning of each period, we must multiply the result ($335,504.07) by ( + i). PV = $335, = $362, Joe Salazar purchased some vacant land 4 years ago for $28,500. He just sold the land for $40,000. What interest rate, compounded annually, did Joe earn on the investment? Use 5 decimal places in your final answer. We are solving for i and know FV and PV, so we use Formula 3: FV = $40,000; PV = $28,500; n = Jack Willis purchased some corporate stock 0 years ago for $2,000. He has received quarterly dividends of $200 (starting 3 months after he purchased the stock). Immediately after receiving the 40th quarterly dividend check, Jack sold the stock for $5,000. Can Jack use Formula 3 of Illustration 9- to determine the rate he earned? Explain. No, because a periodic payment is involved in the problem. Formula 3 is not designed to solve a problem in which there is a periodic payment. There is no practical formula that can be used to determine Jack s rate of return. Unit 9.3 Compound interest tables [ ] [ ] PV = PMT - = $50,000 - ( + i) n (.08) 0 = $335, i.08 ( ) n 4 ~ ~ ( ) i = FV - = $40, % PV $28,500 For problems in this unit, use the compound interest tables of Illustration 9-2. Notice that some of the decimal values of Illustration 9-2 have 0 digits and others have digits. If your calculator will not accommodate all of the digits of the decimal value, use as much of the value (rounded) as your calculator will allow. 23. Rework Problem 5 using compound interest tables. You invest $5,800 in a savings plan, earning 8% compounded semiannually. What will your balance be at the end of 5 years? We are solving for FV and we know PV, so we use Column A of Illustration 9-2. PV = $5,800 i = 8% 2 = 4% n = 5 2 = 0 We use the row within 4% where n = 0; the decimal value in Column A for that row is FV = PV Appropriate decimal value = $5, = $8, Rework Problem 6. You invest $00 each 6 months (starting in 6 months) in a savings plan, earning 8% compounded semiannually. What will your balance be at the end of 5 years? We are solving for FV and we know PMT, so we use Column B; PMT = $00; i = 8% 2 = 4%; n = 0. We use the row within 4% where n = 0; the decimal value in Column B for that row is FV = PMT Appropriate decimal value = $ = $,200.6 Chapter Review Problems 89
3 25. Refer to Problems 23 and 24. If you invest $5,800 today and $00 each 6 months (starting in 6 months), what will your balance be at the end of 5 years? $8, (answer for Problem 23) + $,200.6 (answer for Problem 24) = $9, Rework Problem 8. Bob s grandfather gives all of his grandchildren $5,000 on their 30th birthdays. Bob just turned 20. What is the value of the $5,000 gift in today s dollars, assuming that Bob can earn 0% compounded annually? We are solving for PV and we know FV, so we use Column D: FV = $5,000; i = 0%; n = 0. We use the row within 0% where n = 0; the decimal value in Column D for that row is PV = FV Appropriate decimal value = $5, = $, Rework Problem 9. You win 3rd place in the lottery and will receive 0 annual payments of $50,000, starting in year. What is the real value of your prize, in today s dollars, assuming you can earn 8% compounded annually? We are solving for PV and we know PMT, so we use Column E: PMT = $50,000; i = 8%; n = 0. We use the row within 8% where n = 0; the decimal value in Column E for that row is PV = PMT Appropriate decimal value = $50, = $335, Refer to Problem 27. What is the real value of your prize if payments are made at the beginning of each year? As noted at the top of Illustration 9-2, if payments are made at the beginning of each period we must, for Column E, multiply the result by ( + i). Logically, if payments are made sooner, the PV should be greater; multiplying the result of Problem 27 by ( + i) will give a greater value. PV = $335, = $362, If compound interest tables are used, for which of the five variables must a value be estimated: PV, PMT, FV, rate, n? The tables are not designed to solve for rate and n. The values for rate and n can be estimated by finding a decimal value within the tables that is close to a target decimal value. Unit 9.4 Financial calculators 30. If you make a total of six $00 payments, you should enter $600 in the PMT register. (T or F) False. You do not make a payment of $600, so you should not enter $600 in the PMT register. Instead, you should enter $00 (actually, negative $00) in the PMT register. 3. If loan payments are made on the 5th of each month, you must set your calculator in middle-of-the-month mode. (T or F) False; there is no middle-of-the-month mode. For Problems 32 39, rework the indicated problems. Record given data. Then find the answer. Finally, record your answer. Problem 32 is completed as an example (with answer in bold). Rework Problem = = 4-5,800 8, , ,800 9, , , , , , ,000 Begin * ,500 40, = = , ,000 *Note: Don t forget to put your calculator back in End mode after finishing Problem Chapter 9 Time-Value-of-Money Problems: An Introduction
