Use the savings plan formula to calculate the balance after 12 months for an APR of 12% and monthly payments of $900. *Round to the nearest cent*

The savings plan formula is:

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

Where:
- $ A $ = future balance
- $ P $ = monthly payment
- $ r $ = monthly interest rate
- $ n $ = number of payments

### Given:
- Annual Percentage Rate (APR) = 12% = 0.12
- Monthly payment ($P$) = $900
- Number of payments ($n$) = 12 months

### Step 1: Convert the annual rate to a monthly rate
\[
r = \frac{APR}{12} = \frac{0.12}{12} = 0.01
\]

### Step 2: Substitute the values into the formula
\[
A = 900 \times \frac{{(1 + 0.01)^{12} - 1}}{0.01}
\]

Now I'll calculate the result.The balance after 12 months, with an APR of 12% and monthly payments of $900, is **$11,414.25**, rounded to the nearest cent.

Do you want further details or have any questions?

Here are five related questions to deepen your understanding:
1. What would the balance be if the APR was reduced to 6%?
2. How does increasing the monthly payment affect the final balance?
3. How can we adjust the formula if payments are made biweekly instead of monthly?
4. What if the savings plan is compounded daily rather than monthly?
5. How does the length of time saving (e.g., 24 months) affect the total amount accumulated?

**Tip:** The key factor influencing compound savings is the interest rate and the frequency of compounding. The more often the interest is compounded, the more you save.

Use the savings plan formula to calculate the balance after 12 months for an APR of 12% and monthly payments of $900. *Round to the nearest cent*

Learn how to calculate the balance of a savings plan after 12 months, with an APR of 12% and monthly payments of $900. This example uses the savings plan formula, covering concepts like compound interest and algebraic calculations. Suitable for students in Grades 10-12.

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