How much should you deposit at the end of each month into an investment account that pays 7.5% compounded monthly to have $2 million when you retire in 41 years? How much of the $2 million comes from interest? How much should you deposit?

To calculate the amount you should deposit at the end of each month, we can use the concept of future value of an ordinary annuity. The formula for calculating the future value of an ordinary annuity is:

FV = P * [(1 + r)^n - 1] / r

Where:
FV is the future value of the annuity (in this case, $2 million)
P is the amount deposited at the end of each month
r is the monthly interest rate (7.5% divided by 12, or 0.075/12)
n is the number of compounding periods (41 years multiplied by 12 months, or 41 * 12)

We can rearrange the formula to solve for P:

P = FV * (r / [(1 + r)^n - 1])

Now we can plug in the values:

FV = $2,000,000
r = 0.075/12
n = 41 * 12

P = $2,000,000 * (0.075/12) / [(1 + 0.075/12)^(41*12) - 1]

Calculating this expression gives us the amount you should deposit at the end of each month.

To determine how much of the $2 million comes from interest, we can subtract the total amount of deposits made over 41 years. The total amount deposited can be calculated by multiplying the monthly deposit amount by the number of months (41 years * 12 months). Subtracting this total from $2 million will give you the amount of interest earned.

Keep in mind that investment returns are not guaranteed, and this calculation assumes a constant interest rate over the entire investment period. It's important to consult a financial advisor or professional for personalized advice.