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

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

Where:
- $A$ is the amount in the account after interest.
- $P$ is the principal (initial amount), which is $800.
- $r$ is the annual interest rate (in decimal form), so 5% becomes $0.05$.
- $n$ is the number of times interest is compounded per year (since it's compounded quarterly, $n = 4$).
- $t$ is the time the money is invested for in years, which is 7 years.

Let's plug in the values:

\[
A = 800 \left(1 + \frac{0.05}{4}\right)^{4 \times 7}
\]

This simplifies to:

\[
A = 800 \left(1 + 0.0125\right)^{28} = 800 \left(1.0125\right)^{28}
\]

Now, let's calculate the value of $A$.The total amount in the account after 7 years, with quarterly compounding, will be approximately **$1,132.79**.

Would you like further details or have any questions about this calculation?

Here are some follow-up questions:
1. What happens to the total amount if the interest rate increases to 6%?
2. How does the result change if the compounding is done monthly instead of quarterly?
3. What would be the total amount if the investment period was only 5 years instead of 7 years?
4. How does continuous compounding differ from quarterly compounding?
5. What formula should be used if interest is compounded annually instead of quarterly?

**Tip:** When dealing with compound interest, small changes in the interest rate or compounding frequency can lead to significant differences in the final amount.

Find the amount in the account for the given principal, interest rate, time, and compounding period. P = $800, r = 5%, t = 7 years; compounded quarterly.

Learn how to calculate compound interest for a principal of $800 with an interest rate of 5% compounded quarterly over 7 years. This problem involves the compound interest formula and exponential growth, making it suitable for high school students in Grades 10-12.

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