To achieve a retirement goal of $4 million in a taxable account over 45 years with an annual return of 7%, what is the required monthly investment?

To determine the required monthly investment to achieve a retirement goal of $4 million over 45 years with an annual return of 7%, we can apply the future value of a series formula, which takes into account regular contributions made at regular intervals. The formula used is:

[ FV = P \times \frac{(1 + r)^n - 1}{r} ]

Where:

• ( FV ) = future value of the investment (in this case, $4,000,000)

• ( P ) = monthly contribution (the value we are trying to find)

• ( r ) = monthly interest rate (annual rate divided by 12)

• ( n ) = total number of contributions (number of years times 12)

First, we convert the annual interest rate into a monthly rate:

• 7% annual return translates to (\frac{0.07}{12} \approx 0.0058333).

Next, calculate the total number of contributions over 45 years:

• ( 45 \times 12 = 540 ) months.

Plugging these values into the formula to find P:

[ 4,000,000 = P \times \frac{(1