Which of the following are characteristics of a perpetuity? Check all that apply. O In a perpetuity, returns-in the form of a series of identical cash flows-are earned. O A perpetuity continues for a fixed time period. O The present value of a perpetuity is calculated by dividing the amount of the payment by the investor's opportunity interest rate. O A perpetuity is a series of regularly timed, equal cash flows that is assumed to continue indefinitely into the future.
Which of the following are characteristics of a perpetuity? Check all that apply. O In a perpetuity, returns-in the form of a series of identical cash flows-are earned. O A perpetuity continues for a fixed time period. O The present value of a perpetuity is calculated by dividing the amount of the payment by the investor's opportunity interest rate. O A perpetuity is a series of regularly timed, equal cash flows that is assumed to continue indefinitely into the future.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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
Transcribed Image Text:# Perpetuities: An Overview
Perpetuities, also known as **annuities with an extended or unlimited life**, are a critical concept in finance. Below is an exploration of their characteristics and application in determining the funding of a perpetual scholarship.
## Characteristics of a Perpetuity
- **Returns in perpetuity**: A perpetuity involves earning returns in the form of a series of identical cash flows.
- **Unlimited duration**: A perpetuity continues indefinitely, not for a fixed period.
- **Present value calculation**: The present value is determined by dividing the payment amount by the investor's opportunity interest rate.
## Scenario: Establishing a Scholarship Fund
Imagine you need to fund a $10,000 annual scholarship indefinitely. Assuming the account will earn an annual interest rate, you must deposit a specific amount now to ensure continuous funding.
### Calculation Steps
Given:
- Scholarship value: $10,000 annually
- Initial assumed interest rate: 6.00%
#### Choices for Deposit Amount:
- Option A: $166,667
- Option B: $160,667
- Option C: $233,334
- Option D: $133,334 *(initially selected)*
### Interest Rate Adjustment
After learning the actual interest rate is 4.75%, you should adjust your deposit amount:
- **Correct Value**: $210,526
## Relationship Insight
This adjustment shows the **inverse relationship** between the interest rate and the present value of the perpetuity. As the interest rate decreases, the required present value increases, emphasizing the significance of accurate rate estimations in financial planning.
This example demonstrates applying perpetuity concepts in real-world financial decisions, such as establishing scholarships or endowments.
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