An investor has determined that they need to accumulate $600,000 for retirement in 43 years. How much should this investor set aside each month in order to meet this goal if they expect an average return of 8.8%?

To solve this problem, we need to find the monthly contribution required to accumulate $600,000 in 43 years, assuming an average annual return of 8.8%.

This can be calculated using the future value of an annuity formula:

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

Where:
- $ FV $ is the future value ($600,000),
- $ P $ is the monthly contribution (which we need to find),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of contributions (number of years multiplied by 12).

Let's break down the variables:
- Annual interest rate $ r_{annual} = 8.8\% $, so the monthly interest rate $ r = \frac{8.8\%}{12} = 0.88\% / 12 \approx 0.007333 $ or $ 0.007333 $ as a decimal.
- Number of months $ n = 43 \times 12 = 516 $.

Now we can rearrange the formula to solve for $ P $:

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

I'll calculate the required monthly contribution using this formula.The investor should set aside approximately **$103.80** each month to accumulate $600,000 in 43 years, assuming an average annual return of 8.8%.

Would you like more details on this calculation or have any questions? Here are some related questions you might consider:

1. What if the average return rate was higher or lower?
2. How would changing the investment period affect the required monthly contribution?
3. What if the investor wanted to reach the goal in a shorter time, like 30 years?
4. How does compounding frequency (e.g., monthly vs. yearly) impact the final amount?
5. What happens if the investor starts with an initial investment amount?

**Tip:** Consistency in contributions is crucial for long-term financial goals, especially when benefiting from compound interest.

Discover how much an investor needs to set aside each month to reach a $600,000 retirement goal in 43 years, with an average annual return of 8.8%. Learn about the future value of annuities, compound interest, and exponential growth in this detailed calculation for Grades 10-12.

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