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 solve this problem, we can use the **Future Value of an Annuity formula** since you are contributing a fixed amount ($290) monthly into an account with compound interest. The formula is:

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

Where:
- $FV$ is the future value (the retirement goal, $2.1 million),
- $P$ is the monthly payment ($290),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of months (which we want to find).

### Steps:

1. **Determine the monthly interest rate:**
   The APR is 10.1% annually, so the monthly rate is:

   \[
   r = \frac{10.1\%}{12} = \frac{0.101}{12} = 0.00841667
   \]

2. **Set up the equation:**

   \[
   2,100,000 = 290 \times \frac{{(1 + 0.00841667)^n - 1}}{0.00841667}
   \]

3. **Solve for $n$:**

Let me compute the solution.The time it will take to reach your retirement goal is approximately **41.03 years**. Therefore, the correct answer is:

**41.03 years**.

Do you want more details or have any questions about the calculation?

Here are 5 related questions you might be interested in:
1. What if the interest rate was compounded annually instead of monthly?
2. How would increasing the monthly contributions affect the time to retire?
3. What happens if the interest rate is lower, like 8% APR?
4. How much total money will you have contributed after 41.03 years?
5. What would be the impact if you started with an initial balance in your retirement account?

**Tip:** Compounding more frequently (e.g., monthly vs. annually) results in faster growth of your investments due to the power of compound interest.

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?

Discover how long it will take to reach $2.1 million in your retirement account by saving $290 per month with an APR of 10.1% compounded monthly. This detailed breakdown uses the Future Value of an Annuity formula, making it perfect for students in Grades 10-12 looking to understand compound interest and long-term savings.

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