How much money needs to be invested each month to reach a goal of $3 million in a taxable account over 40 years at an interest rate of 8%?

How much money needs to be invested each month to reach a goal of $3 million in a taxable account over 40 years at an interest rate of 8%?

• A. $1,498.91
• B. $800.35
• C. $2,000.00
• D. $1,200.50

Answer: (A)

To determine how much money needs to be invested each month to reach a goal of $3 million in 40 years at an interest rate of 8%, we can use the future value of an annuity formula. This formula calculates the future value of a series of equal payments made at regular intervals, taking into account a specified interest rate. The formula for the future value of an annuity is: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is the future value of the investment (in this case, $3 million), - \( P \) is the amount invested each month, - \( r \) is the monthly interest rate (annual rate divided by 12), - \( n \) is the total number of investments (months). For an annual interest rate of 8%, the monthly interest rate would be 0.08 / 12 = 0.0066667. Over 40 years, the total number of months is 40 * 12 = 480. Substituting these values into the formula allows us to solve for \( P \), the monthly investment. When the calculations are performed accurately, it results

To determine how much money needs to be invested each month to reach a goal of $3 million in 40 years at an interest rate of 8%, we can use the future value of an annuity formula. This formula calculates the future value of a series of equal payments made at regular intervals, taking into account a specified interest rate.

The formula for the future value of an annuity is:

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

Where:

• ( FV ) is the future value of the investment (in this case, $3 million),

• ( P ) is the amount invested each month,

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

• ( n ) is the total number of investments (months).

For an annual interest rate of 8%, the monthly interest rate would be 0.08 / 12 = 0.0066667. Over 40 years, the total number of months is 40 * 12 = 480. Substituting these values into the formula allows us to solve for ( P ), the monthly investment.

When the calculations are performed accurately, it results