Question

6. Perpetuities

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.

A. A perpetuity is a series of regularly timed, equal cash flows that is assumed to continue indefinitely into the future.

B. The principal amount of a perpetuity is repaid as a lump-sum amount.

C. The present value of a perpetuity is calculated by dividing the amount of the payment by the investor’s opportunity interest rate.

D. In a perpetuity, returns—in the form of a series of identical cash flows—are earned.

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 $10,000 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 6.00% 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 4.75%. 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

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ANSWER:

In a perpetuity returns in the form of a series of identical cash flows are earned.

A perpetuity is a series of regularly timed equal cash flows that is assumed to continue indefinitely into the future.

The present value of a perpetuity is calculated by dividing the amount of the payment by the investor's opportunity interest rate.

2nd part.

you will need to deposit $181,818..

working: annual payment / interest rate

=>10,000/5.50%

=>$181,818.

3rd part.

deposit should be revised to $285,714.

working:

$10,000 / 3.50%.

4th part

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

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