4 Unit 9.5 Checking answers 40. In Problem 6, you deposited $00 each 6 months (starting in 6 months) in a savings plan for 5 years, earning 8% compounded semiannually. Use estimating to determine if the answer of $,200.6 is reasonable. You will deposit a total of $,000 (0 deposits $00 = $,000). In addition, you will earn some interest, so the answer of $,200.6 seems reasonable. 4. Refer to Problem 40. Use a longhand proof to determine if the answer of $,200.6 is correct. Remember, in your proof, don t round intermediate results. Balance in 6 months: $00.00 Balance in 2 months: + 4% + $00 = $ Balance in 8 months: + 4% + $00 = $32.6 Balance in 24 months: + 4% + $00 = $ Balance in 30 months: + 4% + $00 = $54.63 Balance in 36 months: + 4% + $00 = $ Balance in 42 months: + 4% + $00 = $ Balance in 48 months: + 4% + $00 = $92.42 Balance in 54 months: + 4% + $00 = $, Balance in 60 months: + 4% + $00 = $,200.6 (Answer is identical) 42. In Problem 2, Joe Salazar purchased some vacant land 4 years ago for $28,500. He just sold the land for $40,000. We determined that Joe earned an annual rate of % on his investment. Use estimating to determine if the answer is reasonable. Annual rate: 40.35% 4 years 0.09% per year Because interest is compounded each year, a lower interest rate will result in the same ending value, so the rate of % seems reasonable. 43. Refer to Problem 42. Use a longhand proof to determine if the answer of % is correct. Theoretical value in year: $28, % = $3, Theoretical value in 2 years: % = $33, Theoretical value in 3 years: % = $36, Theoretical value in 4 years: % = $40, (The rate of % works!) 44. Percent increase = Amount of increase = $40,000 - $28,500 = $, % Original amount $28,500 $28,500 ~ ~ Challenge problems For Problems 44 47, use the given data to solve for the unknown. Then write a word problem that matches the data. 4 2 = * 5, *Note: Don t make the mistake of entering a rounded periodic rate (0.96). By dividing.5 by 2 and transferring the result in the interest rate register, we enter the internal, more accurate, value ( ). One possibility: If I borrow $5,000 at.5% to buy a new sports car and the loan requires monthly payments for 4 years, my payment will be $ = ,000 8,68.76 One possibility: If I deposit $5,000 in a savings account for 4 years and the account earns interest at 5.5% compounded monthly, I will have $8,68.76 at the end of 4 years = ,000 20,000 One possibility: I purchased some IBM stock 5 years ago for $5,000. If I sold the stock today for $20,000, I earned 5.92% per year on my investment. Chapter Review Problems 9
5 = ,000 One possibility: If I deposit $500 each at the end of each 6 months and earn 6.50% compounded semiannually, I will have $50,000 in 37.3 years (74.26 six-month periods). 48. You buy a bond for $955. You receive semiannual interest checks of $38.75 at the end of each 6 months. You receive the $,000 maturity value in 4 years. What is your rate of return? 4 2 = ~ 8.30* ,000 *Note: Remember i represents the interest rate per period, so we must multiply by the number of periods per year. For Problems 49 53, assume that you want to accumulate $0,000 for a down payment on a home. You start a savings plan today by depositing $2,000. We will find what additional amount you must deposit each 6 months (starting in 6 months) to have $0,000 in 4 years, assuming that you can earn 8% compounded semiannually? 49. Determine your monthly payment using compound interest formulas. We are solving for PMT, so we use Formula 4. Remember, for Formulas 4 and 5, we must treat dollar amounts with proper sign convention (as a positive or negative value). PV = - $2,000; the value is negative because you give the money to the bank FV = $0,000; the value is positive because you will receive this money from the bank in 4 years i = 8% 2 = 4% =.04 n = 4 2 = 8 According to the mathematical order of operations, we first perform multiplication and then addition, so we perform multiplication on FV and then add PV to the result. PMT = PV + FV [ = -$2,000 + $0,000 ( + i) ] [ n (.04) ] 8 = -$ ( + i) n (.04) 8 i.04 Because the arithmetic is a bit complicated on this problem, calculator keystrokes are shown. Although there are several different ways to do the arithmetic on our calculators, the keystrokes below are done by storing values. Storage register : Storage register 2: Entire numerator Storage register 3: Entire denominator (.04) 8 HP 0BII.04 _ y x 8 =.37 _ /x 0.73 _ STO 0.73* 0,000 = 7, ,000 = 5, _ STO 2 5, RCL = = _ STO RCL 2 5, RCL = TI BAII PLUS.04 y x 8 =.37 /x 0.73 STO 0.73* 0,000 = 7, ,000 = 5, STO 2 5, RCL = = STO RCL 2 5, RCL = * Note: The internal, more accurate, value is stored. 92 Chapter 9 Time-Value-of-Money Problems: An Introduction
