For your job as the business reporter for a local newspaper, you are given the task of putting together a series of articles that explain the power of the time value of money to your readers. Your editor would like you to address several specific questions in addition to demonstrating for the readership the use of time value of money techniques by applying them to several problems. What would be your response to the following memorandum from your editor? To: Business Reporter From: Perry White, Editor, Daily Planet Re: Upcoming Series on the Importance and Power of the Time Value of Money In your upcoming series on the time value of money, I would like to make sure you cover several specific points. In addition, before you begin this assignment, I want to make sure we are all reading from the same script, as accuracy has always been the cornerstone of the Daily Planet. In this regard, I'd like a response to the following questions before we proceed: a. What is the relationship between discounting and compounding? b. What is the relationship between the present-value factor and the annuity present-value factor? c. i. What will $5,100 invested for 27 years at 11 percent compounded annually grow to? ii. How many years will it take $450 to grow to $2,442.34 if it is invested at 7 percent compounded annually? iii. At what rate would $1,900 have to be invested to grow to $9,712.20 in 28 years? d. Calculate the future sum of $1,600, given that it will be held in the bank for 15 years and earn 17 percent compounded semiannually. e. What is an annuity due? How does this differ from an ordinary annuity? bordir f. What is the present value of an ordinary annuity of $2,300 per year for 17 years discounted back to the present at 17 percent? What would be the present value if it were an annuity due? ver g. What is the future value of an ordinary annuity of $2,300 per year for 17 years compounded at 17 percent? What would be the future value if it were an annuity due? v. h. You have just borrowed $110,000, and you agree to pay it back over the next 30 years in 30 equal end-of-year payments plus 16 percent compound interest on the unpaid balance. What will be the size of these payments? i. What is the present value of a perpetuity of $1,300 per year discounted back to the present at 7 percent? j. What is the present value of an annuity of $1,800 per year for 10 years, with the first payment occurring at the end of year 10 (that is, ten $1,800 payments occurring at the end of year 10 through year 19), given a discount rate of 8 percent? k. Given a discount rate of 9 percent, what is the present value of a perpetuity of $1,200 per year if the first payment does not begin until the end of year 10
