Time Value of Money: Single Cash Flows Introduction

Time value of money (TVM) is the foundation of mathematical finance. This assignment is designed to show you how the TVM concept can be applied to corporate finance, as well as to personal finances. You will also learn various technical terms used in finance, such as discount rate, present value, and future value.

Instructions

Answer the following questions and complete the following problems, as applicable. Unless otherwise directed, assume annual compounding periods in computational problems.

You may solve the following problems algebraically, or you may use a financial calculator or Excel spreadsheet. If you choose to solve the problems algebraically, be sure to show your computations. If you use a financial calculator, show your input values. If you use an Excel spreadsheet, show your input values and formulas.

Note: In addition to your solution to each computational problem, you must show the supporting work leading to your solution to receive credit for your answer.

• Question 1:
  • Proficient-level: "List and describe the purpose of each part of a time line with an initial cash inflow and a future cash outflow. Which cash flows should be negative and which positive?" (Cornett, Adair, and Nofsinger, 2016, p. 95).
  • Distinguished-level: State the reason for showing both a negative and positive amount on the time line.
• Question 2:
  • Proficient-level: "How are the present value and future value related?" (Cornett, Adair, & Nofsinger, 2016, p. 95).
  • Distinguished-level: Explain why a dollar is worth more today than a dollar received a year from now.
• Question 3:
  • Proficient-level: "How are present values affected by changes in interest rates?" (Cornett, Adair, & Nofsinger, 2016, p. 95).
  • Distinguished-level: Explain how future values are affected by changes in interest rates.
• Question 4:
  • Proficient-level: "How much would be in your savings account in 11 years after depositing $150 today, if the bank pays 7 percent per year?" (Cornett, Adair, & Nofsinger, 2016).
    • Recalculate the savings account balance, using a 6 percent interest rate, and again, using an 8 percent interest rate.
  • Distinguished-level: Describe the relationship between changes in interest rates and the ensuing changes in future values.
• Question 5:
  • Proficient-level: "A deposit of $350 earns the following interest rates: (a) 8 percent in the first year, (b) 6 percent in the second year, and (c) 5.5 percent in the third year. What would be the third year future value?" (Cornett, Adair, & Nofsinger, 2016).
  • Distinguished-level: Explain why the future value is not calculated as the average of the annual interest rates.
• Question 6:
  • Proficient-level: "Compute the present value of a $850 payment made in 10 years when the discount rate is 12 percent" (Cornett, Adair, & Nofsinger, 2016, p. 96).
    • Recalculate the present value, using an 11-percent discount rate, and again, using a 13-percent discount rate.
  • Distinguished-level: Describe the relationship between changes in interest rates and the ensuing changes in present values.
• Question 7:
  • Proficient-level: "What annual rate of return is earned on a $5,000 investment when it grows to $9,500 in five years?" (Cornett, Adair, & Nofsinger, 2016, p. 97).
    • Recalculate the rate of return, assuming the growth occurred in four years, and again, assuming the growth occurred in six years.
  • Distinguished-level: Describe the relationship between changes in the amount of time and the changes in annual rate of return.

Submit your completed assignment as an attachment in the assignment area. You may use either a Word document or an Excel spreadsheet for your work, but not both. Prior to submitting your assignment, review the Time Value of Money: Single Cash Flows Scoring Guide to ensure you have met all of the requirements and as a self-assessment of your work.

Reference

Cornett, M. M., Adair, T. A., & Nofsinger J. (2016). M: Finance (3rd ed.). New York, NY: McGraw-Hill.

Part 2:

Time Value of Money: Annuity Cash Flows Introduction

In the previous assignment, you learned about the TVM concept as applied to single cash flow. However, in real life you come across financial applications that require multiple or annuity cash flows. In this assignment, you will apply the TVM concept to annuity cash flows; for example, how to amortize a mortgage or car loan.

Instructions

Answer the following questions and complete the following problems, as applicable. Unless otherwise directed, assume annual compounding periods in computational problems.

You may solve the following problems algebraically, or you may use a financial calculator or Excel spreadsheet. If you choose to solve the problems algebraically, be sure to show your computations. If you use a financial calculator, show your input values. If you use an Excel spreadsheet, show your input values and formulas.

Note: In addition to your solution to each computational problem, you must show the supporting work leading to your solution to receive credit for your answer.