6 50. Determine your monthly payment using compound interest tables. In Illustration 9-2, Columns C and F are used to solve for PMT. But Column C is used when we know FV, and Column F is used when we know PV. Unfortunately, in this problem, we know both FV and PV. So, the only way we can do this problem using compound interest tables is as a two-step problem. First, we will find the payment, without the initial $2,000 deposit required to accumulate $0,000. Then, we will find the PMT that will be saved by depositing $2,000. The answer is the difference between the two steps. Step (find PMT required to accumulate $0,000): Use Column C, i = 4%, n = 8 PMT = FV Appropriate decimal value = $0, = $, Step 2 (find PMT resulting from a deposit of $2,000): Use Column F, i = 4%, n = 8 PMT = PV Appropriate decimal value = $2, = Difference $ Determine your monthly payment using time-value-of-money registers. 4 2 = = 4-2, , Determine whether the answer ($788.22) seems reasonable. Initial deposit $2, Semiannual deposits: 8 $ , Total amount deposited $8, The ending balance will actually be greater after interest is added, so deposits of $ seem reasonable to end up with $0, Determine whether the answer ($788.22) is correct. Balance in 6 months: $2, % + $ = $2, Balance in 2 months: + 4% + $ = $3,77.7 Balance in 8 months: + 4% + $ = $4,70.24 Balance in 24 months: + 4% + $ = $5, Balance in 30 months: + 4% + $ = $6, Balance in 36 months: + 4% + $ = $7, Balance in 42 months: + 4% + $ = $8, Balance in 48 months: + 4% + $ = $9, Because the deposit amount ($788.22) was rounded to the nearest penny (instead of the more accurate ), the ending balance is a few pennies different from the desired $0,000, but the deposit amount is correct, to the nearest penny. Practice Test. You deposit $500 today in a savings account that earns 6% compounded quarterly and leave the money there for 5 years. What is the n-value? n = 5 years 4 periods per year = You deposit $00 at the end of each month in a savings account that earns 4.5% compounded monthly. Use the compound interest formulas of Illustration 9- to find the balance at the end of 5 years. We need to know FV and we know PMT, so we use Formula 2B. PMT = $00 i = 4.5% 2 =.375% = n = 5 2 = 80 [ ] [ ] n 80 FV = PMT ( + i) - = $00 (.00375) - = $25,64.47 i Practice Test 93
7 3. Find the value of -$5,000 + $2,000 [ ] (.04) 6 - (.04) 6.04 ~ -$5,000 + $2,000 ( ) ~ -$5,000 + $6, ~ $, ~ -$ Your Uncle Ben gives you $5,000 at the beginning of each year for college. You will receive a total of four payments, and you can earn 8% compounded annually. Use the compound interest tables of Illustration 9-2 to determine the real value of his gift, in today s dollars. We are solving for PV and we know PMT, so we use Column E: PMT = $5,000; i = 8%; n = 4. We use the row within 8% where n = 4; the decimal value in Column E for that row is PV = PMT Appropriate decimal value = $5, = $6, Because payments are at the beginning of each period, we multiply by ( + i): $6, = $7, You deposit $525 in a savings account earning 3.5% compounded semiannually. You let the money sit for 3 years. If you use the compound interest tables of Illustration 9-2 to find the ending balance, what decimal value do you multiply by $525? Note: Don t solve the problem; just find the decimal value. We are solving for FV and we know PV, so we use Column A: PV = $525; i = 3.5% 2 =.75%; n = 3 2 = 6. We use the row within 4 3 % where n = 6; the decimal value in Column A for that row is You open a savings plan by depositing $00. Then you deposit $50 at the end of each quarter for 52 years. You earn 7.85%, compounded quarterly. Use time-value-of-money registers to determine your savings plan balance at the end of 52 years = ~ , You buy a bond for $975. You receive semiannual interest checks of $40 at the end of each 6 months. You receive the $,000 maturity value in 2 years. What is your rate of return? 2 2 = ~ 8.33* ,000 *8.33% compounded semiannually 8. You deposit $0,000 and let the money sit for 2 years, earning 4.50%, compounded semiannually. Use a longhand approach to determine the ending balance. Balance in 6 months: $0, % = $0, Balance in 2 months: % = $0, Balance in 8 months: % = $0, Balance in 24 months: % = $0, Chapter 9 Time-Value-of-Money Problems: An Introduction
Calculator Keystrokes (Get Rich Slow) - Hewlett Packard 12C
Calculator Keystrokes (Get Rich Slow) - Hewlett Packard 12C Keystrokes for the HP 12C are shown in the following order: (1) Quick Start, pages 165-169 of the Appendix. This will provide some basics for
More informationTexas Instruments 83 Plus and 84 Plus Calculator
Texas Instruments 83 Plus and 84 Plus Calculator For the topics we cover, keystrokes for the TI-83 PLUS and 84 PLUS are identical. Keystrokes are shown for a few topics in which keystrokes are unique.
