Step 1 :We are given a principal amount of \(P = \$10,000\), an annual interest rate of \(r = 5\%\) or \(0.05\) in decimal, the number of times that interest is compounded per year \(n = 2\) (since it's semiannually), and the time \(t = 5\) years.
Step 2 :We are asked to find the amount of money that will be in the account after 5 years. We can use the formula for compound interest, which 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 \(A=10000(1+\frac{0.05}{2})^{2*5}\).
Step 4 :Solving the equation, we find that \(A = \$12800.85\).
Step 5 :Thus, the amount of money that will be in the account after 5 years is approximately \(\boxed{\$12800.85}\).