To solve this problem, we can use the future value of a savings plan formula:

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

Where:

• $FV$ is the future value of the fund, which is $85,000.
• $P$ is the monthly deposit amount we need to find.
• $r$ is the monthly interest rate (APR / 12).
• $n$ is the total number of payments (number of months).

Let's break it down:

• APR = 6% = 0.06 annually, so the monthly interest rate $r = \frac{0.06}{12} = 0.005$.
• The total number of months over 13 years is $n = 13 \times 12 = 156$.

We need to solve for $P$, the monthly deposit. Let's rearrange the formula:

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

Now, let's plug in the values and calculate.The monthly deposit you should make to accumulate $85,000 in 13 years at an APR of 6% is approximately $361.01.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What happens to the monthly deposit amount if the APR increases?
2. How would the required deposit change if the investment period was 15 years instead of 13 years?
3. What is the total amount of money deposited by the end of the 13 years?
4. How much interest would be earned over the 13-year period?
5. What would happen if the deposits were made quarterly instead of monthly?

Tip: Small differences in interest rates or deposit frequencies can have a significant impact on the accumulated savings over time.