More informationCasio 9750G PLUS Calculator
Casio 9750G PLUS Calculator Keystrokes for the Casio 9750G PLUS are shown for a few topics in which keystrokes are unique. Start by reading the Quik Start section. Then, before beginning a specific unit
More informationHOME EQUITY CONVERSION MORTGAGE Using an HP12C to Calculate Payments to Borrowers
4235.1 REV-1 HOME EQUITY CONVERSION MORTGAGE Using an HP12C to Calculate Payments to Borrowers This appendix illustrates use of an HP12C for calculating payments to borrowers under the Home Equity Conversion
More informationFINANCE FOR EVERYONE SPREADSHEETS
FINANCE FOR EVERYONE SPREADSHEETS Some Important Stuff Make sure there are at least two decimals allowed in each cell. Otherwise rounding off may create problems in a multi-step problem Always enter the
More informationHewlett Packard 17BII Calculator
Hewlett Packard 17BII Calculator Keystrokes for the HP 17BII are shown for a few topics in which keystrokes are unique. Start by reading the Quik Start section. Then, before beginning a specific unit of
More informationThe TVM Solver. When you input four of the first five variables in the list above, the TVM Solver solves for the fifth variable.
1 The TVM Solver The TVM Solver is an application on the TI-83 Plus graphing calculator. It displays the timevalue-of-money (TVM) variables used in solving finance problems. Prior to using the TVM Solver,
More informationSection 5.1 Simple and Compound Interest
Section 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
More informationQuick Guide to Using the HP12C
Quick Guide to Using the HP12C Introduction: The HP- 12C is a powerful financial calculator that has become the de facto standard in the financial services industry. However, its operation differs from
More informationCHAPTER 2 TIME VALUE OF MONEY
CHAPTER 2 TIME VALUE OF MONEY True/False Easy: (2.2) Compounding Answer: a EASY 1. One potential benefit from starting to invest early for retirement is that the investor can expect greater benefits from
More informationChapter 5. Finance 300 David Moore
Chapter 5 Finance 300 David Moore Time and Money This chapter is the first chapter on the most important skill in this course: how to move money through time. Timing is everything. The simple techniques
More informationSimple and Compound Interest
Chp 11/24/08 5:00 PM Page 171 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
More informationSimple Interest: Interest earned only on the original principal amount invested.
53 Future Value (FV): The amount an investment is worth after one or more periods. Simple Interest: Interest earned only on the original principal amount invested. Compound Interest: Interest earned on
More information9. Time Value of Money 1: Understanding the Language of Finance
9. Time Value of Money 1: Understanding the Language of Finance Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this
More informationThese terms are the same whether you are the borrower or the lender, but I describe the words by thinking about borrowing the money.
Simple and compound interest NAME: These terms are the same whether you are the borrower or the lender, but I describe the words by thinking about borrowing the money. Principal: initial amount you borrow;
More informationLESSON 2 INTEREST FORMULAS AND THEIR APPLICATIONS. Overview of Interest Formulas and Their Applications. Symbols Used in Engineering Economy
Lesson Two: Interest Formulas and Their Applications from Understanding Engineering Economy: A Practical Approach LESSON 2 INTEREST FORMULAS AND THEIR APPLICATIONS Overview of Interest Formulas and Their
More informationFINANCIAL DECISION RULES FOR PROJECT EVALUATION SPREADSHEETS
FINANCIAL DECISION RULES FOR PROJECT EVALUATION SPREADSHEETS This note is some basic information that should help you get started and do most calculations if you have access to spreadsheets. You could
More informationMBF1223 Financial Management Prepared by Dr Khairul Anuar
MBF1223 Financial Management Prepared by Dr Khairul Anuar L4 Time Value of Money www.mba638.wordpress.com 2 Learning Objectives 1. Calculate future values and understand compounding. 2. Calculate present
More informationMBF1223 Financial Management Prepared by Dr Khairul Anuar
MBF1223 Financial Management Prepared by Dr Khairul Anuar L3 Time Value of Money www.mba638.wordpress.com 2 4 Learning Objectives 1. Calculate future values and understand compounding. 2. Calculate present
More informationManual for SOA Exam FM/CAS Exam 2.
Manual for SOA Exam FM/CAS Exam 2. Chapter 1. Basic Interest Theory. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics.
