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To solve the questions in this assignment, let’s break down the given details:

### Question 1 (Rocio's Investment):
Rocio invests $200 per month for 6 years in an account with a monthly compounded interest rate of 9% annually.

1. **Calculate the amount Rocio has after the first 6 years of deposits.**
   - Use the future value of an annuity formula:
     \[
     FV = P \cdot \frac{(1 + i)^n - 1}{i}
     \]
   - Here:
     - $ P = 200 $ (monthly deposit),
     - $ i = \frac{9\%}{12} = 0.0075 $ (monthly interest rate),
     - $ n = 6 \times 12 = 72 $ (total number of deposits over 6 years).

2. **Calculate the compounded amount after 12 more years.**
   - Use the future value of a single sum for 12 years with no additional deposits:
     \[
     FV = PV \cdot (1 + i)^n
     \]
   - Here:
     - $ PV $ is the amount from part 1,
     - $ i = 0.0075 $,
     - $ n = 12 \times 12 = 144 $.

3. **Calculate total deposits.**
   - This is simply $ 200 \times 72 $.

### Question 2 (Lucille's Investment):
Lucille starts depositing $200 per month only after the first 6 years, investing for 12 years with the same monthly compounded interest rate.

1. **Calculate the amount Lucille has after 12 years of deposits.**
   - Use the future value of an annuity with:
     - $ P = 200 $,
     - $ i = 0.0075 $,
     - $ n = 12 \times 12 = 144 $.

2. **Calculate total deposits.**
   - This is $ 200 \times 144 $.

Would you like me to calculate these values step-by-step? 

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### Follow-Up Questions:
1. How does the monthly interest rate affect the growth of the account over time?
2. What is the difference in final amount if Rocio continued depositing for the full 18 years?
3. How would a different interest rate (e.g., 6%) affect the calculations?
4. Can this model be applied to a different frequency of deposits, such as quarterly?
5. What would be the impact of inflation on the value of Rocio’s or Lucille’s savings?

### Tip:
Always double-check the interest rate's compounding frequency (e.g., monthly vs. annually) to ensure accurate calculations.

Rocio invests $200.00 a month for 6 years into an account earning 9% compounded monthly. After 6 years, she leaves the money, without making additional deposits, in the account for another 12 years. How much will she have in the end and what is the total amount of her deposits?

Lucille didn’t invest anything for the first 6 years, then deposited $200.00 a month for 12 years into an account earning 9% compounded monthly. How much will she have in the end and what is the total amount of her deposits?

Learn how to calculate the final amount and total deposits for payout annuities with monthly contributions and compound interest. Understand key concepts such as the future value of an annuity and compound interest, applied to scenarios of continuous deposits and deposits with a delay. Suitable for high school students studying finance or algebra.

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