• Question 1:
  • Proficient-level: Would you rather have a savings account that paid interest compounded on a monthly basis, or one that compounded interest on an annual basis? Why?
  • Distinguished-level: State why a borrower would prefer more, or less, frequent compounding periods.
• Question 2:
  • Proficient-level: What is an amortization schedule, and what are some of its uses?
  • Distinguished-level: Explain why more interest is incurred at the beginning of the amortization period than at the end of the amortization period.
• Question 3:
  • Proficient-level: "The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful in reducing taxes than in the later years?" (Cornett, Adair, & Nofsinger, 2016, p. 123).
  • Distinguished-level: Explain why the tax benefit of interest is even larger for longer-term loans?
• Question 4:
  • Proficient-level: What is the difference between an ordinary annuity and an annuity due?
  • Distinguished-level: Explain why the future value of an annuity due is greater than the future value of an ordinary annuity.
• Question 5:
  • Proficient-level: "What is the future value of a $900 annuity payment over five years if interest rates are 9 percent?" (Cornett, Adair, & Nofsinger, 2016).
    • Recalculate the future value at 8 percent interest, and again, at 10 percent interest.
  • Distinguished-level: Describe the relationship between changes in interest rates and the ensuing changes in future values.
• Question 6:
  • Proficient-level: "What is the present value of a $700 annuity payment over six years if interest rates are 10 percent?" (Cornett, Adair, & Nofsinger, 2016, p. 123).
    • Recalculate the present value at 9 percent interest, and again, at 11 percent interest.
  • Distinguished-level: Describe the relationship between changes in interest rates and the ensuing changes in present values.

Submit your completed assignment as an attachment in the assignment area. You may use either a Word document or an Excel spreadsheet for your work, but not both. Prior to submitting your assignment, review the Time Value of Money: Annuity Cash Flows Scoring Guide to ensure you have met all of the requirements and as a self-assessment of your work.

Reference

Cornett, M. M., Adair, T. A., & Nofsinger J. (2016). M: Finance (3rd ed.). New York, NY: McGraw-Hill.

I HAVE ATTACHED A DOCUMENT ON HINTS AND STRATEGIES TO USE WHEN ANSWERING THESE QUESTIONS.

