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 $3,800 invested for 29 years at 16 percent compounded annually grow to? ii. How many years will it take $250 to grow to $1,849.09 if it is invested at 8 percent compounded annually? iii. At what rate would $1,300 have to be invested to grow to $11,633.92 in 21 years?

d. Calculate the future sum of $1,500, given that it will be held in the bank for 5 years and earn 13 percent compounded semiannually.

e. What is an annuity due? How does this differ from an ordinary annuity?

f. What is the present value of an ordinary annuity of $2,600 per year for 21 years discounted back to the present at 15 percent? What would be the present value if it were an annuity due?

g. What is the future value of an ordinary annuity of $2,600 per year for 21 years compounded at 15 percent? What would be the future value if it were an annuity due?

h. You have just borrowed $290,000, and you agree to pay it back over the next 10 years in 10 equal end-of-year payments plus 11 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 $1,200 per year discounted back to the present at 14 percent?

j. What is the present value of an annuity of $1,100 per year for 10 years, with the first payment occurring at the end of year 10 (that is, ten $1,100 payments occurring at the end of year 10 through year 19), given a discount rate of 18 percent?

k. Given a discount rate of 16 percent, what is the present value of a perpetuity of $1,800 per year if the first payment does not begin until the end of year 10?