Find the accumulated value of an investment of $\$ 2000$ at $10 \%$ compounded semiannually for 7 years. $\$ 3959.86$ $\$ 2814.20$ $\$ 3897.43$ $\$ 3400.00$

Step 1 ：Given an initial investment (P) of $2000, an annual interest rate (r) of 10% or 0.10, the number of times the interest is compounded per year (n) is 2 (since it's compounded semiannually), and the time the money is invested for (t) is 7 years.

Step 2 ：We can use the formula for compound interest to find the accumulated value (A). The formula is \(A = P(1 + \frac{r}{n})^{nt}\).

Step 3 ：Substitute the given values into the formula: \(A = 2000(1 + \frac{0.10}{2})^{2*7}\).

Step 4 ：Solving the equation gives us the accumulated value A = 3959.8631988787974.

Step 5 ：Rounding to two decimal places, the accumulated value of the investment is approximately $3959.86.

Step 6 ：Final Answer: The accumulated value of an investment of $2000 at 10% compounded semiannually for 7 years is approximately \(\boxed{3959.86}\).