a) What is the relationship between discounting and compounding?

b) Does present value decrease at a linear rate, at an increasing rate, or at a decreasing rate with the discount rate? Why?

c) What is the relationship between the present-value factor and the annuity present-value factor?

d) 1. What will $5,000 invested for 10 years at 8 percent compounded annually grow to?

2. How many years will it take $400 to grow to $1,671 if it is invested at 10 percent compounded annually?

3. At what rate would $1,000 have to be invested to grow to $4,046 in 10 years?

e) Calculate the future sum of $1,000, given that it will be held in the bank for 5 years and earn 10 percent compounded semiannually.

f) What is an annuity due? How does this differ from an ordinary annuity?