We appreciate your visit to Find the balance if 3600 is invested at an annual interest rate of 6 for 8 years compounded continuously. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the balance of an investment compounded continuously, we use the formula for continuous compounding:
[tex]\[ A = P \times e^{(rt)} \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form).
- [tex]\( t \)[/tex] is the time the money is invested for, in years.
- [tex]\( e \)[/tex] is the base of the natural logarithm (approximately equal to 2.71828).
Given:
- The principal amount [tex]\( P \)[/tex] is [tex]$3600.
- The annual interest rate \( r \) is 6%, which is 0.06 in decimal form.
- The time \( t \) is 8 years.
Substitute these values into the formula:
\[ A = 3600 \times e^{(0.06 \times 8)} \]
Calculate the exponent:
\[ 0.06 \times 8 = 0.48 \]
Now, calculate \( e^{0.48} \).
Finally, multiply the result by 3600 to find the balance.
After performing the calculations using continuous compounding, the balance comes out to be approximately $[/tex]5817.87.
So, the balance after 8 years with continuous compounding is about $5817.87.
[tex]\[ A = P \times e^{(rt)} \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form).
- [tex]\( t \)[/tex] is the time the money is invested for, in years.
- [tex]\( e \)[/tex] is the base of the natural logarithm (approximately equal to 2.71828).
Given:
- The principal amount [tex]\( P \)[/tex] is [tex]$3600.
- The annual interest rate \( r \) is 6%, which is 0.06 in decimal form.
- The time \( t \) is 8 years.
Substitute these values into the formula:
\[ A = 3600 \times e^{(0.06 \times 8)} \]
Calculate the exponent:
\[ 0.06 \times 8 = 0.48 \]
Now, calculate \( e^{0.48} \).
Finally, multiply the result by 3600 to find the balance.
After performing the calculations using continuous compounding, the balance comes out to be approximately $[/tex]5817.87.
So, the balance after 8 years with continuous compounding is about $5817.87.
Thanks for taking the time to read Find the balance if 3600 is invested at an annual interest rate of 6 for 8 years compounded continuously. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