Information relating to both Unit 2 Assignment: These Time Value of Money (TV$) chapters are CRITICALLY IMPORTANT CHAPTERS as they serve as the foundation for working problems and understanding certain concepts in future chapters of study in this course. Many learners find it necessary to read and review these two chapters multiple times. Also, to assist in the working certain time value of money problems, Excel worksheets have been included at the Course Tools tab, under: Discussions, Updates and Handouts. It is also strongly recommended you attend an SI session for this unit. Spending extra time in this unit will be time well spent! If you would like to learn or refresh your knowledge of Microsoft Excel, Capella has a tutorial for your use. At the top right of the initial iGuide page click on/select 'Tutorials,' then click on/select the spyglass icon that is the 'Search' field, then enter "Microsoft Tutorials." At the subsequent Results page, select the 'Microsoft Office Software-Capella University' link. Then, under the 'Basic Tips Sheet' caption, select the 'Basic Tasks in Excel' for the version of Excel you are using and proceed with the tutorial. u02 part 1 Hints/Suggestions In the u02a1 assignment, you are to respond to the various time value of money for a single cash flow questions. Make sure you review the scoring guide rubric to ensure you respond to both the Proficient and Distinguished levels to receive all possible points for each question/problem. Questions 4, 5, 6, and 7 entail working quantitative problems demonstrating your understanding of the time value of money concepts. You may solve these problems using algebraic formulas, a financial calculator, or an Excel spreadsheet. If you do not have a preference in approaching these problems, you might consider using the Excel spreadsheet method because examples of similar types of time value of money problems are reviewed in the Excel worksheet included at the Course Tools tab, under: Discussions, Updates and Handouts. (It is important that whatever method you select, you show your input variables ... in addition to stating the answer to the problem.) As stated above, the text reviews solving similar problems that are given in this assignment using various methods. Examples of similar types of time value of money problems are reviewed in the Excel worksheet for this assignment and are included at the Course Tools tab, under: Discussions, Updates and Handouts. You can use these Excel worksheets in solving the problems in this assignment. To help ensure you are on the right track, the following are some check figures for certain problems in the u02a1 assignment: u02a1 Question 4 - In this problem you are asked to calculate future values using three different interest rates. When asked to recalculate the problem using a 6% interest rate, here are some check point figures: Present value = 150; Interest rate = 6%; period of time = 11; and solving for Future Value (FV) you should obtain the correct answer of 284.74. (REMINDER: YOU ARE ALSO REQUIRED TO SHOW AND IDENTIFY THE KNOWN VARIABLES IN ORDER TO OBTAIN THIS CORRECT (FV); i.e., identify the amount of Present Value (PV), Interest Rate (I), and the Number of periods (N) used in order to solve for FV = 284.74 in this, and in all, quantitative problems.) So, how you would show your response to this part of question 4 (regardless of whether you used an algebraic formula, a financial calculator, or an Excel worksheet) would be as follows: "Answer is FV = 284.74; using PV =150; I = 6%; and N = 11." u02a1 Question 5 - The correct response for this problem falls between the range of $419.50 and $429.99. REMINDER, YOU ARE REQUIRED TO SHOW AND IDENTIFY THE KNOWN VARIABLES IN ORDER TO OBTAIN THE THIRD YEAR FUTURE VALUE AMOUNT. u02a1 Question 6 - In this problem you are asked to calculate present values using three different interest rates. When asked to recalculate the problem using an 11% discount (interest) rate, here are some check point figures: Future value = 850; Interest rate = 11%; period of time = 10; and solving for Present Value (PV) you should obtain the correct answer of 299.36. (REMINDER: YOU ARE ALSO REQUIRED TO SHOW AND IDENTIFY THE KNOWN VARIABLES IN ORDER TO OBTAIN THIS CORRECT PRESENT VALUE (PV) IN THIS, AND IN ALL, QUANTITATIVE PROBLEMS.) So, how you would show your response to this part of question 6 (regardless of whether you used an algebraic formula, a financial calculator, or an Excel worksheet) would be as follows: "Answer is: PV = 299.36; using FV =850; I = 11%; and N = 10." u02a1 Question 7 - In this problem you are asked to calculate the annual rate of return (I) using three different periods of time. When asked to recalculate the problem using a 4 year period of time, here are some check point figures: Present value = (-)5,000; Future value = 9,500; period of time = 4; and solving for the annual rate of return (I) you should obtain the correct answer of 17.41%. MAKE SURE YOUR SHOW YOUR ANNUAL RATE OF RETURN TO FOUR DECIMAL PLACES as is shown in the 17.41% response. (Reminder: you are also required to identify the known variables in order to obtain this Interest rate (I) in this and in all quantitative problems.) So, how you would show your response to