$\$ 5000$ are invested in a bank account at an interest rate of 10 percent per year. Find the amount in the bank after 13 years if interest is compounded annually.

Step 1 ：Given that the principal amount P is $5000, the annual interest rate r is 10% or 0.10, the number of times interest is compounded per year n is 1 (since it's compounded annually), and the time t is 13 years.

Step 2 ：We can use the formula for compound interest to calculate the future value of the investment. The formula is: \(A = P(1 + \frac{r}{n})^{nt}\)

Step 3 ：Substitute the given values into the formula: \(A = 5000(1 + \frac{0.1}{1})^{1*13}\)

Step 4 ：Solving the equation gives us the future value of the investment: \(A = 17261.356071965518\)

Step 5 ：Rounding to two decimal places, the amount in the bank after 13 years if interest is compounded annually is approximately $17261.36.

Step 6 ：\(\boxed{17261.36}\) is the final answer.