To solve this problem, we can use the formula for compound interest:

Final Amount = Initial Investment * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Time)

In this case, we know that the final amount is twice the initial investment, the interest rate is 0.08 (8%), and the number of compounding periods per year is 12 (monthly). We want to find the initial investment after 9 years:

2 * Initial Investment = Initial Investment * (1 + (0.08 / 12))^(12 * 9)

Divide both sides by the initial investment:

2 = (1 + (0.08 / 12))^(12 * 9)

Now, let's isolate the initial investment:

Initial Investment = 2 / ((1 + (0.08 / 12))^(12 * 9))

Calculate the expression inside the parentheses:

Initial Investment = 2 / ((1 + 0.0066667)^108)
                               = 2 / (1.94863)

Finally, divide 2 by 1.94863:

Initial Investment ≈ 1.02634

Since the question asks for the initial investment when the final amount is twice the initial investment, we can choose any multiple of 1.02634 as our answer. For example, if the initial investment was $1026.34, then after 9 years, it would grow to twice its value, or $2052.68.
If a sum of money invested at an annual interest rate of 8% compounded monthly grows to twice its initial amount in 9 years, what was the initial investment?