Find the savings plan balance after 12 months with an APR of 8​% and monthly payments of ​$300.

To find the savings plan balance after 12 months with an APR of 8% and monthly payments of $300, we can use the future value of an ordinary annuity formula:

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

Where:
- $FV$ is the future value (the balance after 12 months),
- $P$ is the monthly payment ($300),
- $r$ is the monthly interest rate (APR divided by 12),
- $n$ is the total number of payments (12 months).

### Step-by-step solution:

1. **Convert APR to monthly interest rate**:
   \[
   r = \frac{8\%}{12} = \frac{0.08}{12} = 0.00667
   \]

2. **Total number of payments**:
   \[
   n = 12 \, \text{months}
   \]

3. **Calculate the future value**:
   \[
   FV = 300 \times \left( \frac{(1 + 0.00667)^{12} - 1}{0.00667} \right)
   \]

Let me calculate this for you.The savings plan balance after 12 months with an APR of 8% and monthly payments of $300 will be approximately **$3,734.98**.

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:
1. How would the balance change if the APR were 6% instead of 8%?
2. What would the balance be after 24 months with the same APR and payment?
3. How does increasing the monthly payment to $400 affect the final balance?
4. What is the impact of making one extra payment of $300 at the start of the period?
5. How would the calculation change if payments were made at the beginning of each month instead of the end?

**Tip**: The earlier and more frequently you make payments into a savings plan, the more you benefit from compound interest!

Discover how to calculate the future savings plan balance after 12 months with an 8% APR and $300 monthly payments. This guide walks through the steps using the future value of an ordinary annuity formula, covering key financial and compound interest concepts. Ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation