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

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

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (the initial money invested).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the number of years the money is invested or borrowed for.

Given:

• $P = 19,000$ dollars
• $r = 3\% = 0.03$
• $n = 1$ (since the interest is compounded annually)
• $t = 8$ years

The formula simplifies to:

$A = 19,000 \left(1 + \frac{0.03}{1}\right)^{1 \times 8}$

$A = 19,000 \left(1 + 0.03\right)^{8}$

$A = 19,000 \times (1.03)^8$

Now, we calculate:

$A = 19,000 \times 1.26677 \approx 24,068.63$

Rounding this to the nearest hundred dollars:

$A \approx 24,100$

Final Answer: After 8 years, Lucy would have approximately $24,100 in the account.

Would you like more details on any part of this solution? Here are some additional questions you could explore:

1. What if the interest were compounded quarterly instead of annually?
2. How would the outcome change if the interest rate were 4% instead of 3%?
3. What would be the balance after 5 years instead of 8 years?
4. How much interest would be earned in total after 8 years?
5. What is the formula for continuous compounding, and how would it apply here?

Tip: When rounding, remember to consider whether you're rounding up or down based on the decimal value.