How long does it take for $4825 to double if it is invested at 9 % compounded continuously? Round your answer to two decimal places. Answer How to enter your answer (opens in new window) years Kaypa Keyboard Shortc
How long does it take for $4825 to double if it is invested at 9 % compounded continuously? Round your answer to two decimal places. Answer How to enter your answer (opens in new window) years Kaypa Keyboard Shortc
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Financial Mathematics: Continuous Compounding**
**Problem Statement:**
Determine the time period required for an investment of $4825 to double, assuming a continuous compounding interest rate of 9%. Be sure to round your answer to two decimal places.
**Solution Format:**
- Type your answer in the provided text box.
- Enter the time period in years.
- Click "Submit Answer" once you have completed the calculation.
**Instructions:**
To solve this problem, use the formula for continuous compounding:
\[ A = Pe^{rt} \]
Where:
- \( A \) is the amount of money accumulated after time \( t \), including interest.
- \( P \) is the principal amount (initial investment).
- \( e \) is the base of the natural logarithm.
- \( r \) is the annual interest rate (in decimal form).
- \( t \) is the time in years.
Since the goal is to double the investment, set \( A = 2P \) and solve for \( t \):
\[ 2P = Pe^{0.09t} \]
Divide both sides by \( P \):
\[ 2 = e^{0.09t} \]
Take the natural logarithm of both sides:
\[ \ln(2) = 0.09t \]
Solve for \( t \):
\[ t = \frac{\ln(2)}{0.09} \]
Calculate the value of \( t \) and round it to two decimal places to find the time required for the investment to double.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2dd91b83-9757-4690-9b37-5d4650824402%2F7b603f2a-eef9-4d5a-8998-ebf597b48921%2Figqk04a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Financial Mathematics: Continuous Compounding**
**Problem Statement:**
Determine the time period required for an investment of $4825 to double, assuming a continuous compounding interest rate of 9%. Be sure to round your answer to two decimal places.
**Solution Format:**
- Type your answer in the provided text box.
- Enter the time period in years.
- Click "Submit Answer" once you have completed the calculation.
**Instructions:**
To solve this problem, use the formula for continuous compounding:
\[ A = Pe^{rt} \]
Where:
- \( A \) is the amount of money accumulated after time \( t \), including interest.
- \( P \) is the principal amount (initial investment).
- \( e \) is the base of the natural logarithm.
- \( r \) is the annual interest rate (in decimal form).
- \( t \) is the time in years.
Since the goal is to double the investment, set \( A = 2P \) and solve for \( t \):
\[ 2P = Pe^{0.09t} \]
Divide both sides by \( P \):
\[ 2 = e^{0.09t} \]
Take the natural logarithm of both sides:
\[ \ln(2) = 0.09t \]
Solve for \( t \):
\[ t = \frac{\ln(2)}{0.09} \]
Calculate the value of \( t \) and round it to two decimal places to find the time required for the investment to double.
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