Find the future value for a $85,000 investment for 15 years at a compounded continuously at 5%.
Find the future value for a $85,000 investment for 15 years at a compounded continuously at 5%.
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 future value for a $85,000 investment for 15 years at a continuously compounded rate of 5%.
**Answer Attempt:**
$176708.89 (marked as incorrect).
**Explanation:**
In this exercise, you're tasked with determining the future value of a given investment using the formula for continuous compounding. The continuous compounding formula is:
\[ FV = Pe^{rt} \]
Where:
- \( FV \) is the future value of the investment.
- \( P \) is the principal amount ($85,000 in this case).
- \( r \) is the annual interest rate (5% or 0.05).
- \( t \) is the time the money is invested for (15 years).
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
The provided solution of $176708.89 seems to be incorrect based on the continuous compounding calculation.
**Graph/Diagram Analysis:**
No graphs or diagrams are present in this image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57a80892-6d38-4c33-b12d-e676cd98c4f8%2F04e416e4-457d-4fd4-873a-75197ad9bdc6%2Fy40u3un_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the future value for a $85,000 investment for 15 years at a continuously compounded rate of 5%.
**Answer Attempt:**
$176708.89 (marked as incorrect).
**Explanation:**
In this exercise, you're tasked with determining the future value of a given investment using the formula for continuous compounding. The continuous compounding formula is:
\[ FV = Pe^{rt} \]
Where:
- \( FV \) is the future value of the investment.
- \( P \) is the principal amount ($85,000 in this case).
- \( r \) is the annual interest rate (5% or 0.05).
- \( t \) is the time the money is invested for (15 years).
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
The provided solution of $176708.89 seems to be incorrect based on the continuous compounding calculation.
**Graph/Diagram Analysis:**
No graphs or diagrams are present in this image.
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