A demand loan for $\$ 4600.45$ with interest at $4.8 \%$ compounded semi-annually is repaid after 9 years, 4 months. What is the amount of interest paid?
The amount of interest is $\$ \square$.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Given a demand loan for $4600.45 with an interest rate of 4.8% compounded semi-annually, we are asked to find the amount of interest paid after 9 years and 4 months.

Step 2 ：We can calculate the total amount repaid after 9 years and 4 months using the formula for the future value of a loan with compound interest: \(FV = P * (1 + r/n)^{nt}\), where \(FV\) is the future value of the loan, \(P\) is the principal amount (the initial loan amount), \(r\) 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, \(P = \$4600.45\), \(r = 4.8/100 = 0.048\), \(n = 2\) (since interest is compounded semi-annually), and \(t = 9 + 4/12 = 9.333\) years.

Step 4 ：Substituting these values into the formula, we find that the future value of the loan is approximately \$7162.53.

Step 5 ：We can then find the amount of interest paid by subtracting the principal amount from the future value, which gives us approximately \$2562.08.

Step 6 ：Final Answer: The amount of interest paid is \(\boxed{\$2562.08}\).