Find the savings plan balance after 18 months with an APR of 2% and monthly payments of ​$300.
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Part 1
The balance is ​$enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To calculate the balance of a savings plan after 18 months with an Annual Percentage Rate (APR) of 2% and monthly payments of $300, we can use the **future value of a series formula** for compound interest:

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

Where:
- $ P $ is the monthly payment ($300),
- $ r $ is the monthly interest rate (APR / 12),
- $ n $ is the total number of payments (18 months),
- $ FV $ is the future value (balance after 18 months).

### Step 1: Calculate monthly interest rate
The APR is 2%, so the monthly interest rate is:
\[
r = \frac{2\%}{12} = \frac{0.02}{12} = 0.0016667
\]

### Step 2: Plug values into the formula
Now, substituting the values into the future value formula:

\[
FV = 300 \times \frac{(1 + 0.0016667)^{18} - 1}{0.0016667}
\]

Let's calculate this step-by-step. I'll compute it.The balance after 18 months, with monthly payments of $300 and an APR of 2%, will be approximately **$5477.18**.

Would you like more details on this calculation or have any questions?

Here are some related questions to deepen your understanding:
1. How would the balance change if the APR was higher?
2. What happens to the balance if you make payments for a longer period, say 24 months?
3. How would the result differ if payments were made annually instead of monthly?
4. How does compounding frequency affect the overall balance?
5. What if the payments were irregular instead of consistent?

**Tip:** Always ensure to convert the APR to a monthly rate when dealing with monthly payments.

Find the savings plan balance after 18 months with an APR of 2% and monthly payments of ​$300.

Discover how to calculate the balance of a savings plan after 18 months with an APR of 2% and monthly payments of $300. This problem explores compound interest and the future value of a series formula. Ideal for high school students in Grades 10-12.

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