To solve this problem, we can use the formula for the future value of a series of monthly deposits with compound interest:

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

Where:

• $A$ is the future value of the account after the deposits and interest,
• $P$ is the monthly deposit amount ($300),
• $r$ is the monthly interest rate (annual rate divided by 12),
• $n$ is the total number of deposits (number of months),
• $t$ is the number of years.

Step 1: Identify the variables

• $P = 300$ (monthly deposit),
• Annual interest rate = 8%, so monthly interest rate $r = \frac{8\%}{12} = \frac{0.08}{12} = 0.00667$,
• $n = 25 \times 12 = 300$ months (for 25 years).

Step 2: Apply the formula

$A = 300 \times \left( \frac{(1 + 0.00667)^{300} - 1}{0.00667} \right)$

Now, we can calculate the result:

1. $(1 + 0.00667)^{300} = (1.00667)^{300} \approx 6.84848$
2. Subtract 1: $6.84848 - 1 = 5.84848$
3. Divide by the interest rate: $\frac{5.84848}{0.00667} \approx 876.78$
4. Multiply by the monthly deposit: $300 \times 876.78 \approx 263,034$

Final Answer:

You will have approximately $263,034 in the account after 25 years.

Would you like more details on any step or have further questions?

Here are some related questions:

1. How would the total change if you deposit for 30 years instead?
2. What if the interest rate was 6% instead of 8%?
3. How much of the total amount comes from the interest earned?
4. What would the final amount be with quarterly compounding?
5. How would a one-time lump sum deposit compare to monthly deposits over time?

Tip: Increasing the deposit frequency (e.g., biweekly instead of monthly) can slightly increase the final balance due to more frequent compounding.