https://file.aiquickdraw.com/mathbot/file/17272136963919tnhtxl9.jpg

To solve this problem, we can use the formula for compound interest:

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

Where:
- $A$ is the future value of the investment/loan, including interest.
- $P$ is the principal investment amount (the initial deposit or loan amount).
- $r$ is the annual interest rate (decimal).
- $n$ is the number of times that interest is compounded per year.
- $t$ is the time the money is invested or borrowed for, in years.

Given values from the image:
- $P = 8,000$ (initial investment)
- $r = 7\%$ (annual interest rate, which is 0.07 in decimal)
- $n = 4$ (since the interest is compounded quarterly)
- $t = 6$ years

Let's calculate the future value, $A$, using these values.The future value of the $8,000 investment, compounded quarterly at 7% interest for 6 years, is **$12,131.54**.

Would you like more details on this calculation or have any questions?

Here are some related questions to expand on this topic:
1. How does the frequency of compounding affect the future value?
2. What would the future value be if the interest was compounded annually instead?
3. How does the future value change if the interest rate increases to 8%?
4. Can you calculate the future value for different durations, such as 10 years?
5. How does continuous compounding differ from quarterly compounding?

**Tip**: More frequent compounding periods (e.g., quarterly vs. annually) result in higher future values due to interest being applied more often.

Calculate the future value of $8,000 earning 7% interest compounded quarterly for 6 years.

Learn how to calculate the future value of an $8,000 investment, with 7% interest compounded quarterly over 6 years. This problem involves using the compound interest formula and covers key concepts like exponential growth. Ideal for high school students in Grades 10-12.

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