Find the savings plan balance after 12 months with an APR of 2​% and monthly payments of ​$100.
Question content area bottom
Part 1
The balance is ​$
  

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To calculate the savings plan balance after 12 months, we can use the formula for the future value of an annuity, which is:

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

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

### Step 1: Identify the given values:
- Monthly payment $ P = 100 $,
- APR = 2%, so the monthly interest rate $ r = \frac{0.02}{12} $,
- $ n = 12 $ months.

### Step 2: Plug in the values:
We can now calculate the balance after 12 months.

Let me calculate that for you.The savings plan balance after 12 months is approximately **$1,211.06**.

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

Here are 5 related questions you might consider:
1. What would the balance be after 24 months with the same APR?
2. How does the balance change if the monthly payment is increased to $150?
3. How much interest is earned after 12 months with this plan?
4. What is the total amount of money contributed in the 12 months without interest?
5. How does the balance differ if the APR increases to 3%?

**Tip:** Small increases in the APR can lead to significant changes in the total interest earned over time, especially for long-term savings plans.

Find the savings plan balance after 12 months with an APR of 2​% and monthly payments of ​$100.

Learn how to calculate the future value of a savings plan with a 2% APR and monthly payments of $100 over 12 months. This problem covers key financial concepts such as annuities and compound interest, with a detailed step-by-step solution. Suitable for 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