More informationBasic Calculator Course
Basic Calculator Course For use in evaluating notes and other income streams. Purpose: This course is intended to provide a basic introduction to the use of a financial calculator in evaluating notes and
More informationtroduction to Algebra
Chapter Six Percent Percents, Decimals, and Fractions Understanding Percent The word percent comes from the Latin phrase per centum,, which means per 100. Percent means per one hundred. The % symbol is
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 informationLearning Plan 3 Chapter 3
Learning Plan 3 Chapter 3 Questions 1 and 2 (page 82) To convert a decimal into a percent, you must move the decimal point two places to the right. 0.72 = 72% 5.46 = 546% 3.0842 = 308.42% Question 3 Write
More informationMath 166: Topics in Contemporary Mathematics II
Math 166: Topics in Contemporary Mathematics II Xin Ma Texas A&M University October 28, 2017 Xin Ma (TAMU) Math 166 October 28, 2017 1 / 10 TVM Solver on the Calculator Unlike simple interest, it is much
More information6.1 Simple and Compound Interest
6.1 Simple and Compound 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 Accumulated
More informationTime Value of Money, Part 5 Present Value aueof An Annuity. Learning Outcomes. Present Value
Time Value of Money, Part 5 Present Value aueof An Annuity Intermediate Accounting I Dr. Chula King 1 Learning Outcomes The concept of present value Present value of an annuity Ordinary annuity versus
More informationThe Time Value. The importance of money flows from it being a link between the present and the future. John Maynard Keynes
The Time Value of Money The importance of money flows from it being a link between the present and the future. John Maynard Keynes Get a Free $,000 Bond with Every Car Bought This Week! There is a car
More information7.7 Technology: Amortization Tables and Spreadsheets
7.7 Technology: Amortization Tables and Spreadsheets Generally, people must borrow money when they purchase a car, house, or condominium, so they arrange a loan or mortgage. Loans and mortgages are agreements
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationFinance 197. Simple One-time Interest
Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for
More informationMath 1324 Finite Mathematics Chapter 4 Finance
Math 1324 Finite Mathematics Chapter 4 Finance Simple Interest: Situation where interest is calculated on the original principal only. A = P(1 + rt) where A is I = Prt Ex: A bank pays simple interest at
More informationSection 5.1 Compound Interest
Section 5.1 Compound Interest Simple Interest Formulas: Interest: Accumulated amount: I = P rt A = P (1 + rt) Here P is the principal (money you start out with), r is the interest rate (as a decimal),
More information6.1 Simple Interest page 243
page 242 6 Students learn about finance as it applies to their daily lives. Two of the most important types of financial decisions for many people involve either buying a house or saving for retirement.
More informationExcelBasics.pdf. Here is the URL for a very good website about Excel basics including the material covered in this primer.
Excel Primer for Finance Students John Byrd, November 2015. This primer assumes you can enter data and copy functions and equations between cells in Excel. If you aren t familiar with these basic skills
More informationPRE COURSE WORKBOOK DOESTPENCIL.NET. DOES IT PENCIL / PRE COURSE WORKBOOK 2017 Still Training, LLC 1
PRE COURSE WORKBOOK DOESTPENCIL.NET 2017 Still Training, LLC 1 HOW TO USE THIS WORKBOOK This workbook and the pre course videos integral to the DOES IT PENCIL training. The training is designed for you
More informationhp calculators HP 20b Loan Amortizations The time value of money application Amortization Amortization on the HP 20b Practice amortizing loans
The time value of money application Amortization Amortization on the HP 20b Practice amortizing loans The time value of money application The time value of money application built into the HP 20b is used
More informationLesson TVM xx. Present Value Annuity Due
Lesson TVM-10-060-xx Present Value Annuity Due This workbook contains notes and worksheets to accompany the corresponding video lesson available online at: Permission is granted for educators and students
More informationActivity 1.1 Compound Interest and Accumulated Value
Activity 1.1 Compound Interest and Accumulated Value Remember that time is money. Ben Franklin, 1748 Reprinted by permission: Tribune Media Services Broom Hilda has discovered too late the power of compound
More informationCopyright 2015 by the McGraw-Hill Education (Asia). All rights reserved.
Copyright 2015 by the McGraw-Hill Education (Asia). All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash to be received
More informationSample Investment Device CD (Certificate of Deposit) Savings Account Bonds Loans for: Car House Start a business
Simple and Compound Interest (Young: 6.1) In this Lecture: 1. Financial Terminology 2. Simple Interest 3. Compound Interest 4. Important Formulas of Finance 5. From Simple to Compound Interest 6. Examples
More information5-1 FUTURE VALUE If you deposit $10,000 in a bank account that pays 10% interest ann~ally, how much will be in your account after 5 years?
