A demand loan for $\mathrm{\$}4600.45$ with interest at $4.8\mathrm{\%}$ compounded semi-annually is repaid after 9 years, 4 months. What is the amount of interest paid?
The amount of interest is $\mathrm{\$}◻$.
(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: $FV=P\ast (1+r/n{)}^{nt}$, 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, $P=\mathrm{\$}4600.45$, $r=4.8/100=0.048$, $n=2$ (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 $\boxed{{\displaystyle \mathrm{\$}2562.08}}$.