To determine how much the $10,000 investment will be worth at retirement, we can use the formula for compound interest:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount of money accumulated after interest.
• $P$ is the principal amount (the initial investment), which is $10,000.
• $r$ is the annual interest rate, which is 7.5% or 0.075.
• $n$ is the number of times the interest is compounded per year. In this case, since it's a mutual fund, we can assume the interest is compounded annually, so $n = 1$.
• $t$ is the number of years the investment will grow. The investment is made on January 1, 2024, and retirement is on December 31, 2061, so $t = 2061 - 2024 = 37$ years.

Now, applying the values to the formula:

$A = 10,000 \left(1 + \frac{0.075}{1}\right)^{1 \times 37}$

Let me calculate that for you.The $10,000 investment made on January 1, 2024, would grow to approximately $145,249 by your retirement on December 31, 2061, assuming a 7.5% annual return.

Would you like more details or have any questions about the calculation?

Here are some related questions to explore:

1. How would the final amount change if the interest rate were higher or lower?
2. What if you invested more money initially, say $20,000 instead of $10,000?
3. How would the final amount change if you made monthly contributions in addition to the initial $10,000?
4. What if the investment return is compounded monthly instead of annually?
5. How would taking a year off before investing affect the final amount?

Tip: Regularly reviewing your investment strategy can help adjust for changes in market conditions or personal goals.