Suppose that $\$ 2000$ is loaned at a rate of $12 \%$, compounded annually. Assuming that no payments are made, find the amount owed after 7 years. Do not round any intermediate computations, and round your answer to the nearest cent.

Step 1 ：Given that the principal amount (P) is \$2000, the annual interest rate (r) is 12% or 0.12, the number of times that interest is compounded per year (n) is 1 (since it's compounded annually), and the time the money is invested for in years (t) is 7 years.

Step 2 ：We can use the formula for compound interest to find the amount owed after 7 years. The formula is \(A = P(1 + \frac{r}{n})^{nt}\), where A is the amount of money accumulated after n years, including interest.

Step 3 ：Substituting the given values into the formula, we get \(A = 2000(1 + \frac{0.12}{1})^{1*7}\)

Step 4 ：Solving the equation, we find that \(A = 4421.3628148121625\)

Step 5 ：Rounding to the nearest cent, the amount owed after 7 years is approximately \$4421.36

Step 6 ：\(\boxed{4421.36}\) is the final answer.