Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Related questions
Question
thumb_up100%
![**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.](https://content.bartleby.com/qna-images/question/2dd91b83-9757-4690-9b37-5d4650824402/7b603f2a-eef9-4d5a-8998-ebf597b48921/igqk04a_processed.jpeg)
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps
Knowledge Booster
Similar questions
- ??arrow_forwardYou invest $4000 in an account with an APR of 3% and daily compounding. How much will you have after 5 years? Round to the nearest hundredth.arrow_forwardAlexi made monthly contributions of $450 to his retirement account that earns interest at a rate of 5%/year compounded monthly for 25 years. At the age of 50 he needed to stop contributions to help his parents financially. He made no additional contributions and no withdrawals for the next 15 years, but the money in the account continued to earn interest. How much money is in his account when he turns 65? Use units and context in your answer, round to two decimal places.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSON
Contemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning 
Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSON
Introduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education