To calculate the total amount in the account at the end of 18 years, we use the Future Value of an Ordinary Annuity formula:

$FV = P \cdot \frac{(1 + r)^n - 1}{r}$

Where:

• $P$ = annual deposit = $600$
• $r$ = annual interest rate = $7.7\% = 0.077$
• $n$ = number of years = $18$

Step-by-step Calculation:

1. Calculate $(1 + r)^n$: $(1 + 0.077)^{18} = 1.077^{18} \approx 4.031019$

2. Subtract 1 from $(1 + r)^n$: $4.031019 - 1 = 3.031019$

3. Divide the result by $r$: $\frac{3.031019}{0.077} \approx 39.3641$

4. Multiply by $P$: $600 \cdot 39.3641 \approx 23618.46$

Final Answer:

$\text{The total amount in the account is } 23618.46.$

Let me know if you'd like a detailed breakdown of these steps or have further questions. Here are some related questions for further exploration:

1. What is the formula for the future value of an ordinary annuity, and how does it differ from a present value calculation?
2. How does compounding frequency affect the final amount in a savings account?
3. If the interest rate increased to 8%, how much would be in the account after 18 years?
4. What would happen if deposits were made at the beginning of the year instead of the end?
5. How does the future value change if deposits were only made for 15 years?

Tip: Always double-check the interest rate's compounding frequency to ensure accurate calculations.