174 Part 2 Fundamental Concepts in Financial Management QuESTIONS 5-1 What is an opportunity cost? How is this concept used in TVM analysis, and where is it shown on a time line? Is a single number used
More informationSECTION 6.1: Simple and Compound Interest
1 SECTION 6.1: Simple and Compound Interest Chapter 6 focuses on and various financial applications of interest. GOAL: Understand and apply different types of interest. Simple Interest If a sum of money
More informationGLOBAL EDITION. Using and Understanding Mathematics. A Quantitative Reasoning Approach SIXTH EDITION. Jeffrey Bennett William Briggs
GLOBAL EDITION Using and Understanding Mathematics A Quantitative Reasoning Approach SIXTH EDITION Jeffrey Bennett William Briggs Why Should you Care About Quantitative reasoning? Quantitative reasoning
More informationACCT 652 Accounting. Payroll accounting. Payroll accounting Week 8 Liabilities and Present value
11-1 ACCT 652 Accounting Week 8 Liabilities and Present value Some slides Times Mirror Higher Education Division, Inc. Used by permission 2016, Michael D. Kinsman, Ph.D. 1 1 Payroll accounting I am sure
More informationTVM Menu: Time Value of Money Calculations
TVM Menu: Time Value of Money Calculations TMV primary menu TMV secondary menu TMV Amortization menu The RLM-19BII TVM menu calculates Compound Interest problems involving money earning interest over a
More informationSequences, Series, and Limits; the Economics of Finance
CHAPTER 3 Sequences, Series, and Limits; the Economics of Finance If you have done A-level maths you will have studied Sequences and Series in particular Arithmetic and Geometric ones) before; if not you
More informationTime Value of Money Menu
Time Value of Money Menu The Time-Value-of-Money (TVM) menu calculates Compound Interest problems involving money earning interest over a period of time. To show it, touch the OPT key and in the section
More informationIntroduction to the Hewlett-Packard (HP) 10B Calculator and Review of Mortgage Finance Calculations
Introduction to the Hewlett-Packard (HP) 0B Calculator and Review of Mortgage Finance Calculations Real Estate Division Faculty of Commerce and Business Administration University of British Columbia Introduction
More informationChapter 03 - Basic Annuities
3-1 Chapter 03 - Basic Annuities Section 3.0 - 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
More informationSimple Interest. Simple Interest is the money earned (or owed) only on the borrowed. Balance that Interest is Calculated On
MCR3U Unit 8: Financial Applications Lesson 1 Date: Learning goal: I understand simple interest and can calculate any value in the simple interest formula. Simple Interest is the money earned (or owed)
More informationChapter Review Problems
Chapter Review Problems State all stock and bond prices in dollars and cents. Unit 14.1 Stocks 1. When a corporation earns a profit, the board of directors is obligated by law to immediately distribute
More informationMath 147 Section 6.4. Application Example
Math 147 Section 6.4 Present Value of Annuities 1 Application Example Suppose an individual makes an initial investment of $1500 in an account that earns 8.4%, compounded monthly, and makes additional
More informationUsing the Finance Menu of the TI-83/84/Plus calculators
Using the Finance Menu of the TI-83/84/Plus calculators To get to the FINANCE menu On the TI-83 press 2 nd x -1 On the TI-83, TI-83 Plus, TI-84, or TI-84 Plus press APPS and then select 1:FINANCE The FINANCE
More informationBefore How can lines on a graph show the effect of interest rates on savings accounts?
Compound Interest LAUNCH (7 MIN) Before How can lines on a graph show the effect of interest rates on savings accounts? During How can you tell what the graph of simple interest looks like? After What
More informationChapter 5: Finance. Section 5.1: Basic Budgeting. Chapter 5: Finance
Chapter 5: Finance Most adults have to deal with the financial topics in this chapter regardless of their job or income. Understanding these topics helps us to make wise decisions in our private lives
More informationReal Estate. Refinancing
Introduction This Solutions Handbook has been designed to supplement the HP-12C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or step-by-step keystroke procedures
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concept Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value decreases. 2. Assuming positive
More informationJanuary 29. Annuities
January 29 Annuities An annuity is a repeating payment, typically of a fixed amount, over a period of time. An annuity is like a loan in reverse; rather than paying a loan company, a bank or investment
More informationFinance 2400 / 3200 / Lecture Notes for the Fall semester V.4 of. Bite-size Lectures. on the use of your. Hewlett-Packard HP-10BII
Finance 2400 / 3200 / 3700 Lecture Notes for the Fall semester 2017 V.4 of Bite-size Lectures on the use of your Hewlett-Packard HP-10BII Financial Calculator Sven Thommesen 2017 Generated on 6/9/2017
More informationThe time value of money and cash-flow valuation
The time value of money and cash-flow valuation Readings: Ross, Westerfield and Jordan, Essentials of Corporate Finance, Chs. 4 & 5 Ch. 4 problems: 13, 16, 19, 20, 22, 25. Ch. 5 problems: 14, 15, 31, 32,
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 informationMATH 111 Worksheet 21 Replacement Partial Compounding Periods
MATH 111 Worksheet 1 Replacement Partial Compounding Periods Key Questions: I. XYZ Corporation issues promissory notes in $1,000 denominations under the following terms. You give them $1,000 now, and eight
More informationTexas Credit Opening/Closing Date: 7/19/08 08/18/08
Anatomy of a Credit Card Statement The following is a monthly statement from a typical credit card company. Parts left out intentionally are denoted by??? and highlighted in gray. Texas Credit Opening/Closing
More informationhp 12c financial calculator user's guide H Edition 5 HP Part Number 0012C-90001
hp 12c financial calculator user's guide H Edition 5 HP Part Number 0012C-90001 Notice THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED AS IS AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD
More informationIntroductory Financial Mathematics DSC1630
/2018 Tutorial Letter 202/1/2018 Introductory Financial Mathematics DSC130 Semester 1 Department of Decision Sciences Important Information: This tutorial letter contains the solutions of Assignment 02
More informationThe Monthly Payment. ( ) ( ) n. P r M = r 12. k r. 12C, which must be rounded up to the next integer.
