To calculate the final balance in Lamar's account, we will use the formula for compound interest:

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

Where:

• $A$ is the final amount in the account.
• $P$ is the principal (initial deposit), which is $4,000.
• $r$ is the annual interest rate as a decimal, so $r = 0.01$ for 1%.
• $n$ is the number of times interest is compounded per year. Since it is compounded annually, $n = 1$.
• $t$ is the number of years the money is left to grow, so $t = 9$.

Now, we can plug these values into the formula:

$A = 4000 \left( 1 + \frac{0.01}{1} \right)^{1 \times 9}$

$A = 4000 \left( 1 + 0.01 \right)^9$

$A = 4000 \times (1.01)^9$

Next, calculate $(1.01)^9$:

$(1.01)^9 \approx 1.0935$

Now, multiply this by the principal amount:

$A = 4000 \times 1.0935 \approx 4374.00$

So, the balance in the account after 9 years is approximately $4,374.00.

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Would you like further explanation on any part of the calculation?

Here are some related questions for you to explore:

1. How does changing the interest rate affect the final amount in a compound interest account?
2. What would happen if the interest were compounded monthly instead of annually?
3. How would the final balance change if the money were invested for 10 years instead of 9?
4. What is the difference between compound interest and simple interest?
5. How do you calculate compound interest when the interest rate is greater than 100%?

Tip: When working with compound interest, the more frequently the interest is compounded (like monthly or daily), the higher the final amount will be due to the "compounding effect."