Find the accumulated present value of an investment over a 9 year period if there is a continuous money flow of $6,000 per year and the interest rate is 0.6% compounded continuously.
Find the accumulated present value of an investment over a 9 year period if there is a continuous money flow of $6,000 per year and the interest rate is 0.6% compounded continuously.
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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Question
![**Problem Statement:**
Find the accumulated present value of an investment over a 9-year period if there is a continuous money flow of $6,000 per year and the interest rate is 0.6% compounded continuously.
**Solution:**
To find the accumulated present value (APV) of a continuous income stream compounded continuously, we use the formula:
\[ \text{APV} = \int_{0}^{T} C \cdot e^{-rt} \, dt \]
Where:
- \( C \) is the continuous cash flow per year ($6,000),
- \( r \) is the interest rate (0.006 as a decimal),
- \( T \) is the time in years (9 years).
**Graph/Diagram Explanation:**
N/A (There are no graphs or diagrams to explain in the provided image).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e51674d-3d29-4cb4-94ad-529601d10286%2Fdf4c6766-e2d9-48f1-a331-0daf8bbe4d9c%2Fz4t7qv_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the accumulated present value of an investment over a 9-year period if there is a continuous money flow of $6,000 per year and the interest rate is 0.6% compounded continuously.
**Solution:**
To find the accumulated present value (APV) of a continuous income stream compounded continuously, we use the formula:
\[ \text{APV} = \int_{0}^{T} C \cdot e^{-rt} \, dt \]
Where:
- \( C \) is the continuous cash flow per year ($6,000),
- \( r \) is the interest rate (0.006 as a decimal),
- \( T \) is the time in years (9 years).
**Graph/Diagram Explanation:**
N/A (There are no graphs or diagrams to explain in the provided image).
![Suppose the demand function for a product is given by the function:
\[ D(q) = -0.016q + 56 \]
Find the Consumer's Surplus corresponding to \( q = 1,450 \) units.
(Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at \( q = 3,500 \).)
Answer: [ ] dollars](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e51674d-3d29-4cb4-94ad-529601d10286%2Fdf4c6766-e2d9-48f1-a331-0daf8bbe4d9c%2F3ybmry8_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose the demand function for a product is given by the function:
\[ D(q) = -0.016q + 56 \]
Find the Consumer's Surplus corresponding to \( q = 1,450 \) units.
(Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at \( q = 3,500 \).)
Answer: [ ] dollars
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