this part of question 7 (regardless of whether you used an algebraic formula, a financial calculator, or an Excel worksheet) would be as follows: "Answer is I = 17.41%; using PV = (-)5,000; FV =9,500; and N = 4." To receive a Distinguished-level ranking for a question, you must completely and correctly respond to the Proficient-level question AND completely and correctly respond to the Distinguished-level question. Submit your completed assignment with your work document attached to the assignment. You may use either a Word document or an Excel spreadsheet for your work, but not both. However, it is preferred you submit your assignment as a Word document, and for those questions relating to solving a quantitative problem, simply list your input variables and the variable for which you have solved (as is shown above), and any other information relating to the problem, if applicable. ONLY ONE DOCUMENT ATTACHMENT PER ASSIGNMENT WILL BE ACCEPTED. u02 part 2 Hints/Suggestions In the u02a2 assignment, you are to respond to the various time value of money questions relating to annuities and multiple cash flows. Make sure you review the scoring guide rubric to ensure you respond to both the Proficient and Distinguished levels to receive all possible points for each question/problem. Questions 5 and 6 entail working quantitative problems demonstrating your understanding of the time value of money concepts of annuities. You may solve these problems using algebraic formulas, a financial calculator, or an Excel spreadsheet. If you do not have a preference in approaching these problems, you might consider using the Excel spreadsheet method because examples of similar types of time value of money problems are reviewed in the Excel worksheet included at the Course Tools tab, under: Discussions, Updates and Handouts. (It is critically important that whatever method you select, you must show your input variables ... in addition to stating the answer to the problem.) As stated above, the text reviews solving similar problems that are given in this assignment using various methods. Examples of similar types of time value of money problems are reviewed in the Excel worksheet for this assignment and are included at the Course Tools tab, under: Discussions, Updates and Handouts. You can use these Excel worksheets in solving the problems in this assignment. To help ensure you are on the right track, the following are some check figures for problems in the u02a2 assignment: u02a2 Question 5 - In this problem you are asked to calculate future values of an annuity payment using three different interest rates. When asked to recalculate the problem using an 8% interest rate, here are some check point figures: Payment = 900; Interest rate = 8%; period of time = 5; and solving for Future Value (FV) you should obtain the correct answer of 5,279.94. (REMINDER: YOU ARE ALSO REQUIRED TO SHOW AND IDENTIFY THE KNOWN VARIABLES IN ORDER TO OBTAIN THIS CORRECT (FV); i.e., show and identify the Payment (PMT), Interest Rate (I), and the Number of periods (N) used in order to solve for FV = 5,279.94 in this, and in all, quantitative problems.) So, how you would show your response to this part of question 5 (regardless of whether you used an algebraic formula, a financial calculator, or an Excel worksheet) would be as follows: "Answer is FV = 5,279.94; using Payment =900; I = 8%; and N =5." u02a2 Question 6 - In this problem you are asked to calculate present value of an annuity payment using three different interest rates. When asked to recalculate the problem using a 9% discount (interest) rate, here are some check point figures: Payment = 700; Interest rate = 9%; period of time = 6; and solving for Present Value (PV) you should obtain the correct answer of 3,140.14. (REMINDER: YOU ARE ALSO REQUIRED TO IDENTIFY THE KNOWN VARIABLES IN ORDER TO OBTAIN THIS CORRECT PRESENT VALUE (PV) IN THIS, AND IN ALL, QUANTITATIVE PROBLEMS.) So, how you would show your response to this part of question 6 (regardless of whether you used an algebraic formula, a financial calculator, or an Excel worksheet) would be as follows: "Answer is PV = 3,140.14; using Payment =700; I = 9%; and N =6." To receive a Distinguished-level ranking for a question, you must completely and correctly respond to the Proficient-level question AND completely and correctly respond to the Distinguished-level question. Submit your completed assignment with your work document attached to the assignment. You may use either a word document or an excel spreadsheet for your work, but not both. However, it is preferred you submit your assignment as a Word document, and for those questions relating to solving a quantitative problem, simply list your input variables and the variable for which you have solved, and any other information relating to the problem, if applicable. ONLY ONE DOCUMENT ATTACHMENT PER ASSIGNMENT WILL BE ACCEPTED. (More) Information relating to both Unit 2 Assignments: All questions/problems from the assignments can be responded to directly from the assignment page. Be advised on some questions/problems there are references citing our "M: Finance\" text by Cornett, Adair and Nofsinger text when an assignment uses a question/problem that has been used from