When an initial amount of p dollars is invested at r% annual interest compounded m times per year, the value of the account (4) after years is given by the equation mt A-P(1 + =) ** m Write an equation that represents the value in an account that starts out with an initial investment of $13,000 and pays 16% interest compounded monthly. The equation that represents the value of the account is A = 1 + 8º. X
When an initial amount of p dollars is invested at r% annual interest compounded m times per year, the value of the account (4) after years is given by the equation mt A-P(1 + =) ** m Write an equation that represents the value in an account that starts out with an initial investment of $13,000 and pays 16% interest compounded monthly. The equation that represents the value of the account is A = 1 + 8º. X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![### Compound Interest Formula
When an initial amount of \( P \) dollars is invested at \( r\% \) annual interest compounded \( m \) times per year, the value of the account \( (A) \) after \( t \) years is given by the equation:
\[ A = P \left(1 + \frac{r}{m}\right)^{mt} \]
### Example Calculation
Write an equation that represents the value in an account that starts out with an initial investment of \$13,000 and pays 16% interest compounded monthly.
#### Solution
Given:
- Initial investment, \( P = \$13,000 \)
- Annual interest rate, \( r = 16\% = 0.16 \)
- Number of times interest is compounded per year, \( m = 12 \) (monthly)
Substitute these values into the compound interest formula:
\[ A = 13000 \left(1 + \frac{0.16}{12}\right)^{12t} \]
Therefore, the equation that represents the value of the account is:
\[ A = 13000 \left(1 + \frac{0.16}{12}\right)^{12t} \]
### Diagrams and Graphs
- Diagram and graph details were not applicable in this context, as the instruction did not include any visual content requiring detailed explanation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf54cc92-fe70-42ec-a5a5-6c03b8447a69%2F06e916ec-956e-4560-825e-0202d3e73a87%2Fr3o6s2f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Compound Interest Formula
When an initial amount of \( P \) dollars is invested at \( r\% \) annual interest compounded \( m \) times per year, the value of the account \( (A) \) after \( t \) years is given by the equation:
\[ A = P \left(1 + \frac{r}{m}\right)^{mt} \]
### Example Calculation
Write an equation that represents the value in an account that starts out with an initial investment of \$13,000 and pays 16% interest compounded monthly.
#### Solution
Given:
- Initial investment, \( P = \$13,000 \)
- Annual interest rate, \( r = 16\% = 0.16 \)
- Number of times interest is compounded per year, \( m = 12 \) (monthly)
Substitute these values into the compound interest formula:
\[ A = 13000 \left(1 + \frac{0.16}{12}\right)^{12t} \]
Therefore, the equation that represents the value of the account is:
\[ A = 13000 \left(1 + \frac{0.16}{12}\right)^{12t} \]
### Diagrams and Graphs
- Diagram and graph details were not applicable in this context, as the instruction did not include any visual content requiring detailed explanation.
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