How much should you deposit at the end of each month into an investment account that pays $7.5 \%$ compounded monthly to have $\$ 3$ million when you retire in 38 years? How much of the $\$ 3$ million comes from interest?
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In order to have $\$ 3$ million in 38 years, you should deposit $\$ \square$ each month. (Round up to the nearest dollar.)
$\$ \square$ of the $\$ 3$ million comes from interest.
(Use the answer from part (a) to find this answer. Round to the nearest dollar as needed.)

Step 1 ：Given that the future value (FV) is $3 million, the monthly interest rate (r) is 7.5% / 12 / 100, the number of times the interest is compounded per year (n) is 12, and the number of years (t) is 38, we can use the formula for the future value of an ordinary annuity to find the monthly deposit (P). The formula is: \(FV = P * [(1 + r)^{nt} - 1] / r\)

Step 2 ：We can rearrange the formula to solve for P: \(P = FV * r / [(1 + r)^{nt} - 1]\)

Step 3 ：Substituting the given values into the formula, we get: \(P = 3000000 * 0.00625 / [(1 + 0.00625)^{12*38} - 1]\)

Step 4 ：Calculating the above expression, we get: \(P \approx 1162.06\)

Step 5 ：However, we are asked to round up to the nearest dollar. Therefore, the monthly deposit should be $1163

Step 6 ：Final Answer: In order to have $3 million in 38 years, you should deposit \(\boxed{1163}\) each month.