Calculate, to the nearest cent, the future value $F V$ of an investment of $\$ 10,000$ at the stated interest rate after the stated amount of time. HINT [See Quick Examples 1 and 2.]
$0.1 \%$ per month, compounded monthly, after 6 years
\[
F V=\$ \square
\]
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Step 1 ：Given that the principal amount (P) is $10,000, the annual interest rate (r) is 0.1% per month which is equivalent to 0.001 per month or 0.012 per year, the number of times that interest is compounded per year (n) is 12, and the time the money is invested for (t) is 6 years.

Step 2 ：We can calculate the future value of the investment using the formula for compound interest: \(FV = P * (1 + r/n)^{nt}\)

Step 3 ：Substituting the given values into the formula, we get \(FV = 10000 * (1 + 0.012/12)^{12*6}\)

Step 4 ：Solving the equation, we find that the future value of the investment is $10746.17

Step 5 ：Final Answer: The future value of the investment, to the nearest cent, is \(\boxed{10746.17}\)