Mullins Rose
07/22/2024 · Middle School
You deposit \( \$ 2000 \) in an account earning \( 6 \% \) interest compounded continuously. How much will you have in the account in 15 years?
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To calculate the amount in an account with continuous compounding interest, we can use the formula:
\[
A = Pe^{rt}
\]
where:
- \( A \) is the amount of money accumulated after time \( t \),
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the annual interest rate (in decimal),
- \( t \) is the time the money is invested or borrowed for, in years,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
Given:
- \( P = 2000 \)
- \( r = 0.06 \) (which is \( 6\% \) expressed as a decimal)
- \( t = 15 \)
Now, we can substitute these values into the formula:
\[
A = 2000 \cdot e^{0.06 \cdot 15}
\]
Calculating \( 0.06 \cdot 15 \):
\[
0.06 \cdot 15 = 0.9
\]
Now, we can calculate \( e^{0.9} \):
\[
e^{0.9} \approx 2.4596
\]
Now, substituting this back into the formula:
\[
A \approx 2000 \cdot 2.4596 \approx 4919.20
\]
Thus, the amount in the account after 15 years will be approximately:
\[
\boxed{4919.20}
\]
Quick Answer
The amount in the account after 15 years will be approximately \$4919.20.
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit