are considering two equally risky annuities, each of which pays $5,000 per year for 10 years.Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due.Which of the following statements is CORRECT?
A)The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.
B)The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
C)The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
D)The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.
E)If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.

Question

Quizplus · Accepted Answer

The present value of an annuity due will always be greater than the present value of an ordinary annuity due to the fact that each payment is received one period earlier. Therefore, the present value of DUE exceeds the present value of ORD. Additionally, since the two annuities are equally risky and offer the same payments and duration, the only difference between the two is the timing of payments. Therefore, the future value of DUE will also exceed the future value of ORD. Option D is the only choice that reflects both of these facts.

Option E is incorrect because the difference between the present values of the two annuities will decrease as the interest rate decreases, as the value of earlier cash flows increase at a lower interest rate.

Are Considering Two Equally Risky Annuities, Each of Which Pays