The principal $P$ is borrowed at a simple interest rate $r$ for a period of time $t$. Find the loan's future value $A$, or the total amount due at time $t$. \[ P=\$ 5000, r=7.5 \%, t=3 \text { months } \] The loan's future value is $\$$ (Do not round until the final answer. Then round to the nearest cent as needed.)

Step 1 ：Given that the principal $P = \$5000$, the annual interest rate $r = 7.5\% = 0.075$ (converted from percentage to decimal), and the time $t = 3$ months $= 0.25$ years (converted from months to years).

Step 2 ：The formula for the future value of a loan with simple interest is given by: \[A = P(1 + rt)\] where $A$ is the future value of the loan, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), and $t$ is the time the money is invested for, in years.

Step 3 ：Substitute the given values into the formula to find the future value of the loan: \[A = 5000(1 + 0.075 * 0.25)\]

Step 4 ：Simplify the expression to find the future value of the loan: \[A = \$5093.75\]

Step 5 ：Final Answer: The future value of the loan is \(\boxed{\$5093.75}\)