Marge has been dollar cost averaging by investing $2,000 quarterly for 7 years at a compounded annual return of 11%. What is the total value of her investment today?

Marge has been dollar cost averaging by investing $2,000 quarterly for 7 years at a compounded annual return of 11%. What is the total value of her investment today?

• A. $82,721.95
• B. $93,902.42
• C. $91,389.22
• D. $84,996.80

Answer: (A)

To determine the total value of Marge's investment today after dollar-cost averaging for 7 years at a compounded annual return of 11%, we need to use the future value of a series formula, particularly for investments made at regular intervals. When an investor contributes a fixed amount at regular intervals, the value of these contributions accumulates based on the interest that compounds over time. In this scenario, Marge is investing $2,000 every quarter for 7 years, which amounts to 28 contributions (7 years x 4 quarters). The future value of each individual quarterly contribution must be calculated to reflect how long each contribution has had to accrue interest by the end of 7 years. To find the total future value, you can sum the future value of each individual contribution using the formula for future value of a single sum, adjusted for the number of quarters each contribution has to grow. The formula can be stated as follows: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is the future value of the investment. - \( P \) is the amount of each contribution ($2,000). - \( r \) is the quarterly interest rate

To determine the total value of Marge's investment today after dollar-cost averaging for 7 years at a compounded annual return of 11%, we need to use the future value of a series formula, particularly for investments made at regular intervals. When an investor contributes a fixed amount at regular intervals, the value of these contributions accumulates based on the interest that compounds over time.

In this scenario, Marge is investing $2,000 every quarter for 7 years, which amounts to 28 contributions (7 years x 4 quarters). The future value of each individual quarterly contribution must be calculated to reflect how long each contribution has had to accrue interest by the end of 7 years.

To find the total future value, you can sum the future value of each individual contribution using the formula for future value of a single sum, adjusted for the number of quarters each contribution has to grow. The formula can be stated as follows:

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

Where:

• ( FV ) is the future value of the investment.

• ( P ) is the amount of each contribution ($2,000).

• ( r ) is the quarterly interest rate