Carla deposits $3,000 a year into her retirement account. if these funds have an average earning of 8 percent over the 40 years until her retirement, what will be the value of her retirement account?

To determine the future value of Carla's retirement account, we can use the future value of an annuity formula since she is making regular deposits each year. The formula is:

FV = P * [(1 + r)^n - 1] / r

where: FV = future value of the annuity P = annual payment (deposit) r = annual interest rate (as a decimal) n = number of payments (years)

In Carla's case: P = $3,000 r = 8% or 0.08 n = 40

Now, let's plug the numbers into the formula and calculate:

FV = $3,000 * [(1 + 0.08)^40 - 1] / 0.08

First, we calculate (1 + 0.08)^40:

(1 + 0.08)^40 = 1.08^40 ≈ 21.7245

Now, subtract 1:

21.7245 - 1 ≈ 20.7245

Then we divide by the interest rate:

20.7245 / 0.08 ≈ 259.05625

Finally, we multiply by the annual payment:

$3,000 * 259.05625 ≈ $777,168.75

So, the future value of Carla's retirement account after 40 years, assuming an 8 percent average annual return, would be approximately $777,168.75.

Extra: Understanding the power of compounding interest is essential for long-term savings goals such as retirement. The 8 percent return assumed in this scenario means that the account will earn 8 percent of its value each year. With an annuity, Carla is adding a fixed amount regularly which then also earns interest. Over a long period, such as 40 years, the compound interest significantly boosts the growth of her investment. This demonstrates why it is beneficial to start saving for retirement as early as possible, as the interest has more time to compound, leading to a much larger retirement account. It's also important to remember that while the markets can fluctuate, an average earning of 8 percent is a reasonable estimate based on historical stock market returns, though actual returns can be more unpredictable.