How much should you deposit at the end of each month into an investment account that pays $8.5 \%$ compounded monthly to have $\$ 4$ million when you retire in 43 years? How much of the $\$ 4$ million comes from interest? (1) Click the icon to view some finance formulas. In order to have $\$ 4$ million in 43 years, you should deposit $\$$ each month. (Round up to the nearest dollar.)

Step 1 ：We are given that the future value (FV) is \$4 million, the annual interest rate (r) is 8.5% or 0.085, the interest is compounded monthly so n = 12, and the number of years (t) is 43. We need to find the monthly deposit (P).

Step 2 ：We can use the formula for the future value of a series of payments (or an annuity): \(FV = P \times \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}}\)

Step 3 ：We can rearrange the formula to solve for P: \(P = FV \times \frac{\frac{r}{n}}{(1 + \frac{r}{n})^{nt} - 1}\)

Step 4 ：Substituting the given values into the formula, we get: \(P = 4000000 \times \frac{\frac{0.085}{12}}{(1 + \frac{0.085}{12})^{12 \times 43} - 1}\)

Step 5 ：Calculating the above expression, we find that P is approximately 762.21

Step 6 ：Final Answer: You should deposit approximately \(\boxed{762.21}\) dollars each month.