To solve this, we will use the savings plan formula, which is a type of future value formula for an annuity:

$A = P \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}}$

Where:

• $A$ is the future value of the annuity (the amount you want to accumulate).
• $P$ is the monthly deposit.
• $r$ is the annual interest rate (as a decimal).
• $n$ is the number of compounding periods per year.
• $t$ is the number of years.

Given:

• $A = 87,000$ (the goal amount).
• $r = 6\% = 0.06$.
• $n = 12$ (since the deposits are monthly and interest is compounded monthly).
• $t = 12$ years.

We need to solve for $P$ (the monthly deposit).

The formula can be rearranged to:

$P = \frac{A \cdot \frac{r}{n}}{(1 + \frac{r}{n})^{nt} - 1}$

Substituting the given values:

$P = \frac{87000 \cdot \frac{0.06}{12}}{(1 + \frac{0.06}{12})^{12 \times 12} - 1}$

Let’s calculate this step-by-step.The monthly deposit required to accumulate $87,000 in 12 years, with an APR of 6%, is approximately $413.99.

Would you like further details on how this calculation was performed, or do you have any other questions?

Here are five related questions:

1. How would the required deposit change if the interest rate was 8%?
2. What would happen if you wanted to save this amount in 10 years instead of 12?
3. How does changing the compounding frequency (e.g., to quarterly) affect the required monthly deposit?
4. What is the total amount of interest earned over the 12 years?
5. How does inflation affect the future value of the accumulated fund?

Tip: Always account for fees associated with investment plans, as they can affect the effective interest rate you receive.