Find the present value for a $85,000 investment for 11 years at a compounded continuously at 4.2%.
Find the present value for a $85,000 investment for 11 years at a compounded continuously at 4.2%.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
Find the present value for a $85,000 investment for 11 years at a compounded continuously at 4.2%.
**Solution:**
To find the present value of an investment compounded continuously, we use the formula:
\[ PV = FV \times e^{-rt} \]
where:
- \( PV \) is the present value
- \( FV \) is the future value ($85,000)
- \( e \) is the base of the natural logarithm (approximately 2.71828)
- \( r \) is the annual interest rate (4.2% or 0.042)
- \( t \) is the time in years (11 years)
Plug in the values to compute the present value:
\[ PV = 85000 \times e^{-0.042 \times 11} \]
Calculate the exact value to find the present value.
**Graph/Diagram Explanation:**
There are no graphs or diagrams in the image provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57a80892-6d38-4c33-b12d-e676cd98c4f8%2F8332a7a4-a3e5-43e1-bcae-6948844c6e3d%2Fgzzru7_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the present value for a $85,000 investment for 11 years at a compounded continuously at 4.2%.
**Solution:**
To find the present value of an investment compounded continuously, we use the formula:
\[ PV = FV \times e^{-rt} \]
where:
- \( PV \) is the present value
- \( FV \) is the future value ($85,000)
- \( e \) is the base of the natural logarithm (approximately 2.71828)
- \( r \) is the annual interest rate (4.2% or 0.042)
- \( t \) is the time in years (11 years)
Plug in the values to compute the present value:
\[ PV = 85000 \times e^{-0.042 \times 11} \]
Calculate the exact value to find the present value.
**Graph/Diagram Explanation:**
There are no graphs or diagrams in the image provided.
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