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This question involves compound interest, where the investor deposits $1,000 at an annual interest rate of 5%, compounded yearly, and wants to know the amount after 7 years.

The formula for compound interest is:

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

Where:
- $A$ is the amount of money accumulated after $t$ years, including interest.
- $P$ is the principal amount (the initial deposit).
- $r$ is the annual interest rate (decimal).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.

In this case:
- $P = 1000$
- $r = 5\% = 0.05$
- $n = 1$ (since the interest is compounded annually)
- $t = 7$

Substituting the values into the formula:

\[
A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \times 7}
\]

\[
A = 1000 \left(1.05\right)^{7}
\]

Now, we can calculate the final amount. Let me do that for you. Given values
P = 1000  # Principal amount
r = 0.05  # Annual interest rate
n = 1  # Compounded yearly
t = 7  # Time in years

# Calculating the final amount using the compound interest formula
A = P * (1 + r/n)**(n*t)
AAfter 7 years, the amount in the account will be approximately $1,407.10.

Would you like further details on how the calculation works or have any other questions? Here are some related questions for your learning:

1. How does changing the interest rate affect the final amount in compound interest?
2. What would the final amount be if the interest were compounded semi-annually?
3. How would the result differ if the principal amount was doubled?
4. What is the difference between compound interest and simple interest?
5. How can you calculate the time required for an investment to double using compound interest?

**Tip:** The more frequently the interest is compounded, the higher the final amount will be, as interest is calculated on the accumulated interest as well.

An investor deposits $1000 in an account that promises an annual interest rate of 5% compounded at the end of each year. How much will be in the account after seven years?

Learn how to calculate compound interest with $1000 deposited at a 5% annual interest rate for 7 years. This step-by-step explanation includes the formula A = P(1 + r/n)^(nt), suitable for Grades 9-12 students.

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