Find the capital value of a fort at a strategic location, where the annual rent is $750,000, paid in perpetuity, and the interest rate is 8% compounded continuously. The capital value is $
Find the capital value of a fort at a strategic location, where the annual rent is $750,000, paid in perpetuity, and the interest rate is 8% compounded continuously. The capital value is $
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Calculating Capital Value of a Fort Using Perpetuity**
Consider a scenario where we need to evaluate the capital value of a fort positioned at a strategic location. The fort yields an annual rent of $750,000, which is paid in perpetuity. The interest rate applicable is 8%, compounded continuously.
To calculate the capital value, we utilize the formula for the present value of a perpetuity.
**Formula:**
\[ \text{Present Value of Perpetuity} = \frac{A}{r} \]
Where:
- \( A \) is the annual rent ($750,000 in this case)
- \( r \) is the interest rate (8% or 0.08)
**Application:**
\[ \text{Capital Value} = \frac{750,000}{0.08} \]
Calculating the above expression, we get the capital value of the fort as:
\[ \text{Capital Value} = \$9,375,000 \]
Therefore, the capital value of the fort is **$9,375,000**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F756689fc-aa25-4045-a342-f553545a40f2%2F9a2ac848-d9ea-462c-87ad-45d7c4813c69%2F5agx94_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating Capital Value of a Fort Using Perpetuity**
Consider a scenario where we need to evaluate the capital value of a fort positioned at a strategic location. The fort yields an annual rent of $750,000, which is paid in perpetuity. The interest rate applicable is 8%, compounded continuously.
To calculate the capital value, we utilize the formula for the present value of a perpetuity.
**Formula:**
\[ \text{Present Value of Perpetuity} = \frac{A}{r} \]
Where:
- \( A \) is the annual rent ($750,000 in this case)
- \( r \) is the interest rate (8% or 0.08)
**Application:**
\[ \text{Capital Value} = \frac{750,000}{0.08} \]
Calculating the above expression, we get the capital value of the fort as:
\[ \text{Capital Value} = \$9,375,000 \]
Therefore, the capital value of the fort is **$9,375,000**.
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