Ali borrowed $\$ 8000$ at a rate of $13 \%$, compounded semiannually. Assuming he makes no payments, how much will he owe after 8 years?
Do not round any intermediate computations, and round your answer to the nearest cent.

Step 1 ：The problem is asking for the amount of money Ali will owe after 8 years if he borrowed $8000 at a rate of 13% compounded semiannually and makes no payments.

Step 2 ：We can use the formula for compound interest to solve this problem. The formula is: \(A = P (1 + \frac{r}{n})^{nt}\), where: \(A\) is the amount of money accumulated after n years, including interest, \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for in years.

Step 3 ：In this case, \(P = \$8000\), \(r = 13%\) or \(0.13\), \(n = 2\) (since it's compounded semiannually), and \(t = 8\) years.

Step 4 ：We can substitute these values into the formula to find the amount Ali will owe after 8 years: \(A = 8000 (1 + \frac{0.13}{2})^{2*8}\)

Step 5 ：Calculating the above expression, we find that \(A = 21912.085375919818\)

Step 6 ：Rounding to the nearest cent, we find that Ali will owe approximately \(\boxed{\$21912.09}\) after 8 years.