Calculating Annuities Due.
Response to the following problem:
As discussed in the chapter text, an ordinary annuity assumes equal payments at the end of each period over the life of the annuity. An annuity due is the same thing except the payments occur at the beginning of each period instead. Thus, a three-year annual annuity due would have periodic payment cash flows occurring at Years 0, 1 and 2, whereas a three-year annual ordinary annuity would have periodic payment cash flows occurring at Years 1, 2 and 3. Suppose you are going to receive $10 000 per year for five years. The appropriate interest rate is 11%.
a. What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due?
b. Suppose you plan to invest the payments for five years. What is the future value of the payments if they are in the form of an ordinary annuity? What is the future value if the payments are an annuity due?
c. Which has the highest present value, the ordinary annuity or annuity due? Which has the highest future value, the ordinary annuity or annuity due? Will this always be true?