Pam and Tim decide to start saving money for their daughter's college education. They open a college savings 529 plan with a $350 initial investment and next month start to make monthly deposits of $110. If the account pays 7% compounded monthly, how much will the account be worth after 180 deposits? Be sure to include the initial investment in the computation. Round the answer to two decimal places.

To calculate the value of the account after 180 months, we can break the problem into two parts:

1. **Initial investment growth**: The $350 initial investment will grow with compound interest over the 180 months.
2. **Monthly deposit growth**: Each $110 deposit will earn interest as well, compounded monthly.

### 1. Growth of Initial Investment:
The future value $FV_{\text{initial}}$ of the initial investment after 180 months is given by the compound interest formula:

\[
FV_{\text{initial}} = P \times \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- $P = 350$ (initial investment),
- $r = 0.07$ (annual interest rate),
- $n = 12$ (compounded monthly),
- $t = 180/12 = 15$ years.

### 2. Growth of Monthly Deposits:
For the monthly deposits, we use the future value of an annuity formula:

\[
FV_{\text{deposits}} = D \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}
\]
where:
- $D = 110$ (monthly deposit),
- $r = 0.07$ (annual interest rate),
- $n = 12$ (compounded monthly),
- $t = 15$ years.

Now, let's compute both parts.

### Total Future Value:
The total future value of the account is the sum of the future values of the initial investment and the monthly deposits:

\[
FV_{\text{total}} = FV_{\text{initial}} + FV_{\text{deposits}}
\]

I'll calculate that now.The total value of the college savings account after 180 months (including the initial investment and monthly deposits) will be approximately **$35,862.98**.

Would you like further details on any part of this calculation?

Here are 5 related questions to deepen your understanding:
1. How does the compounding frequency affect the final value of the account?
2. What would happen if the interest rate were lower, say 5% instead of 7%?
3. How much of the final value is contributed by the initial investment alone?
4. What if Pam and Tim wanted to make larger monthly deposits? How would that affect the total?
5. How does the number of months affect the final account balance if deposits continue?

**Tip:** When saving for long-term goals, the earlier you start, the more you benefit from compound interest.

Learn how to calculate the future value of a college savings 529 plan with a $350 initial investment and monthly $110 deposits, compounded monthly at a 7% annual interest rate. The detailed step-by-step solution covers compound interest and annuity formulas. Suitable for high school students in Grades 10-12.

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