Use the compound interest formula to determine the accumulated balance after the stated period.
​$7000 invested at an APR of 5​% for 5 years.
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Part 1
If interest is compounded​ annually, what is the amount of money after 5 ​years?
​$
  
enter your response here
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To calculate the accumulated balance using compound interest, we can apply the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $A$ is the amount of money after the interest is applied (the accumulated balance).
- $P$ is the principal amount (initial investment).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.

Given:
- $P = 7000$ (initial investment),
- $r = 0.05$ (5% annual interest rate),
- $n = 1$ (since the interest is compounded annually),
- $t = 5$ years.

Now, we substitute these values into the formula:

\[
A = 7000 \left(1 + \frac{0.05}{1}\right)^{1 \times 5}
\]
\[
A = 7000 \left(1 + 0.05\right)^5
\]
\[
A = 7000 \times (1.05)^5
\]

Let me calculate that.It seems there was an issue with the calculation. Let's try calculating the result manually.

\[
A = 7000 \times (1.05)^5
\]

Calculating $ (1.05)^5 $:

\[
(1.05)^5 = 1.2762815625
\]

Now, multiplying by the principal amount:

\[
A = 7000 \times 1.2762815625 = 8933.97
\]

So, the accumulated amount after 5 years is approximately **$8,933.97**.

Would you like further clarification or details on this? Here are some follow-up questions:

1. What happens if the interest is compounded monthly instead of annually?
2. How does the formula change if the interest is compounded continuously?
3. What is the total interest earned after 5 years?
4. How would the accumulated balance change if the APR was 6% instead of 5%?
5. What would happen if the investment duration increased to 10 years?

**Tip:** Always make sure to convert the percentage to a decimal (by dividing by 100) before using it in the compound interest formula.

Use the compound interest formula to determine the accumulated balance after the stated period. $7000 invested at an APR of 5% for 5 years. If interest is compounded annually, what is the amount of money after 5 years? (Do not round until the final answer. Then round to the nearest cent as needed.)

Learn how to calculate the accumulated balance using the compound interest formula for a $7000 investment at an APR of 5% over 5 years. This problem demonstrates exponential growth through compounding, a key concept in finance and algebra. Suitable for students in Grades 9-12.

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