Suppose someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years. One is an ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is most correct?
a.
The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due.
b.
The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity.
c.
The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.
d.
If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same.
e.
Answers a and d are correct.

The answer is: B) The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity.

Explanation:

An ordinary annuity is a sequence of periodic cash flows that occur at regular intervals over a number of periods.

An annuity due is a sequence of periodic cash flows occurring at the end of each period overtime, with the first payment being done at the present time.

An annuity due has a higher NPV simply because the first payment is done immediately, and money earned now is worth more than money earned later. The future value of the annuity due will be lower simply because it already made the payments.

An example would be income from rent (annuity due) received every first day of the month (higher NPV) versus interest earned in a cash deposit which will be collected at the end of the period (higher future value).