MATH 116 Amortization One of the most useful arithmetic formulas in mathematics is the monthly payment for an amortized loan. Here are some standard questions that apply whenever you borrow money to buy
More informationThe Time Value of Money
CHAPTER 4 NOTATION r interest rate C cash flow FV n future value on date n PV present value; annuity spreadsheet notation for the initial amount C n cash flow at date n N date of the last cash flow in
More information5.3 Amortization and Sinking Funds
5.3 Amortization and Sinking Funds Sinking Funds A sinking fund is an account that is set up for a specific purpose at some future date. Typical examples of this are retirement plans, saving money for
More informationChapter 3 Mathematics of Finance
Chapter 3 Mathematics of Finance Section R Review Important Terms, Symbols, Concepts 3.1 Simple Interest Interest is the fee paid for the use of a sum of money P, called the principal. Simple interest
More informationSimple Interest: Interest earned on the original investment amount only. I = Prt
c Kathryn Bollinger, June 28, 2011 1 Chapter 5 - Finance 5.1 - Compound Interest Simple Interest: Interest earned on the original investment amount only If P dollars (called the principal or present value)
More informationExample. Chapter F Finance Section F.1 Simple Interest and Discount
Math 166 (c)2011 Epstein Chapter F Page 1 Chapter F Finance Section F.1 Simple Interest and Discount Math 166 (c)2011 Epstein Chapter F Page 2 How much should be place in an account that pays simple interest
More informationCopyright 2015 by the McGraw-Hill Education (Asia). All rights reserved.
Copyright 2015 by the McGraw-Hill Education (Asia). All rights reserved. Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple
More information- 1 = $ Notice the answer is a bit different from the calculator solution ($1,161,338.43) because we rounded the periodic rate.
Review Problems Note: Answers are in Appendix B. Solutions are on www.webbertext.com. uture value 1. he average growth rate for stocks over the last 75 years is reported to be about 11%, compounded annually.
More informationCOPYRIGHTED MATERIAL. Time Value of Money Toolbox CHAPTER 1 INTRODUCTION CASH FLOWS
E1C01 12/08/2009 Page 1 CHAPTER 1 Time Value of Money Toolbox INTRODUCTION One of the most important tools used in corporate finance is present value mathematics. These techniques are used to evaluate
More informationChapter 5. Interest Rates ( ) 6. % per month then you will have ( 1.005) = of 2 years, using our rule ( ) = 1.
Chapter 5 Interest Rates 5-. 6 a. Since 6 months is 24 4 So the equivalent 6 month rate is 4.66% = of 2 years, using our rule ( ) 4 b. Since one year is half of 2 years ( ).2 2 =.0954 So the equivalent
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concept Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value decreases. 2. Assuming positive
More informationIntroduction. Once you have completed this chapter, you should be able to do the following:
Introduction This chapter continues the discussion on the time value of money. In this chapter, you will learn how inflation impacts your investments; you will also learn how to calculate real returns
More information3.1 Simple Interest. Definition: I = Prt I = interest earned P = principal ( amount invested) r = interest rate (as a decimal) t = time
3.1 Simple Interest Definition: I = Prt I = interest earned P = principal ( amount invested) r = interest rate (as a decimal) t = time An example: Find the interest on a boat loan of $5,000 at 16% for
More informationH Edition 4 HP Part Number 0012C hp 12c financial calculator. user's guide. Downloaded from manuals search engine
hp 12c financial calculator user's guide H Edition 4 HP Part Number 0012C-90001 File name: hp 12c_user's guide_english_hdpmbf12e44 Page: 1 of 209 Printed Date: 2005/7/29 Notice REGISTER YOUR PRODUCT AT:
More informationFinancial Math Tutorial
SeeWhy Financial Learning recommends the Hewlett Packard (HP) 10B or HP 10B II. This calculator is easy to find, reasonably priced and very user friendly. However, you are free to use any financial calculator
More information3. 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
More informationFinancial institutions pay interest when you deposit your money into one of their accounts.
