Find the savings plan balance after 4

years with an APR of 

8​% 

and monthly payments of 

​$150

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Part 1The balance is $enter your response here. Do not round until the final answer. Then round to the nearest cent as​ needed.)

To find the balance of the savings plan after 4 years with an APR of 8% and monthly payments of $150, we can use the **future value of an annuity formula**:

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

Where:
- $FV$ is the future value (balance after 4 years),
- $P$ is the monthly payment ($150),
- $r$ is the annual interest rate (8% = 0.08),
- $n$ is the number of times the interest is compounded per year (monthly compounding, so $n = 12$),
- $t$ is the number of years (4 years).

Let's plug in the values and calculate the balance.

\[
FV = 150 \times \frac{{(1 + \frac{0.08}{12})^{12 \times 4} - 1}}{{\frac{0.08}{12}}}
\]

I'll calculate this now.The balance after 4 years with an APR of 8% and monthly payments of $150 is approximately **$8,452.49**.

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

Here are five related questions to explore further:
1. How would the balance change if the monthly payment increased to $200?
2. What if the APR was reduced to 6% instead of 8%?
3. How much total interest was earned over the 4 years?
4. How does the formula change for different compounding periods (e.g., daily or quarterly)?
5. What happens to the balance if the payments are made quarterly instead of monthly?

**Tip**: Consistent savings over time, even with small contributions, can lead to significant growth due to compound interest!

Find the savings plan balance after 4 years with an APR of 8% and monthly payments of $150. Do not round until the final answer. Then round to the nearest cent as needed.

Learn how to calculate the savings plan balance after 4 years with an APR of 8% and monthly payments of $150. This step-by-step solution uses the future value of an annuity formula to solve the problem. Ideal for students in Grades 10-12 studying finance and compound interest.

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