Carla Lopez deposits $1,000 a year into her retirement account. If these funds have an average earning of 12 percent over the 50 years until her retirement, what will be the value of her retirement account?

Carla Lopez's retirement account can be calculated using the future value of an annuity formula. The formula is:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the annual payment ($1,000).
- $r$ is the annual interest rate (12% or 0.12).
- $n$ is the number of years (50 years).

Substituting the values:

\[
FV = 1,000 \times \frac{(1 + 0.12)^{50} - 1}{0.12}
\]

Let me calculate that.The future value of Carla Lopez's retirement account after 50 years, with an annual deposit of $1,000 and a 12% annual return, will be approximately **$2,400,018.25**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What if the annual deposit was increased to $2,000 per year?
2. How would the outcome change if the interest rate were lower, say 8%?
3. What if Carla planned to retire in 40 years instead of 50 years?
4. How much would Carla have saved if she only earned a 6% interest rate?
5. How does the future value change if deposits are made monthly instead of annually?

**Tip:** Compounding interest plays a significant role in long-term savings. The earlier you start, the greater your gains due to compounding over time.

Learn how to calculate the future value of Carla Lopez's retirement account using the annuity formula. This example involves annual deposits of $1,000 with a 12% annual return over 50 years, resulting in a retirement account value of approximately $2,400,018.25. Suitable for Grades 10-12.

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