the text. However, since some of the questions/problems have been modified, you do NOT need (and should not) go to the text to review the question/problem. Simply respond to all questions/problems directly from the listing on the assignment page. Question 1 Proficient-level: "List and describe the purpose of each part of a time line with an initial cash inflow and a future cash outflow. Which cash flows should be negative and which positive?" (Cornett, Adair, and Nofsinger, 2016, p. 95). Distinguished-level: State the reason for showing both a negative and positive amount on the time line. Cash flow timeline is usually the visual depiction of the inflows and the outflows which is relative to the period that is under consideration. Cash flows are generally illustrated above the cash flow line within which the corresponding periods that apply appearing under the cash flow diagram. Distinguished-level: State the reason for showing both a negative and positive amount on the time line. Inflows are represented by positive numbers and outflows by negative numbers. Question 2: Proficient-level: "How are the present value and future value related?" (Cornett, Adair, & Nofsinger, 2016, p. 95). Measures that relates the present values to the future values is the interest that rate i. and the present value can be easily moved forward with interest to arrive at the future value in time. ( Future value in N years FVN PV 1 i N ) Distinguished-level: Explain why a dollar is worth more today than a dollar received a year from now. Question 3: Proficient-level: "How are present values affected by changes in interest rates?" (Cornett, Adair, & Nofsinger, 2016, p. 95). Distinguished-level: Explain how future values are affected by changes in interest rates. Interest rates have the inverse relationship to the present values. Distinguished-level: Explain how future values are affected by changes in interest rates. Increases in the expected interest rates may result in the lower present values since future values are discounted at a relatively high rate so as to become smaller present values. Decreases in the expected interest rates can also result in the result in higher present values since the future values are usually discounted at the lower rate. Question 4: Proficient-level: "How much would be in your savings account in 11 years after depositing $150 today, if the bank pays 7 percent per year?" (Cornett, Adair, & Nofsinger, 2016). FV8 = 150 (1 + 0.07)8 = 150 1.71819 = 257.73 FV8 = 150 (1 + 0.06)8 = 150 1.59384 = 239.08 FV8 = 150 (1 + 0.08)8 = 150 1.85093 = 277.64 Question 5: Proficient-level: "A deposit of $350 earns the following interest rates: (a) 8 percent in the first year, (b) 6 percent in the second year, and (c) 5.5 percent in the third year. What would be the third year future value?" (Cornett, Adair, & Nofsinger, 2016). FV = PV (1 + i) (1 + j) (1 + k) FV = 350 (1 + 0.08) (1 + 0.06) (1 + 0.055) = 350 1.08 1.06 1.055 = 422.72 Question 6: Proficient-level: "Compute the present value of a $850 payment made in 10 years when the discount rate is 12 percent" (Cornett, Adair, & Nofsinger, 2016, p. 96). Recalculate the present value, using an 11-percent discount rate, and again, using a 13-percent discount rate. . PV = FV/(1+i)N PV = 850/(1+0.12)10 = 850/3.10585 = 273.68 Question 7: Proficient-level: "What annual rate of return is earned on a $5,000 investment when it grows to $9,500 in five years?" (Cornett, Adair, & Nofsinger, 2016, p. 97). Recalculate the rate of return, assuming the growth occurred in four years, and again, assuming the growth occurred in six years FVN = PV (1 + i)N 9,500 = 5,000 (1 + i)5 (1 + i)5 = 9500/5000 (1 + i)5 = 1.9 i = (1.9)(1/5) -1 = 0.137 or 13.7% FVN = PV (1 + i)N 9,500 = 5,000 (1 + i)4 (1 + i)4 = 9500/5000 (1 + i)4 = 1.9 i = (1.9)(1/4) -1 = 0.174 or 17.4% FVN = PV (1 + i)N 9,500 = 5,000 (1 + i)6 (1 + i)6 = 9500/5000 (1 + i)6 = 1.9 i = (1.9)(1/6) -1 = 0.113 or 11.3% Section 2 Question 1: Proficient-level: Would you rather have a savings account that paid interest compounded on a monthly basis, or one that compounded interest on an annual basis? Why? Distinguished-level: State why a borrower would prefer more, or less, frequent compounding periods. The all the more every now and again interest is paid, the all the more rapidly wealth will manufacture. Distinguished-level: State why a borrower would prefer more, or less, frequent compounding periods Interest that compounds month to month will become quicker than interest that compounds quarterly or yearly. Along these lines, to all the more rapidly get wealth, dependably picked the briefest compounding time frame you can. Question 2: Proficient-level: What is an amortization schedule, and what are some of its uses? An amortization schedule is usually a table that contain the details of the amount of each and every payment that is allocated to both the principal and interest. Every payment that is made on a loan is usually split in between the principal and the interest. An amortization schedule therefore provides the exact amount that is remaining on a loan after each of the payment is made. An amortization schedule is used for the purpose of mortgages, loan specifically on cars, and the other long-term debts. Distinguished-level: