Use the savings plan formula to answer the following question.
Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 5 %. How much should you deposit monthly to accumulate ​$84000 in 16 ​years?

To solve this problem, we will use the savings plan formula, also known as the **Future Value of a Series formula**, which calculates the amount needed to achieve a specific future value by making regular payments:

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

Where:
- $ FV $ is the future value (the amount you want to accumulate),
- $ P $ is the monthly deposit (the unknown we want to find),
- $ r $ is the annual interest rate as a decimal (APR),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years.

### Given values:
- $ FV = 84,000 $ (the amount you want to accumulate),
- $ r = 0.05 $ (5% annual interest rate),
- $ n = 12 $ (monthly compounding since payments are monthly),
- $ t = 16 $ years.

### Rearranging the formula to solve for $ P $:

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

Now, we can plug in the values and compute $ P $.The monthly deposit required to accumulate $84,000 in 16 years at an APR of 5% is approximately **$286.45**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How does changing the APR affect the monthly deposit amount?
2. What would happen if the savings period were reduced to 10 years?
3. How much interest would you have earned by the end of the 16 years?
4. What if the fund compounded quarterly instead of monthly?
5. How does inflation affect the real value of the savings in 16 years?

**Tip:** The more frequently interest is compounded, the more you'll earn on your savings due to compound interest.

Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 5%. How much should you deposit monthly to accumulate $84,000 in 16 years?

Discover how to calculate the monthly deposit needed to accumulate $84,000 in 16 years with a 5% APR using the Future Value of a Series formula. This problem covers essential concepts in algebra and finance, perfect for students in Grades 11-12.

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