The formula to calculate the final balance in the account is:

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

Where:

• $A$ is the final amount (balance),
• $P$ is the principal (initial deposit),
• $r$ is the annual interest rate (in decimal form),
• $n$ is the number of times per year the interest is compounded,
• $t$ is the time in years.

Given:

• $P = 400.00$,
• $r = 0.05$ (5% expressed as a decimal),
• $n = 1$ (compounded annually),
• $t = 2$ years.

Substitute the values into the formula:

$A = 400 \left(1 + \frac{0.05}{1}\right)^{1 \cdot 2}$

Simplify:

$A = 400 \left(1 + 0.05\right)^2$

$A = 400 \left(1.05\right)^2$

$A = 400 \cdot 1.1025$

$A = 440.99$

Final Answer:

The balance after 2 years is $440.99.

Would you like me to provide more details or clarify any part? 😊

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Here are 5 related questions to explore:

1. How would the balance change if the interest were compounded semi-annually?
2. What is the interest earned after 2 years in this scenario?
3. How does the formula work for a different principal amount, say $500?
4. How much time would it take for the balance to double at the same interest rate?
5. What happens to the balance if the annual interest rate is increased to 6%?

Tip: Always double-check if the interest is compounded annually, semi-annually, or quarterly; this greatly affects the result.