Explain why more interest is incurred at the beginning of the amortization period than at the end of the amortization period. More interest is therefore incurred at the beginning since the balance of the loan. Over a period of time, the interest is then paid down and more will be applied to the principal. Question 3: Proficient-level: "The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful in reducing taxes than in the later years?" (Cornett, Adair, & Nofsinger, 2016, p. 123). Distinguished-level: Explain why the tax benefit of interest is even larger for longer-term loans? Mortgage payments in the beginning of any amortization schedule are usually just interest that is with little principal. Generally, interest payments can decline and principal payments may make up an ever increasing part of the payments. Distinguished-level: Explain why the tax benefit of interest is even larger for longer-term loans Hence the tax deductible portion is larger in the beginning the years. Question 4: Proficient-level: What is the difference between an ordinary annuity and an annuity due? The difference between annuity due and ordinary annuity is the timing of the payments. Ordinary annuity payments are at the end of each period while the annuity due payments are usually at the beginning of each period. Distinguished-level: Explain why the future value of an annuity due is greater than the future value of an ordinary annuity The FV of an AD is usually greater since the length of time before the payment allows for the interest to compound. Question 5: Proficient-level: "What is the future value of a $900 annuity payment over five years if interest rates are 9 percent?" (Cornett, Adair, & Nofsinger, 2016). Recalculate the future value at 8 percent interest, and again, at 10 percent interest. 1 0.09 5 1 $900 5.9847 $5,386.23 FVA 5 $900 FVA 5 0.09 5 1 0.08 1 $900 $900 5.2148 $4,693.28 0.08 1 0.10 5 1 $900 6.1051 $5,494.59 FVA 5 $900 0.10 Distinguished-level: Describe the relationship between changes in interest rates and the ensuing changes in future values. As interest rates increase with FVA, the value increases. Question 6: Proficient-level: "What is the present value of a $700 annuity payment over six years if interest rates are 10 percent?" (Cornett, Adair, & Nofsinger, 2016, p. 123). Recalculate the present value at 9 percent interest, and again, at 11 percent interest. 1 1 6 1 0 . 10 $700 4.35526070 $3,048.68 PVA $700 6 0.10 1 1 6 1 0.09 $700 4.48591859 $3,140.14 PVA $700 6 0.09 1 1 6 1 0.11 $700 4.2305378536 $2,961.38 PVA $700 6 0.11 Distinguished-level: Describe the relationship between changes in interest rates and the ensuing changes in present values As interest rates increase with PVA, the value decreases. Question 1 Proficient-level: "List and describe the purpose of each part of a time line with an initial cash inflow and a future cash outflow. Which cash flows should be negative and which positive?" (Cornett, Adair, and Nofsinger, 2016, p. 95). Distinguished-level: State the reason for showing both a negative and positive amount on the time line. Cash flow timeline is usually the visual depiction of the inflows and the outflows which is relative to the period that is under consideration. Cash flows are generally illustrated above the cash flow line within which the corresponding periods that apply appearing under the cash flow diagram. Distinguished-level: State the reason for showing both a negative and positive amount on the time line. Inflows are represented by positive numbers and outflows by negative numbers. Question 2: Proficient-level: "How are the present value and future value related?" (Cornett, Adair, & Nofsinger, 2016, p. 95). Measures that relates the present values to the future values is the interest that rate i. and the present value can be easily moved forward with interest to arrive at the future value in time. ( Future value in N years FVN PV 1 i N ) Distinguished-level: Explain why a dollar is worth more today than a dollar received a year from now. Question 3: Proficient-level: "How are present values affected by changes in interest rates?" (Cornett, Adair, & Nofsinger, 2016, p. 95). Distinguished-level: Explain how future values are affected by changes in interest rates. Interest rates have the inverse relationship to the present values. Distinguished-level: Explain how future values are affected by changes in interest rates. Increases in the expected interest rates may result in the lower present values since future values are discounted at a relatively high rate so as to become smaller present values. Decreases in the expected interest rates can also result in the result in higher present values since the future values are usually discounted at the lower rate. Question 4: Proficient-level: "How much would be in your savings account in 11 years after depositing $150 today, if the bank pays 7 percent per year?" (Cornett, Adair, & Nofsinger, 2016). FV8 = 150 (1 + 0.07)8 = 150 1.71819 = 257.73 FV8 = 150 (1 + 0.06)8 = 150 1.59384 = 239.08 FV8 = 150 (1 + 0.08)8 = 150 1.85093 = 277.64 Question 5: Proficient-level: "A deposit of $350 earns the following interest rates: (a) 8 percent in the first year, (b) 6 percent in the second year, and (c) 5.5 percent