The principal represents an amount of money deposited in a savings account subject to how much money will be in the account after the given number of years (Assume $360 \mathrm{da}$ earned.
\[
A=P\left(1+\frac{r}{n}\right)^{n t}
\]
3) Principal: $\$ 10,000$
Rate: 5\%
Compounded: semiannually Time: 5 years

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 \(\boxed{\$12800.85}\).