Carla Lopez deposits $2,800 a year into her retirement account. If these funds have average earnings of 7 percent over the 40 years until her retirement, what will be the value of... Carla Lopez deposits $2,800 a year into her retirement account. If these funds have average earnings of 7 percent over the 40 years until her retirement, what will be the value of her retirement account? Note: Round your discount factor to 3 decimal places and final answer to the nearest whole dollar. Read more

Steps to Solve

1. Identify the Future Value of Annuity Formula

The formula for the future value of an annuity (FV) is given by:

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

where:

• ( P ) is the annual payment (deposit),
• ( r ) is the annual interest rate (as a decimal),
• ( n ) is the number of years.

2. Substitute the Values into the Formula

Given:

• ( P = 2800 )
• ( r = 0.07 )
• ( n = 40 )

Substituting these values into the formula yields:

$$ FV = 2800 \times \frac{(1 + 0.07)^{40} - 1}{0.07} $$

3. Calculate the Factor and the Future Value

First, calculate ( (1 + 0.07)^{40} ):

$$ (1 + 0.07)^{40} \approx 14.974 $$

Then, substitute this back into the future value formula:

$$ FV = 2800 \times \frac{14.974 - 1}{0.07} $$

4. Simplify and Find the Final Value

Calculate inside the parentheses:

$$ 14.974 - 1 = 13.974 $$

Now substitute this back:

$$ FV = 2800 \times \frac{13.974}{0.07} $$

Calculating ( \frac{13.974}{0.07} ):

$$ \frac{13.974}{0.07} \approx 199.6285714 $$

Now calculate ( FV ):

$$ FV \approx 2800 \times 199.6285714 \approx 558,000 $$

Round to the nearest whole dollar.