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To solve this problem, we need to use the formula for the future value of a compound interest account with regular deposits. Since Pam and Tim are making monthly deposits with an initial investment, we need to account for both the compound interest and the monthly contributions.

The formula for future value $A$ with compound interest and monthly deposits is:

\[
A = P(1 + r/n)^{nt} + \dfrac{D \left( (1 + r/n)^{nt} - 1 \right)}{r/n}
\]

Where:
- $A$ is the future value of the account
- $P$ is the initial investment
- $r$ is the annual interest rate (7% = 0.07)
- $n$ is the number of times the interest is compounded per year (12, since it's compounded monthly)
- $t$ is the time in years
- $D$ is the monthly deposit
- $r/n$ is the monthly interest rate
- $nt$ is the total number of compounding periods

### Given:
- $P = 350$ (initial investment)
- $D = 110$ (monthly deposit)
- $r = 0.07$ (annual interest rate)
- $n = 12$ (monthly compounding)
- Total number of deposits is 180, so $t = 180 / 12 = 15$ years.

We will plug the values into the formula to calculate the future value of the account.

Let me calculate that for you.The future value of Pam and Tim's college savings account after 180 deposits, including the initial investment and monthly deposits, is **$35,862.98**.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What would happen if the interest rate increased to 8% annually?
2. How would the future value change if they made 240 monthly deposits instead of 180?
3. What if they only made an initial investment with no monthly deposits—how would the calculation change?
4. How would the future value be affected if the interest compounded annually instead of monthly?
5. What would be the future value if the monthly deposit was increased to $150?

**Tip:** Understanding how compounding frequency affects the future value can help you optimize savings plans. The more frequently the interest compounds, the greater the account growth.

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.

Calculate how much Pam and Tim's 529 college savings plan will be worth after 180 monthly deposits with an initial investment of $350 and 7% interest compounded monthly. Learn how compound interest affects long-term savings and see the step-by-step solution.

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