Find the savings plan balance after 12 months with an APR of 3% and monthly payments of $75.
              
                Assume monthly deposits and monthly compounding for the following savings plans.

To find the savings plan balance after 12 months with an APR of 3% and monthly payments of $75, we use the formula for the future value of a series of monthly deposits with compounding interest:

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

Where:
- $ FV $ is the future value or savings balance.
- $ P $ is the monthly payment (in this case, $75).
- $ r $ is the monthly interest rate (the annual rate divided by 12 months).
- $ n $ is the number of months (12 months in this case).

### Step 1: Calculate the monthly interest rate
Given the annual percentage rate (APR) of 3%, the monthly interest rate is:

\[
r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025
\]

### Step 2: Calculate the future value
Now, applying the values to the formula:

\[
FV = 75 \times \frac{(1 + 0.0025)^{12} - 1}{0.0025}
\]

Let's break it down:

1. Calculate $ (1 + 0.0025)^{12} $:

\[
(1 + 0.0025)^{12} = 1.030415
\]

2. Subtract 1 from that:

\[
1.030415 - 1 = 0.030415
\]

3. Divide by the monthly interest rate:

\[
\frac{0.030415}{0.0025} = 12.166
\]

4. Multiply by the monthly payment:

\[
75 \times 12.166 = 912.45
\]

### Final Answer:
The savings plan balance after 12 months is **$912.45**.

Would you like further details or have any questions about the steps?

Here are 5 related questions:
1. How does the future value change if the APR increases to 5%?
2. What happens to the future value if the monthly payment is doubled?
3. How does the compounding frequency affect the savings balance over time?
4. What is the future value after 24 months with the same conditions?
5. How can I calculate the balance if the interest compounds daily?

**Tip:** The higher the frequency of compounding (e.g., monthly vs. daily), the more interest you will earn over time.

Find the savings plan balance after 12 months with an APR of 3% and monthly payments of $75. Assume monthly deposits and monthly compounding for the following savings plans.

Learn how to calculate the savings plan balance after 12 months with an APR of 3% and monthly payments of $75. This solution covers the future value formula for monthly deposits and compounding interest, suitable for Grades 10-12.

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