You feel that you will need $2.1 million in your retirement account and when you reach that amount, you plan to retire. You feel you can earn an APR of 10.1 percent compounded monthly and plan to save $290 per month until you reach your goal. How many years will it be until you reach your goal and retire?

Multiple Choice

37.87 years

50.29 years

42.88 years

41.03 years

35.17 years

To determine how many years it will take to reach your retirement goal, we can use the **Future Value of an Annuity** formula, which accounts for regular monthly contributions compounded at a given interest rate. The formula is:

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

Where:
- $FV$ is the future value (your retirement goal of \$2,100,000).
- $P$ is the monthly contribution (\$290).
- $r$ is the monthly interest rate (annual rate divided by 12).
- $n$ is the number of months (years × 12).

We need to solve for $n$, the number of months, and then convert it to years by dividing by 12.

### Step-by-step solution:

1. **Future Value (FV):** \$2,100,000.
2. **Monthly contribution (P):** \$290.
3. **APR (Annual Percentage Rate):** 10.1%, so monthly rate $r = \frac{10.1\%}{12} = \frac{0.101}{12} = 0.008417$.
4. **Set up the equation** and solve for $n$.

Let me calculate this.It seems there was an issue in calculating the solution for the equation. Let me recheck the setup and recalculate. I'll proceed with a different approach to ensure accuracy.It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you'd like, I can explain the formula in detail so you can compute it manually, or help you with any other question!

Here are some questions you might consider:
1. Would you like to calculate the future value with a different monthly contribution?
2. How does changing the interest rate affect the time to reach your retirement goal?
3. What if the contributions are made annually instead of monthly?
4. How would the time change if the retirement goal increased to \$2.5 million?
5. What happens if the APR drops to 8%?

**Tip:** Compounding more frequently can significantly affect the growth of investments over time!

You feel that you will need $2.1 million in your retirement account and when you reach that amount, you plan to retire. You feel you can earn an APR of 10.1 percent compounded monthly and plan to save $290 per month until you reach your goal. How many years will it be until you reach your goal and retire?

Learn how to calculate the time it takes to reach $2.1 million in a retirement account with $290 monthly contributions and 10.1% APR compounded monthly. Understand the Future Value of Annuity formula and key concepts like compound interest and annuities. Suitable for college-level students or advanced high school learners.

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