To reach a retirement goal of $5 million with a 7% annual return, how much should you invest monthly from a starting point of $0?

To determine how much you need to invest monthly to reach a retirement goal of $5 million with an annual return of 7%, it's essential to understand the concepts of future value of annuities and the impact of compound interest.

Considering that the investment is starting from $0, you are working towards accumulating a specific future value through a series of regular contributions. The formula for the future value of a series of equal payments (annuity) is expressed as:

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

Where:

• ( FV ) is the future value you want, which in this case is $5 million.

• ( P ) is the monthly payment you need to find.

• ( r ) is the monthly interest rate (annual rate divided by 12 months).

• ( n ) is the total number of payments (number of years until retirement times 12).

Assuming you are planning to retire in a certain number of years (let's say 30 years for this example), you would adjust for the number of periods. In the equation, you replace ( r ) with ( 0.07 / 12