Find the savings plan balance after 12 months with an APR of 6​% and monthly payments of ​$100

To find the balance of a savings plan after 12 months with an APR of 6% and monthly payments of $100, we can apply the **future value of an annuity formula**:

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

Where:
- $FV$ is the future value (balance after 12 months).
- $P$ is the monthly payment ($100).
- $r$ is the monthly interest rate (APR divided by 12 months).
- $n$ is the total number of payments (12 months).

Given:
- APR = 6% = 0.06 annually, so $r = \frac{0.06}{12} = 0.005$ monthly.
- $n = 12$ months.

Now, let’s calculate the future value.Let me manually calculate the future value of this savings plan.

We are given:
- Monthly interest rate $ r = 0.005 $,
- Number of months $ n = 12 $,
- Monthly payment $ P = 100 $.

Now, applying the formula step by step:

\[
FV = 100 \times \frac{(1 + 0.005)^{12} - 1}{0.005}
\]

1. Calculate $ (1 + 0.005)^{12} $:
   \[
   (1.005)^{12} = 1.061677812
   \]

2. Subtract 1:
   \[
   1.061677812 - 1 = 0.061677812
   \]

3. Divide by the monthly interest rate:
   \[
   \frac{0.061677812}{0.005} = 12.3355624
   \]

4. Multiply by the monthly payment $ P = 100 $:
   \[
   100 \times 12.3355624 = 1233.56
   \]

So, the future value after 12 months is approximately **$1,233.56**.

Would you like more details or have any questions? Here are 5 related questions:

1. How would the balance change if the APR was higher, say 8%?
2. What happens if the payments are increased to $150 per month?
3. Can this formula be used for other payment intervals, such as weekly or yearly?
4. How does compound interest affect long-term savings plans?
5. What’s the difference between simple and compound interest?

**Tip:** Small changes in the interest rate can have a big impact on savings over time, so consider long-term growth when making financial plans.

Find the savings plan balance after 12 months with an APR of 6% and monthly payments of $100.

Learn how to calculate the future value of a savings plan after 12 months with a 6% APR and $100 monthly payments. This example uses the future value of annuity formula, applying compound interest to show how savings grow over time. Suitable for high school students and anyone learning about personal finance.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation