Question

Perpetuities are also called annuities with an extended, or unlimited, life.

Based on your understanding of perpetuities, answer the following questions:

Which of the following are characteristics of a perpetuity? Check all that apply.

The value of a perpetuity is equal to the sum of the present value of its expected future cash flows.

The current value of a perpetuity is based more on the discounted value of its nearer (in time) cash flows and less by the discounted value of its more distant (in the future) cash flows.

A perpetuity is a stream of unequal cash flows.

A perpetuity is a stream of regularly timed, equal cash flows that continues forever.

Your grandfather wants to establish a scholarship in his father’s name at a local university and has stipulated that you will administer it. As you’ve committed to fund a $25,000 scholarship every year beginning one year from tomorrow, you’ll want to set aside the money for the scholarship immediately. At tomorrow’s meeting with your grandfather and the bank’s representative, you will need to deposit   (rounded to the nearest whole dollar) so that you can fund the scholarship forever—assuming that the account will earn 5.50% per annum every year.

Oops! The bank representative just reported that he misquoted the available interest rate on the scholarship’s account. Your account should earn 3.50%. The amount of your required deposit should be revised to .

This suggests there is relationship between the interest rate earned on the account and the present value of the perpetuity.

Answer 1

The correct choice is :- A perpetuity is a stream of regularly timed, equal cash flows that continues forever.

Explanation : - It is a constant stream of indentical cash flows that continues forever.

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Amount to set aside for the scholarship at a rate of 5.5% per annum = $ 25,000 0.0550

Amount to set aside for the scholarship = $ 454,545.45

Amount to set aside for the scholarship at a rate of 3.5% per annum = $ 25,000 0.035

Amount to set aside for the scholarship = $ 714,285.71