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

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