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 6 %. How much should you deposit monthly to accumulate ​$85 comma 000 in 13 ​years?
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Part 1
You should invest ​$
  
enter your response here each month.

To calculate how much you need to invest each month, we can use the future value of a savings plan formula for regular monthly deposits:

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

Where:
- $FV$ is the future value (i.e., $85,000).
- $P$ is the monthly deposit (this is what we need to find).
- $r$ is the annual interest rate (6% or 0.06).
- $n$ is the number of compounding periods per year (monthly, so $n = 12$).
- $t$ is the number of years (13 years).

We can rearrange the formula to solve for $P$:

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

Let's plug in the numbers and calculate it.You should invest approximately \$361.01 each month to accumulate \$85,000 in 13 years with an APR of 6%.

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

Here are some related questions:
1. How does compounding frequency affect monthly deposits?
2. What if the interest rate was 5% instead of 6%?
3. How would the time period affect your monthly investment?
4. What if the goal amount were $100,000 instead of $85,000?
5. How can inflation affect the value of the fund after 13 years?

**Tip:** Small increases in interest rates can have a significant impact over long periods due to compounding.

Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6%. How much should you deposit monthly to accumulate $85,000 in 13 years?

Learn how to calculate monthly deposits required to accumulate $85,000 in a college fund over 13 years with a 6% APR. This problem uses the compound interest formula and demonstrates how compounding frequency and interest rates impact savings. Suitable for students in Grades 10-12.

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