A generous benefactor to DePaul plans to make a one-time endowment which would generate $15,000 of income each year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment gift be? a) $300,000 O b) $3,000,000 c) $2,463,985 d) $1,500,000
A generous benefactor to DePaul plans to make a one-time endowment which would generate $15,000 of income each year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment gift be? a) $300,000 O b) $3,000,000 c) $2,463,985 d) $1,500,000
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
Related questions
Question
A generous benefactor to DePaul plans to make a one-time endowment which would generate $15,000 of income each year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment gift be?
(Please show work)
![### Endowment Calculation Problem
A generous benefactor to DePaul plans to make a one-time endowment which would generate $15,000 of income each year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment gift be?
#### Possible Answer Choices:
- a) $300,000
- b) $3,000,000
- c) $2,463,985
- d) $1,500,000
### Explanation:
To solve this problem, you need to use the formula for the perpetuity, which is:
\[ \text{Perpetuity Value} = \frac{\text{Annual Income}}{\text{Interest Rate}} \]
Given:
- Annual Income = $15,000
- Interest Rate = 5% or 0.05
Thus, the Perpetuity Value (Endowment Gift) would be:
\[ \text{Perpetuity Value} = \frac{15,000}{0.05} = 300,000 \]
Therefore, the correct answer is:
- **a) $300,000**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6ce828-7421-4579-a347-7b809a44673d%2F1df02e8e-f0c3-4042-8bc9-329d684f896f%2F6inxcum_processed.png&w=3840&q=75)
Transcribed Image Text:### Endowment Calculation Problem
A generous benefactor to DePaul plans to make a one-time endowment which would generate $15,000 of income each year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment gift be?
#### Possible Answer Choices:
- a) $300,000
- b) $3,000,000
- c) $2,463,985
- d) $1,500,000
### Explanation:
To solve this problem, you need to use the formula for the perpetuity, which is:
\[ \text{Perpetuity Value} = \frac{\text{Annual Income}}{\text{Interest Rate}} \]
Given:
- Annual Income = $15,000
- Interest Rate = 5% or 0.05
Thus, the Perpetuity Value (Endowment Gift) would be:
\[ \text{Perpetuity Value} = \frac{15,000}{0.05} = 300,000 \]
Therefore, the correct answer is:
- **a) $300,000**
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
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
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
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…
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