in the third year. What would be the third year future value?" (Cornett, Adair, & Nofsinger, 2016). FV = PV (1 + i) (1 + j) (1 + k) FV = 350 (1 + 0.08) (1 + 0.06) (1 + 0.055) = 350 1.08 1.06 1.055 = 422.72 Question 6: Proficient-level: "Compute the present value of a $850 payment made in 10 years when the discount rate is 12 percent" (Cornett, Adair, & Nofsinger, 2016, p. 96). Recalculate the present value, using an 11-percent discount rate, and again, using a 13-percent discount rate. . PV = FV/(1+i)N PV = 850/(1+0.12)10 = 850/3.10585 = 273.68 Question 7: Proficient-level: "What annual rate of return is earned on a $5,000 investment when it grows to $9,500 in five years?" (Cornett, Adair, & Nofsinger, 2016, p. 97). Recalculate the rate of return, assuming the growth occurred in four years, and again, assuming the growth occurred in six years FVN = PV (1 + i)N 9,500 = 5,000 (1 + i)5 (1 + i)5 = 9500/5000 (1 + i)5 = 1.9 i = (1.9)(1/5) -1 = 0.137 or 13.7% FVN = PV (1 + i)N 9,500 = 5,000 (1 + i)4 (1 + i)4 = 9500/5000 (1 + i)4 = 1.9 i = (1.9)(1/4) -1 = 0.174 or 17.4% FVN = PV (1 + i)N 9,500 = 5,000 (1 + i)6 (1 + i)6 = 9500/5000 (1 + i)6 = 1.9 i = (1.9)(1/6) -1 = 0.113 or 11.3% Section 2 Question 1: Proficient-level: Would you rather have a savings account that paid interest compounded on a monthly basis, or one that compounded interest on an annual basis? Why? Distinguished-level: State why a borrower would prefer more, or less, frequent compounding periods. The all the more every now and again interest is paid, the all the more rapidly wealth will manufacture. Distinguished-level: State why a borrower would prefer more, or less, frequent compounding periods Interest that compounds month to month will become quicker than interest that compounds quarterly or yearly. Along these lines, to all the more rapidly get wealth, dependably picked the briefest compounding time frame you can. Question 2: Proficient-level: What is an amortization schedule, and what are some of its uses? An amortization schedule is usually a table that contain the details of the amount of each and every payment that is allocated to both the principal and interest. Every payment that is made on a loan is usually split in between the principal and the interest. An amortization schedule therefore provides the exact amount that is remaining on a loan after each of the payment is made. An amortization schedule is used for the purpose of mortgages, loan specifically on cars, and the other long-term debts. Distinguished-level: Explain why more interest is incurred at the beginning of the amortization period than at the end of the amortization period. More interest is therefore incurred at the beginning since the balance of the loan. Over a period of time, the interest is then paid down and more will be applied to the principal. Question 3: Proficient-level: "The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful in reducing taxes than in the later years?" (Cornett, Adair, & Nofsinger, 2016, p. 123). Distinguished-level: Explain why the tax benefit of interest is even larger for longer-term loans? Mortgage payments in the beginning of any amortization schedule are usually just interest that is with little principal. Generally, interest payments can decline and principal payments may make up an ever increasing part of the payments. Distinguished-level: Explain why the tax benefit of interest is even larger for longer-term loans Hence the tax deductible portion is larger in the beginning the years. Question 4: Proficient-level: What is the difference between an ordinary annuity and an annuity due? The difference between annuity due and ordinary annuity is the timing of the payments. Ordinary annuity payments are at the end of each period while the annuity due payments are usually at the beginning of each period. Distinguished-level: Explain why the future value of an annuity due is greater than the future value of an ordinary annuity The FV of an AD is usually greater since the length of time before the payment allows for the interest to compound. Question 5: Proficient-level: "What is the future value of a $900 annuity payment over five years if interest rates are 9 percent?" (Cornett, Adair, & Nofsinger, 2016). Recalculate the future value at 8 percent interest, and again, at 10 percent interest. 1 0.09 5 1 $900 5.9847 $5,386.23 FVA 5 $900 FVA 5 0.09 5 1 0.08 1 $900 $900 5.2148 $4,693.28 0.08 1 0.10 5 1 $900 6.1051 $5,494.59 FVA 5 $900 0.10 Distinguished-level: Describe the relationship between changes in interest rates and the ensuing changes in future values. As interest rates increase with FVA, the value increases. Question 6: Proficient-level: "What is the present value of a $700 annuity payment over six years if interest rates are 10 percent?" (Cornett, Adair, & Nofsinger, 2016, p. 123). Recalculate the present value at 9 percent interest, and again, at 11 percent interest. 1 1 6 1 0 . 10 $700 4.35526070 $3,048.68 PVA $700 6 0.10 1 1 6 1 0.09 $700 4.48591859 $3,140.14 PVA $700 6 0.09 1 1 6 1 0.11 $700 4.2305378536 $2,961.38 PVA $700 6 0.11 Distinguished-level: Describe the relationship between changes in interest rates and the ensuing changes in present values As interest rates increase with PVA, the value decreases