We will use the savings plan formula to calculate the required monthly deposit.

The formula for the future value of a savings plan is:

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

Where:

• $A$ = Future value (desired retirement amount) = $1,200,000
• $P$ = Monthly deposit (what we are solving for)
• $r$ = Annual interest rate (APR) = 4% = 0.04
• $n$ = Number of compounding periods per year (monthly compounding, so $n = 12$)
• $t$ = Number of years = 27 years

Now, we can substitute the values into the formula and solve for $P$. First, rearrange the formula to isolate $P$:

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

Let's calculate this step by step. I'll compute the monthly deposit $P$.The required monthly deposit to reach $1.2 million in 27 years with a 4% APR is approximately $2062.50.

Would you like more details on how this was calculated, or have any other questions?

Here are some related questions to consider:

1. What happens to the monthly deposit if the APR increases to 5%?
2. How much would you need to deposit annually instead of monthly to reach the same goal?
3. How much total money will you have deposited by the end of 27 years?
4. What would happen if the retirement time frame is reduced by 5 years?
5. How much would your savings grow with no monthly deposit but an initial lump sum investment?

Tip: Starting retirement savings early, even with smaller amounts, can significantly reduce how much you need to deposit monthly!