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To find the compounded amount for a deposit, we use the compound interest formula:

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

where:
- $ A $ is the amount of money accumulated after $ n $ years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ 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 for, in years.

Given the problem:
- $ P = 1000 $ dollars
- $ r = 0.04 $ (4% annual interest rate)
- $ n = 1 $ (compounded annually)
- $ t = 7 $ years

Plugging these values into the formula:

\[ A = 1000 \left(1 + \frac{0.04}{1}\right)^{1 \cdot 7} \]
\[ A = 1000 \left(1 + 0.04\right)^7 \]
\[ A = 1000 \left(1.04\right)^7 \]
\[ A = 1000 \times 1.316074 \]
\[ A \approx 1316.07 \]

So, the compounded amount after 7 years is approximately \$1316.07.

Would you like any further details or have any questions?

Here are 5 related questions:
1. How would the compounded amount change if the interest rate was 5% instead of 4%?
2. What would be the compounded amount if the interest were compounded semi-annually?
3. How does the number of compounding periods per year affect the total amount accumulated?
4. What is the formula for continuous compounding, and how does it differ from annual compounding?
5. How can we calculate the effective annual rate (EAR) from the nominal rate?

**Tip:** When dealing with compound interest problems, always ensure you convert the interest rate into a decimal before plugging it into the formula.

$1000 at 4% compounded annually for 7 years

Learn how to calculate the compounded amount for $1000 at a 4% annual interest rate compounded annually over 7 years. This example uses the compound interest formula and covers key financial math concepts suitable for students in Grades 9-12.

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