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
Section: Chapter Questions
Problem 1PS
icon
Related questions
Question
I need help with the (((((((red)))))) check marks..
# 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.
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Techniques of Time Value Of Money
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Essentials Of Investments
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
FUNDAMENTALS OF CORPORATE FINANCE
FUNDAMENTALS OF CORPORATE FINANCE
Finance
ISBN:
9781260013962
Author:
BREALEY
Publisher:
RENT MCG
Financial Management: Theory & Practice
Financial Management: Theory & Practice
Finance
ISBN:
9781337909730
Author:
Brigham
Publisher:
Cengage
Foundations Of Finance
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
ISBN:
9780077861759
Author:
Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:
McGraw-Hill Education