Step 1 :Recall the formula for compound interest, which is \(A=P\left(1+\frac{r}{n}\right)^{nt}\), where \(A\) is the end balance, \(P\) is the principal, \(r\) is the interest rate, \(t\) is the number of years, and \(n\) is the number of times the interest is compounded in a year.
Step 2 :Substitute the given values into the formula. The principal \(P\) is \$39,000, the interest rate \(r\) is 2\%, or 0.02, the number of years \(t\) is 7, and the number of times the interest is compounded in a year \(n\) is 2 (since it's compounded semiannually). So we have \(A=39000\left(1+\frac{0.02}{2}\right)^{2 \cdot 7}\).
Step 3 :Simplify the expression inside the parentheses to get \(A=39000\left(1+0.01\right)^{14}\).
Step 4 :Calculate the power to get \(A=39000\cdot 1.01^{14}\).
Step 5 :Calculate the multiplication to get \(A=44798.74\).
Step 6 :Round to the nearest cent to get \(\boxed{\$44798.74}\).