Question

Which of the following comparison statements is (are) true?

I. An annuity has equal payments, a perpetuity does not.
II. Both an annuity and a perpetuity have equal payments.
III. An annuity covers a longer period of time than a perpetuity.
IV. An annuity has a constant rate of return, a perpetuity does not.

Answer 1

The statement that both annuities and perpetuities have equal payments is true. Annuities have a fixed duration, whereas perpetuities last indefinitely. The statement about rate of return being constant is generally false for both.

Step-by-step explanation:

In finance, both annuities and perpetuities are types of cash flows to investors. In response to the comparison statements:

1. An annuity has equal payments, a perpetuity does not. - False. Both annuities and perpetuities typically have equal periodic payments.
2. Both an annuity and a perpetuity have equal payments. - True. The defining feature of both is that they have regular, equal payments.
3. An annuity covers a longer period of time than a perpetuity. - False. A perpetuity is an annuity that continues forever, i.e., it has no end, while an annuity has a fixed end period.
4. An annuity has a constant rate of return, a perpetuity does not. - False. The rate of return can vary in both annuities and perpetuities, it depends on the underlying agreement and cannot be generalized in this way.

Therefore, the only true statement among the ones provided is that both an annuity and a perpetuity have equal payments.