How much will be accumulated from investing $4,000/year at 8% interest compounded annually over 30 years?

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Multiple Choice

How much will be accumulated from investing $4,000/year at 8% interest compounded annually over 30 years?

Explanation:
To determine how much will be accumulated from investing $4,000 annually at an 8% interest rate compounded annually over 30 years, we use the future value of an annuity formula. This formula accounts for regular contributions (in this case, $4,000 each year) and compounding interest applied to each of those contributions over the specified time period. The formula for the future value of an annuity is: \[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \] Where: - \( FV \) is the future value of the annuity. - \( P \) is the annual payment (contribution). - \( r \) is the annual interest rate (as a decimal). - \( n \) is the number of years the money is invested. In this scenario: - The annual contribution \( P \) is $4,000. - The interest rate \( r \) is 0.08 (8%). - The investment duration \( n \) is 30 years. Plugging the values into the formula: \[ FV = 4000 \times \left( \frac{(1 + 0.08

To determine how much will be accumulated from investing $4,000 annually at an 8% interest rate compounded annually over 30 years, we use the future value of an annuity formula. This formula accounts for regular contributions (in this case, $4,000 each year) and compounding interest applied to each of those contributions over the specified time period.

The formula for the future value of an annuity is:

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

Where:

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

  • ( P ) is the annual payment (contribution).

  • ( r ) is the annual interest rate (as a decimal).

  • ( n ) is the number of years the money is invested.

In this scenario:

  • The annual contribution ( P ) is $4,000.

  • The interest rate ( r ) is 0.08 (8%).

  • The investment duration ( n ) is 30 years.

Plugging the values into the formula:

[ FV = 4000 \times \left( \frac{(1 + 0.08

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