KEY CONCEPTS Financial institutions pay interest when you deposit your money into one of their accounts. Often, financial institutions charge fees or service charges for providing you with certain services
More informationOur Own Problems and Solutions to Accompany Topic 11
Our Own Problems and Solutions to Accompany Topic. A home buyer wants to borrow $240,000, and to repay the loan with monthly payments over 30 years. A. Compute the unchanging monthly payments for a standard
More informationCASH FLOW. Dr. Derek Farnsworth Assistant Professor
CASH FLOW Dr. Derek Farnsworth Assistant Professor The Beer Game Let s play a game to introduce some of the concepts of this section! Split into groups The Beer Game What happened? Where do agricultural
More informationTime Value of Money: A Self-test
Personal Finance: Another Perspective Time Value of Money: A Self-test Updated 2017-01-20 1 Objectives A. Understand the importance compound interest and time B. Pass an un-graded assessment test with
More informationChapter 15B and 15C - Annuities formula
Chapter 15B and 15C - Annuities formula Finding the amount owing at any time during the term of the loan. A = PR n Q Rn 1 or TVM function on the Graphics Calculator Finding the repayment amount, Q Q =
More informationMathematics of Finance
CHAPTER 55 Mathematics of Finance PAMELA P. DRAKE, PhD, CFA J. Gray Ferguson Professor of Finance and Department Head of Finance and Business Law, James Madison University FRANK J. FABOZZI, PhD, CFA, CPA
More informationIntroduction to the Compound Interest Formula
Introduction to the Compound Interest Formula Lesson Objectives: students will be introduced to the formula students will learn how to determine the value of the required variables in order to use the
More informationMath 373 Test 1 Spring 2015 February 17, 2015
Math 373 Test 1 Spring 2015 February 17, 2015 1. Hannah is the beneficiary of a trust that will pay her an annual payment of 10,000 with the first payment made twelve years from today. Once the payments
More information3. Time value of money
1 Simple interest 2 3. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationTime Value of Money. All time value of money problems involve comparisons of cash flows at different dates.
Time Value of Money The time value of money is a very important concept in Finance. This section is aimed at giving you intuitive and hands-on training on how to price securities (e.g., stocks and bonds),
More informationI. Warnings for annuities and
Outline I. More on the use of the financial calculator and warnings II. Dealing with periods other than years III. Understanding interest rate quotes and conversions IV. Applications mortgages, etc. 0
More informationName Date. Goal: Solve problems that involve simple interest. 1. term: The contracted duration of an investment or loan.
F Math 12 1.1 Simple Interest p.6 Name Date Goal: Solve problems that involve simple interest. 1. term: The contracted duration of an investment or loan. 2. interest (i): The amount of money earned on
More informationUnit 9 Financial Mathematics: Borrowing Money. Chapter 10 in Text
Unit 9 Financial Mathematics: Borrowing Money Chapter 10 in Text 9.1 Analyzing Loans Simple vs. Compound Interest Simple Interest: the amount of interest that you pay on a loan is calculated ONLY based
More informationUnit 9 Financial Mathematics: Borrowing Money. Chapter 10 in Text
Unit 9 Financial Mathematics: Borrowing Money Chapter 10 in Text 9.1 Analyzing Loans Simple vs. Compound Interest Simple Interest: the amount of interest that you pay on a loan is calculated ONLY based
More informationhp calculators HP 17bII+ Frequently Asked Questions
1. Q. Why are some functions shown on the keyboard in color? A. That is to distinguish them from the functions shown in white on the face of the key. If you press a key, you will activate that function
More informationAdvanced Mathematical Decision Making In Texas, also known as
Advanced Mathematical Decision Making In Texas, also known as Advanced Quantitative Reasoning Unit VI: Decision Making in Finance This course is a project of The Texas Association of Supervisors of Mathematics
More informationFoundations of Finance
GLOBAL EDITION Foundations of Finance The Logic and Practice of Financial Management EIGHTH EDITION Keown Martin Petty Editor in Chief: Donna Battista Acquisitions Editor: Katie Rowland Publisher, Global
More informationThe three formulas we use most commonly involving compounding interest n times a year are
Section 6.6 and 6.7 with finance review questions are included in this document for your convenience for studying for quizzes and exams for Finance Calculations for Math 11. Section 6.6 focuses on identifying
More information