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To solve the given problem, we need to:

1. **Determine the periodic deposit** required to reach the financial goal using the future value formula for a series of monthly deposits with compound interest.
   
2. **Determine how much of the financial goal comes from the deposits themselves and how much comes from interest.**

### a. Formula to Determine the Periodic Deposit:
The future value $ FV $ of a series of monthly payments can be calculated using the future value of an annuity formula:

\[
FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}
\]

Where:
- $ FV $ is the future value (financial goal), $ 180,000 $
- $ P $ is the periodic deposit (what we need to find)
- $ r $ is the annual interest rate (5.5% or 0.055)
- $ n $ is the number of times the interest is compounded per year (monthly, so $ n = 12 $)
- $ t $ is the number of years (12 years)

Rearranging the formula to solve for $ P $:

\[
P = \frac{FV}{\frac{(1 + r/n)^{nt} - 1}{r/n}}
\]

### b. Contribution from Deposits and Interest:
- **Deposits**: The total amount deposited is simply $ P \times \text{number of payments} $.
- **Interest**: The interest is the difference between the financial goal and the total deposits.

Let me calculate the values.### Results:
a. **Periodic Deposit**:  
The required monthly deposit is approximately **$885.31**.

b. **Contribution Breakdown**:  
- Total deposits made over 12 years: **$127,484.63**  
- Interest earned: **$52,515.37**

Would you like further clarification on this calculation or any of its components?

Here are 5 related questions for deeper understanding:
1. How would the periodic deposit change if the interest rate were higher?
2. What is the impact of increasing the compounding frequency (e.g., daily instead of monthly)?
3. How does the length of time affect the total interest earned?
4. What if the deposits were made at the beginning of each month instead of the end?
5. How would the financial goal change if the deposits were reduced by half?

**Tip:** The power of compounding increases significantly with more frequent contributions, leading to larger growth in the long run.

a. Use the appropriate formula to determine the periodic deposit.

b. How much of the financial goal comes from deposits and how much comes from interest?

Periodic Deposit: $? at the end of each month
Rate: 5.5% compounded monthly
Time: 12 years
Financial Goal: $180,000

Learn how to calculate the required monthly deposit to reach a financial goal of $180,000 in 12 years, with 5.5% compounded monthly interest. Understand how much of the goal comes from deposits versus interest using the Future Value of an Annuity formula.

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